Algomintis in the Blockchain Infrastructure Industry

Algomint

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Not Accounting for Sensitive Factors Doesn’t Mean Your Algorithm Won’t be Biased Being colorblind doesn’t mean that color doesn’t exist. Similarly, not including sensitive factors such as race and sex into algorithms doesn’t mean the algorithms won’t carry biases formed on race or sex. Those biases are ingrained into society, hence the data. Most algorithms are literal; their outputs are a function of the patterns they observe. Nonetheless, a common technique that developers have applied is straight omission despite its continuous failure. Kwok from Yale’s School of Management explains when race is removed from racially biased algorithms, a subtler biased “latent discrimination” is introduced where other factors, such as income or location that are correlated with race, essentially serve as proxies for race. The Harvard Business Review also investigated an employment recruitment scenario and found that proxies could predict gender with 91% accuracy in data. The omission strategy extends beyond just individual scenarios, though. During a recent conference on AI Regulation at California Western School of Law, a French panelist noted that France doesn’t have to deal with the racial bias issue since they simply do not collect race as a factor. This is due to the GDPR, which prohibits the use of ‘special categories of data’ (Article 9). This includes sensitive factors as well as proxies that may reveal them. It is phrased as follows: Processing of personal data revealing racial or ethnic origin, political opinions, religious or philosophical beliefs, or trade union membership, and the processing of genetic data, biometric data for the purpose of uniquely identifying a natural person, data concerning health or data concerning a natural person’s sex life or sexual orientation shall be prohibited. Countries subject to the GDPR, such as France, still have racial biases. They are just unable to be measured since the data is never collected. However, one could argue that perhaps biases don’t need to be “fixed” since our algorithm should reflect real life. When ProPublica criticized the maker of COMPAS, a recidivism algorithm that found black defendants to be nearly twice as likely to be classified as high risk compared to their white counterparts, the algorithm maker and researchers responded that it was mathematically impossible to have an algorithm that didn’t result in such racial gaps due to the impact of race on the recidivism. This reasoning is problematic since algorithms can amplify and perpetuate biases. For example, predictive policing tends to drive law enforcement to black and brown areas based on past data. However, the past data is biased based on heightened racial tensions, and increased law enforcement in such areas increases arrests, skewing future data and increasing the racial disparity among arrestees. We need a solution to prevent algorithms from perpetuating cycles of existing biases, and simply ignoring sensitive factors only masks the issue. The U.S. lacks a regulatory framework that allows organizations to measure and mitigate their own bias. The White House Office of Science and Technology’s AI Blueprint outlines thorough recommendations for best practices. However, the lack of enforcement undermines the Blueprint’s effectiveness, as evidenced by the harmful impact of biased algorithms being deployed. Since sweeping bans such as the GDPR Article 9 will do little to mitigate bias, I argue that the policymakers’ role shouldn’t be to tell developers how to minimize bias but rather do its part as a regulator to strictly hold them accountable through audits. Here is a sample auditing framework that draws heavily from the National Institute of Standards and Technology’s (NIST) identification of three primary categories for AI bias: systemic, computational, and human. Assessment of AI System Objectives


Purpose of System


Assumptions Regarding Fairness and Bias

Definitions of Fairness Model Attempted
Sensitive Factors Accounted For



Organizational Norms (e.g. Implicit Bias Training)


Diversity of Team




Data Management and Analysis


Data Collection Oversight

Representation of Groups in Data
Context of Data



Proxy Identification




Algorithm Development and Model Training


Transparent Design

Documentation of Development with Justifications (Particularly Relevant for Models Used in High-Risk Situations (Courts, Healthcare, etc))



Bias Mitigation Techniques Used




Testing and Evaluation

Independent Validation
Continuous Monitoring
Disclose Bias Audit Findings
Engage Stakeholders Not Accounting for Sensitive Factors Doesn’t Mean Your Algorithm Won’t be Biased Being colorblind doesn’t mean that color doesn’t exist. Similarly, not including sensitive factors such as race and sex into algorithms doesn’t mean the algorithms won’t carry biases formed on race or sex. Those biases are ingrained into society, hence the data. Most algorithms are literal; their outputs are a function of the patterns they observe. Nonetheless, a common technique that developers have applied is straight omission despite its continuous failure. Kwok from Yale’s School of Management explains when race is removed from racially biased algorithms, a subtler biased “latent discrimination” is introduced where other factors, such as income or location that are correlated with race, essentially serve as proxies for race. The Harvard Business Review also investigated an employment recruitment scenario and found that proxies could predict gender with 91% accuracy in data. Kwok 91% The omission strategy extends beyond just individual scenarios, though. During a recent conference on AI Regulation at California Western School of Law, a French panelist noted that France doesn’t have to deal with the racial bias issue since they simply do not collect race as a factor. This is due to the GDPR , which prohibits the use of ‘special categories of data’ (Article 9). This includes sensitive factors as well as proxies that may reveal them. It is phrased as follows: GDPR Processing of personal data revealing racial or ethnic origin, political opinions, religious or philosophical beliefs, or trade union membership, and the processing of genetic data, biometric data for the purpose of uniquely identifying a natural person, data concerning health or data concerning a natural person’s sex life or sexual orientation shall be prohibited. Processing of personal data revealing racial or ethnic origin, political opinions, religious or philosophical beliefs, or trade union membership, and the processing of genetic data, biometric data for the purpose of uniquely identifying a natural person, data concerning health or data concerning a natural person’s sex life or sexual orientation shall be prohibited. Processing of personal data revealing racial or ethnic origin, political opinions, religious or philosophical beliefs, or trade union membership, and the processing of genetic data, biometric data for the purpose of uniquely identifying a natural person, data concerning health or data concerning a natural person’s sex life or sexual orientation shall be prohibited. Countries subject to the GDPR, such as France, still have racial biases. They are just unable to be measured since the data is never collected. However, one could argue that perhaps biases don’t need to be “fixed” since our algorithm should reflect real life. When ProPublica criticized the maker of COMPAS, a recidivism algorithm that found black defendants to be nearly twice as likely to be classified as high risk compared to their white counterparts , the algorithm maker and researchers responded that it was mathematically impossible to have an algorithm that didn’t result in such racial gaps due to the impact of race on the recidivism. unable to be measured black defendants to be nearly twice as likely to be classified as high risk compared to their white counterparts mathematically impossible This reasoning is problematic since algorithms can amplify and perpetuate biases. For example, predictive policing tends to drive law enforcement to black and brown areas based on past data. However, the past data is biased based on heightened racial tensions, and increased law enforcement in such areas increases arrests, skewing future data and increasing the racial disparity among arrestees. We need a solution to prevent algorithms from perpetuating cycles of existing biases, and simply ignoring sensitive factors only masks the issue. The U.S. lacks a regulatory framework that allows organizations to measure and mitigate their own bias. The White House Office of Science and Technology’s AI Blueprint outlines thorough recommendations for best practices. However, the lack of enforcement undermines the Blueprint’s effectiveness, as evidenced by the harmful impact of biased algorithms being deployed. Since sweeping bans such as the GDPR Article 9 will do little to mitigate bias, I argue that the policymakers’ role shouldn’t be to tell developers how to minimize bias but rather do its part as a regulator to strictly hold them accountable through audits. AI Blueprint Here is a sample auditing framework that draws heavily from the National Institute of Standards and Technology’s (NIST) identification of three primary categories for AI bias: systemic, computational, and human. (NIST) Assessment of AI System Objectives


Purpose of System


Assumptions Regarding Fairness and Bias

Definitions of Fairness Model Attempted
Sensitive Factors Accounted For



Organizational Norms (e.g. Implicit Bias Training)


Diversity of Team Data Management and Analysis


Data Collection Oversight

Representation of Groups in Data
Context of Data



Proxy Identification Algorithm Development and Model Training


Transparent Design

Documentation of Development with Justifications (Particularly Relevant for Models Used in High-Risk Situations (Courts, Healthcare, etc))



Bias Mitigation Techniques Used Testing and Evaluation

Independent Validation
Continuous Monitoring
Disclose Bias Audit Findings
Engage Stakeholders Assessment of AI System Objectives Purpose of System


Assumptions Regarding Fairness and Bias

Definitions of Fairness Model Attempted
Sensitive Factors Accounted For



Organizational Norms (e.g. Implicit Bias Training)


Diversity of Team Assessment of AI System Objectives Purpose of System Assumptions Regarding Fairness and Bias

Definitions of Fairness Model Attempted
Sensitive Factors Accounted For Organizational Norms (e.g. Implicit Bias Training) Diversity of Team Purpose of System Purpose of System Assumptions Regarding Fairness and Bias Definitions of Fairness Model Attempted
Sensitive Factors Accounted For Assumptions Regarding Fairness and Bias Definitions of Fairness Model Attempted Sensitive Factors Accounted For Definitions of Fairness Model Attempted Sensitive Factors Accounted For Organizational Norms (e.g. Implicit Bias Training) Organizational Norms (e.g. Implicit Bias Training) Diversity of Team Diversity of Team Data Management and Analysis Data Collection Oversight

Representation of Groups in Data
Context of Data



Proxy Identification Data Management and Analysis Data Collection Oversight

Representation of Groups in Data
Context of Data Proxy Identification Data Collection Oversight Representation of Groups in Data
Context of Data Data Collection Oversight Representation of Groups in Data Context of Data Representation of Groups in Data Context of Data Proxy Identification Proxy Identification Algorithm Development and Model Training Transparent Design

Documentation of Development with Justifications (Particularly Relevant for Models Used in High-Risk Situations (Courts, Healthcare, etc))



Bias Mitigation Techniques Used Algorithm Development and Model Training Transparent Design

Documentation of Development with Justifications (Particularly Relevant for Models Used in High-Risk Situations (Courts, Healthcare, etc)) Bias Mitigation Techniques Used Transparent Design Documentation of Development with Justifications (Particularly Relevant for Models Used in High-Risk Situations (Courts, Healthcare, etc)) Transparent Design Documentation of Development with Justifications (Particularly Relevant for Models Used in High-Risk Situations (Courts, Healthcare, etc)) Documentation of Development with Justifications (Particularly Relevant for Models Used in High-Risk Situations (Courts, Healthcare, etc)) Bias Mitigation Techniques Used Bias Mitigation Techniques Used Testing and Evaluation Independent Validation
Continuous Monitoring
Disclose Bias Audit Findings
Engage Stakeholders Testing and Evaluation Independent Validation Continuous Monitoring Disclose Bias Audit Findings Engage Stakeholders Independent Validation Continuous Monitoring Disclose Bias Audit Findings Engage Stakeholders

Why Ignoring Sensitive Factors Won't Solve Algorithmic Bias and Discrimination

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Kiriaki Frangias;
(2) Andrew Lin;
(3) Ellen Vitercik;
(4) Manolis Zampetakis. Table of Links Abstract and Introduction Warm-up: Agents with known equal disutility Agents with unknown disutilites Experiments Conclusions and future directions, References A Summary of notation B Omitted proofs from Section 2 C Omitted proofs from Section 3 D Additional Information about Experiments D Additional Information about Experiments D.1 Post-processing algorithm Algorithm 4 takes as input “comparisons”, which is a list of s sublists, each containing the returned results of the binary comparisons performed by an agent. Each result is represented with a string of the form “i < j”, representing that according to the agent, the true score of item Ti is smaller than that of item Tj. The input “identified” is a set containing the indeces of all agents who returned at least one verified comparison incorrectly. Algorithm 4 iterates through the comparisons returned by agents not in the set “identified” and adds them to the set “condensed”, which will be returned at the end. If the comparison is already in the set “condensed”, then it is not added again. If there has been another agent whose returned comparison disagrees with it, then the comparison is added to the set “conflicts” (if not already added), and is removed from the set “condensed”. D.2 Principal’s utility vs. parameter π The plot shows a monotonic increase in the principal’s utility as π increases. The shaded region corresponds to a 90% confidence interval across 15 iterations. We notice that for any value of π that is greater than 0.35, it is in the principal’s best interest to implement our contract instead of performing all pairwise comparisons herself. D.3 Additional Hyper-parameter settings from Section 4 For the remainder of this section, we fix the hyper-parameter settings found in Section 4, unless otherwise stated. Namely, we assume that π = 0.8, δ = 0.01, n = 100, s = 100, ψ¯ = 2, and ψ = 0.01. Discussion of Figure 5. In Figure 5 we provide additional hyper-parameter settings for Figure 1a in Section 4. First, we select the probability of an effortful agent being “good” to be a value in {0.3, 0.6, 0.9} and the number of agents and items to be in the set {50, 200}. In plots 5a-5c results are averaged across 15 trials, while in plots 5d- 5f, results are averaged across 10 trials. The blue shading corresponds to a 90% confidence interval. We notice that the confidence intervals decrease with the number of agents, even for a small number of trials. The confidence intervals also decrease, as the agents’ work becomes more predictable (π increases). We find that as π increases, the principal’s utility also increases along with the threshold for ψ, below which it is in the principal’s best interest to run CrowdSort than perform all comparisons herself. This threshold also decreases with the number of agents, s. This implies that there is a sweet spot, in which the expected number of “good” agents is just enough that the ground-truth ordering of the items is retrieved and it is sufficiently small so that the principal can pay all of them. Discussion of Figure 6. In Figure 6 we provide additional hyper-parameter settings for Figure 1a in Section 4. Specifically, we select the per-comparison disutility of the principal, ψ¯, along with the per-comparison utility of the principal, λ, to take values in {4, 6, 8}. The number of agents and items is in the set {200, 500} and our results are averaged across 2 trials with the blue shading corresponding to a 90% confidence interval. We notice that the utility of the principal dramatically increases with the value she assigns to the correct ordering. Interestingly, by comparing Figure 5f to Figures 6a-6a, we find that even when the reliability of the agents is smaller (π = 0.8 in 5f and π = 0.9 in 6a6c), the principal’s point of indifference is higher when her disutility is larger. As before, we notice that when a large number of agents is incentivized, their labor needs to be sufficiently inexpensive (smaller threshold on ψ) for their work to be more profitable to the principal than performing all pairwise comparisons herself. Lastly, our results show, that for a broad range of hyperparameters, our theoretical analysis accurately predicts the value of ψ, for which the principal is indifferent between running CrowdSort or performing all comparisons herself. Discussion of Figure 7. We provide additional parameter settings corresponding to Figure 1b. The parameters π and s along with the number of trials vary as in Figure 5. We find that as the number of agents to be incentivized grows, our theoretical analysis for the principal’s point of indifference becomes more accurate. Also, noise on the disutilites results in many agents not being incentivized to exert effort and therefore get paid. This increases the principal’s utility, especially when parameter π is large, therefore resulting in a less steep slope. As in Figure 1b, we note that the confidence intervals become larger with ψ, as the principal’s utility shows higher variance, when less agents are “good”. Discussion of Figure 10. In Figure 10 we offer a range of parameters corresponding to Figure 3 in Section 4. Specifically, we vary the probability than an effortful agent is “good”, which take values in {0.3, 0.6, 0.9} and the principal’s per-comparison disutility, ψ, and utility λ, which takes values in {4, 6, 8}. The multicolored plots indicate the principal’s utility for different sample sizes (namely, 10, 20, 100, and 500) drawn from D, which in this case is N (0.03, 0.01). Notice that we do not normalize the y-axis in this case. Results are averaged across 10 trials. We see that as agents become more reliable (higher value of π) and as the principal’s value for the correct sorting grows (λ), it becomes increasingly beneficial to the principal to run CrowdSort, than perform all pairwise comparisons on her own. Interestingly, even if π is 0.3, for sufficiently large values of ψ¯, the agent’s work is more profitable to the principal than sorting herself. This suggests that for a sufficiently large value of ψ/ψ ¯ , incentivizing agents under our proposed contract is substantially more beneficial to the principal than sorting the items herself. This paper is available on Arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. Authors: (1) Kiriaki Frangias; (2) Andrew Lin; (3) Ellen Vitercik; (4) Manolis Zampetakis. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Kiriaki Frangias; (2) Andrew Lin; (3) Ellen Vitercik; (4) Manolis Zampetakis. Table of Links Abstract and Introduction Abstract and Introduction Warm-up: Agents with known equal disutility Warm-up: Agents with known equal disutility Agents with unknown disutilites Agents with unknown disutilites Experiments Experiments Conclusions and future directions, References Conclusions and future directions, References A Summary of notation A Summary of notation B Omitted proofs from Section 2 B Omitted proofs from Section 2 C Omitted proofs from Section 3 C Omitted proofs from Section 3 D Additional Information about Experiments D Additional Information about Experiments D Additional Information about Experiments D.1 Post-processing algorithm Algorithm 4 takes as input “comparisons”, which is a list of s sublists, each containing the returned results of the binary comparisons performed by an agent. Each result is represented with a string of the form “ i < j”, representing that according to the agent, the true score of item T i is smaller than that of item T j . The input “identified” is a set containing the indeces of all agents who returned at least one verified comparison incorrectly. s i i j Algorithm 4 iterates through the comparisons returned by agents not in the set “identified” and adds them to the set “condensed”, which will be returned at the end. If the comparison is already in the set “condensed”, then it is not added again. If there has been another agent whose returned comparison disagrees with it, then the comparison is added to the set “conflicts” (if not already added), and is removed from the set “condensed”. D.2 Principal’s utility vs. parameter π The plot shows a monotonic increase in the principal’s utility as π increases. The shaded region corresponds to a 90% confidence interval across 15 iterations. We notice that for any value of π that is greater than 0.35, it is in the principal’s best interest to implement our contract instead of performing all pairwise comparisons herself. D.3 Additional Hyper-parameter settings from Section 4 For the remainder of this section, we fix the hyper-parameter settings found in Section 4, unless otherwise stated. Namely, we assume that π = 0.8, δ = 0.01, n = 100, s = 100, ψ¯ = 2, and ψ = 0.01. Discussion of Figure 5. In Figure 5 we provide additional hyper-parameter settings for Figure 1a in Section 4. First, we select the probability of an effortful agent being “good” to be a value in {0.3, 0.6, 0.9} and the number of agents and items to be in the set {50, 200}. In plots 5a-5c results are averaged across 15 trials, while in plots 5d- 5f, results are averaged across 10 trials. Discussion of Figure 5. The blue shading corresponds to a 90% confidence interval. We notice that the confidence intervals decrease with the number of agents, even for a small number of trials. The confidence intervals also decrease, as the agents’ work becomes more predictable (π increases). We find that as π increases, the principal’s utility also increases along with the threshold for ψ, below which it is in the principal’s best interest to run CrowdSort than perform all comparisons herself. This threshold also decreases with the number of agents, s. This implies that there is a sweet spot, in which the expected number of “good” agents is just enough that the ground-truth ordering of the items is retrieved and it is sufficiently small so that the principal can pay all of them. Discussion of Figure 6. In Figure 6 we provide additional hyper-parameter settings for Figure 1a in Section 4. Specifically, we select the per-comparison disutility of the principal, ψ¯, along with the per-comparison utility of the principal, λ, to take values in {4, 6, 8}. The number of agents and items is in the set {200, 500} and our results are averaged across 2 trials with the blue shading corresponding to a 90% confidence interval. Discussion of Figure 6. We notice that the utility of the principal dramatically increases with the value she assigns to the correct ordering. Interestingly, by comparing Figure 5f to Figures 6a-6a, we find that even when the reliability of the agents is smaller (π = 0.8 in 5f and π = 0.9 in 6a6c), the principal’s point of indifference is higher when her disutility is larger. As before, we notice that when a large number of agents is incentivized, their labor needs to be sufficiently inexpensive (smaller threshold on ψ) for their work to be more profitable to the principal than performing all pairwise comparisons herself. Lastly, our results show, that for a broad range of hyperparameters, our theoretical analysis accurately predicts the value of ψ, for which the principal is indifferent between running CrowdSort or performing all comparisons herself. Discussion of Figure 7. We provide additional parameter settings corresponding to Figure 1b. The parameters π and s along with the number of trials vary as in Figure 5. We find that as the number of agents to be incentivized grows, our theoretical analysis for the principal’s point of indifference becomes more accurate. Discussion of Figure 7. Also, noise on the disutilites results in many agents not being incentivized to exert effort and therefore get paid. This increases the principal’s utility, especially when parameter π is large, therefore resulting in a less steep slope. As in Figure 1b, we note that the confidence intervals become larger with ψ, as the principal’s utility shows higher variance, when less agents are “good”. Discussion of Figure 10. In Figure 10 we offer a range of parameters corresponding to Figure 3 in Section 4. Specifically, we vary the probability than an effortful agent is “good”, which take values in {0.3, 0.6, 0.9} and the principal’s per-comparison disutility, ψ, and utility λ, which takes values in {4, 6, 8}. The multicolored plots indicate the principal’s utility for different sample sizes (namely, 10, 20, 100, and 500) drawn from D, which in this case is N (0.03, 0.01). Discussion of Figure 10. Notice that we do not normalize the y-axis in this case. Results are averaged across 10 trials. We see that as agents become more reliable (higher value of π) and as the principal’s value for the correct sorting grows (λ), it becomes increasingly beneficial to the principal to run CrowdSort, than perform all pairwise comparisons on her own. Interestingly, even if π is 0.3, for sufficiently large values of ψ¯, the agent’s work is more profitable to the principal than sorting herself. This suggests that for a sufficiently large value of ψ/ψ ¯ , incentivizing agents under our proposed contract is substantially more beneficial to the principal than sorting the items herself. This paper is available on Arxiv under CC 4.0 license. This paper is available on Arxiv under CC 4.0 license. Arxiv

Additional Information About the Algorithmic Contract Design Experiments: What You Should Know

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Kiriaki Frangias;
(2) Andrew Lin;
(3) Ellen Vitercik;
(4) Manolis Zampetakis. Table of Links Abstract and Introduction Warm-up: Agents with known equal disutility Agents with unknown disutilites Experiments Conclusions and future directions, References A Summary of notation B Omitted proofs from Section 2 C Omitted proofs from Section 3 D Additional Information about Experiments C Omitted proofs from Section 3 We similarly handle the second case, in which the agent does not exert effort, this time noting that the agent does not experience disutility: For agent ai to be incentivized to exert effort, the payment needs to be such that: Using E[|Ci|] < d and simplifying we get the lower bound: To satisfy individual rationality, we require the following: which holds if and only if: which is always satisfied as long as constraint 12 is satisfied. where the first inequality follows from above. Therefore the optimization problem for a suitable g∗ is the following: such that: This paper is available on Arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. Authors: (1) Kiriaki Frangias; (2) Andrew Lin; (3) Ellen Vitercik; (4) Manolis Zampetakis. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Kiriaki Frangias; (2) Andrew Lin; (3) Ellen Vitercik; (4) Manolis Zampetakis. Table of Links Abstract and Introduction Abstract and Introduction Warm-up: Agents with known equal disutility Warm-up: Agents with known equal disutility Agents with unknown disutilites Agents with unknown disutilites Experiments Experiments Conclusions and future directions, References Conclusions and future directions, References A Summary of notation A Summary of notation B Omitted proofs from Section 2 B Omitted proofs from Section 2 C Omitted proofs from Section 3 C Omitted proofs from Section 3 D Additional Information about Experiments D Additional Information about Experiments C Omitted proofs from Section 3 We similarly handle the second case, in which the agent does not exert effort, this time noting that the agent does not experience disutility: For agent a i to be incentivized to exert effort, the payment needs to be such that: i Using E[|C i |] < d and simplifying we get the lower bound: i To satisfy individual rationality, we require the following: which holds if and only if: which is always satisfied as long as constraint 12 is satisfied. where the first inequality follows from above. Therefore the optimization problem for a suitable g ∗ is the following: g such that: This paper is available on Arxiv under CC 4.0 license. This paper is available on Arxiv under CC 4.0 license. Arxiv

Algorithmic Contract Design for Crowdsourced Ranking: What Was Left Out of Section 3

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Kiriaki Frangias;
(2) Andrew Lin;
(3) Ellen Vitercik;
(4) Manolis Zampetakis. Table of Links Abstract and Introduction Warm-up: Agents with known equal disutility Agents with unknown disutilites Experiments Conclusions and future directions, References A Summary of notation B Omitted proofs from Section 2 C Omitted proofs from Section 3 D Additional Information about Experiments B Omitted proofs from Section 2 With Bayes’ rule and simplifying we get: We similarly handle the second case, in which the agent does not exert effort, this time noting that the agent does not experience disutility: For the agent to be incentivized to exert effort, the payment needs to be such that: We use the quantities from above to get: To satisfy individual rationality, we require that: which holds if and only if: and by simplifying we get: which is always satisfied if constraint 10 is satisfied. Lemma 2.3. If each item in V appears in exactly one pair, then no pair in V is redundant. Lemma 2.5. Suppose v ≥ log (2(1 − π)s/δ). Let be the number of agents each comparison is assigned to. Then with probability 1 − δ, CrowdSort(T, s, v, r, δ) returns the ground-truth ordering. For every subset that the agent is asked to fully sort, the agent can sort items adaptively so the number of pairwise comparisons he will perform is O(q log q). Therefore: Theorem 2.7. Suppose that the principal pays agents p∗ and runs CrowdSort(T, s, v∗, r∗, δ). Then: If the principal decides to set the price to 0, then no agents will induce effort and the principal will need to perform all pairwise comparisons on her own. The expected number of comparisons she will need to perform is 2n log n. Therefore, the disutility of the principal in this case is: For the principal to decide to propose a contract, her expected utility when inducing effort from the agents must be greater than or equal to her utility when she does not. In other words, we require that: This paper is available on Arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. Authors: (1) Kiriaki Frangias; (2) Andrew Lin; (3) Ellen Vitercik; (4) Manolis Zampetakis. This paper is available on arxiv under CC 4.0 license. Authors : Authors (1) Kiriaki Frangias; (2) Andrew Lin; (3) Ellen Vitercik; (4) Manolis Zampetakis. Table of Links Abstract and Introduction Abstract and Introduction Warm-up: Agents with known equal disutility Warm-up: Agents with known equal disutility Agents with unknown disutilites Agents with unknown disutilites Experiments Experiments Conclusions and future directions, References Conclusions and future directions, References A Summary of notation A Summary of notation B Omitted proofs from Section 2 B Omitted proofs from Section 2 C Omitted proofs from Section 3 C Omitted proofs from Section 3 D Additional Information about Experiments D Additional Information about Experiments B Omitted proofs from Section 2 With Bayes’ rule and simplifying we get: We similarly handle the second case, in which the agent does not exert effort, this time noting that the agent does not experience disutility: For the agent to be incentivized to exert effort, the payment needs to be such that: We use the quantities from above to get: To satisfy individual rationality, we require that: which holds if and only if: and by simplifying we get: which is always satisfied if constraint 10 is satisfied. Lemma 2.3. If each item in V appears in exactly one pair, then no pair in V is redundant. Lemma 2.3. If each item in V appears in exactly one pair, then no pair in V is redundant. Lemma 2.5. Suppose v ≥ log (2(1 − π)s/δ). Let Lemma 2.5. be the number of agents each comparison is assigned to. Then with probability 1 − δ, be the number of agents each comparison is assigned to. Then with probability 1 − δ, CrowdSort(T, s, v, r, δ) returns the ground-truth ordering. CrowdSort(T, s, v, r, δ) returns the ground-truth ordering. For every subset that the agent is asked to fully sort, the agent can sort items adaptively so the number of pairwise comparisons he will perform is O(q log q). Therefore: Theorem 2.7. Suppose that the principal pays agents p∗ and runs CrowdSort(T, s, v∗, r∗, δ). Then: Theorem 2.7. If the principal decides to set the price to 0, then no agents will induce effort and the principal will need to perform all pairwise comparisons on her own. The expected number of comparisons she will need to perform is 2n log n. Therefore, the disutility of the principal in this case is: For the principal to decide to propose a contract, her expected utility when inducing effort from the agents must be greater than or equal to her utility when she does not. In other words, we require that: This paper is available on Arxiv under CC 4.0 license. This paper is available on Arxiv under CC 4.0 license. Arxiv

Algorithmic Contract Design for Crowdsourced Ranking: Omitted Proofs From Section 2

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Kiriaki Frangias;
(2) Andrew Lin;
(3) Ellen Vitercik;
(4) Manolis Zampetakis. Table of Links Abstract and Introduction Warm-up: Agents with known equal disutility Agents with unknown disutilites Experiments Conclusions and future directions, References A Summary of notation B Omitted proofs from Section 2 C Omitted proofs from Section 3 D Additional Information about Experiments A Summary of notation This paper is available on Arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. Authors: (1) Kiriaki Frangias; (2) Andrew Lin; (3) Ellen Vitercik; (4) Manolis Zampetakis. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Kiriaki Frangias; (2) Andrew Lin; (3) Ellen Vitercik; (4) Manolis Zampetakis. Table of Links Abstract and Introduction Abstract and Introduction Warm-up: Agents with known equal disutility Warm-up: Agents with known equal disutility Agents with unknown disutilites Agents with unknown disutilites Experiments Experiments Conclusions and future directions, References Conclusions and future directions, References A Summary of notation A Summary of notation B Omitted proofs from Section 2 B Omitted proofs from Section 2 C Omitted proofs from Section 3 C Omitted proofs from Section 3 D Additional Information about Experiments D Additional Information about Experiments A Summary of notation This paper is available on Arxiv under CC 4.0 license. This paper is available on Arxiv under CC 4.0 license. Arxiv

Algorithmic Contract Design for Crowdsourced Ranking: Definitions You Should Know

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Kiriaki Frangias;
(2) Andrew Lin;
(3) Ellen Vitercik;
(4) Manolis Zampetakis. Table of Links Abstract and Introduction Warm-up: Agents with known equal disutility Agents with unknown disutilites Experiments Conclusions and future directions, References A Summary of notation B Omitted proofs from Section 2 C Omitted proofs from Section 3 D Additional Information about Experiments 5 Conclusions and future directions We studied the multifaceted problem of designing a crowdsourcing mechanism that efficiently and accurately ranks a set of items using pairwise comparisons from rational agents. We based our approach on the classic principal-agent model from contract theory. To distribute comparisons among agents, we used an unexpected connection to the social golfer problem which allowed us to simultaneously minimize the agents’ workload and ensure enough agents evaluate each comparison. We showed that by optimizing the payment mechanisms, the principal can incentivize enough agents to exert effort, ensuring our algorithm recovers the ground-truth ranking. Our experiments showed that even when noise is added to our original model, our method consistently aids the principal in retrieving the accurate ground-truth ordering. llude, which allowed us to assign the same set of verified comparisons to all agents. How should our mechanism change if agents can collude? Moreover, we assumed that agents who do not exert effort will return comparisons consistent with a uniformly-random permutation of the items. What other models of agent behavior can we study under this framework? Finally, as is standard in contract theory, we assumed that the principal knows the probability π that an effortful agent is good. How should we handle the case where π is unknown? References [1] Abolfazl Asudeh, Gensheng Zhang, Naeemul Hassan, Chengkai Li, and Gergely V. Zaruba. Crowdsourcing pareto-optimal object finding by pairwise comparisons. In Proceedings of the 24th ACM International on Conference on Information and Knowledge Management (CIKM), 2015. [2] Ralph Allan Bradley and Milton E Terry. Rank analysis of incomplete block designs: I. the method of paired comparisons. Biometrika, 39(3/4):324–345, 1952. [3] Yang Cai, Constantinos Daskalakis, and Christos Papadimitriou. Optimum statistical estimation with strategic data sources. In Conference on Learning Theory (COLT), 2015. [4] Xi Chen, Paul N Bennett, Kevyn Collins-Thompson, and Eric Horvitz. Pairwise ranking aggregation in a crowdsourced setting. In Proceedings of the International Conference on Web Search and Data Mining, pages 193–202, 2013. [5] Yuxin Chen and Changho Suh. Spectral MLE: Top-k rank aggregation from pairwise comparisons. In International Conference on Machine Learning (ICML), 2015. [6] Paul Duetting, Tomer Ezra, Michal Feldman, and Thomas Kesselheim. Combinatorial contracts. In Symposium on Foundations of Computer Science (FOCS), 2022. [7] Anindya Ghose, Panagiotis G Ipeirotis, and Beibei Li. Designing ranking systems for hotels on travel search engines by mining user-generated and crowdsourced content. Marketing Science, 31(3):493–520, 2012. [8] John Guiver and Edward Snelson. Bayesian inference for plackett-luce ranking models. In International Conference on Machine Learning (ICML), 2009. [9] Stephen Guo, Aditya Parameswaran, and Hector Garcia-Molina. So who won? dynamic max discovery with the crowd. In Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data, SIGMOD ’12, page 385–396, New York, NY, USA, 2012. Association for Computing Machinery. ISBN 9781450312479. doi: 10.1145/2213836.2213880. URL https://doi.org/10.1145/2213836.2213880. [10] Guru Guruganesh, Jon Schneider, and Joshua Wang. Contracts under moral hazard and adverse selection. In ACM Conference on Economics and Computation (EC), 2021. [11] R. Jurca and B. Faltings. Mechanisms for making crowds truthful. Journal of Artificial Intelligence Research, 34:209–253, mar 2009. doi: 10.1613/jair.2621. URL https://doi.org/10.1613%2Fjair.2621. [12] Radu Jurca and Boi Faltings. Robust incentive-compatible feedback payments. In Workshop on Trading Agent Design and Analysis, 2006. [13] Radu Jurca and Boi Faltings. Minimum payments that reward honest reputation feedback. In ACM Conference on Economics and Computation (EC), 2006. [14] Jiawen Kang, Zehui Xiong, Dusit Niyato, Dongdong Ye, Dong In Kim, and Jun Zhao. Toward secure blockchain-enabled internet of vehicles: Optimizing consensus management using reputation and contract theory. IEEE Transactions on Vehicular Technology, 68(3):2906–2920, 2019. [15] Ngai Meng Kou, Yan Li, Hao Wang, Leong Hou U, and Zhiguo Gong. Crowdsourced top-k queries by confidence-aware pairwise judgments. Proceedings of the 2017 ACM International Conference on Management of Data, 2017. URL https://api.semanticscholar.org/CorpusID:36647621. [16] Jean-Jacques Laffont and David Martimort. Moral Hazard: The Basic Trade-Offs, pages 145–186. Princeton University Press, 2002. URL http://www.jstor.org/stable/j.ctv7h0rwr.8. [17] Shili Lin. Rank aggregation methods. Wiley Interdisciplinary Reviews: Computational Statistics, 2(5):555–570, 2010. [18] Tyler Lu and Craig Boutilier. Learning mallows models with pairwise preferences. In International Conference on Machine Learning (ICML), 2011. [19] C. L. Mallows. Non-null ranking models. i. Biometrika, 44:114–130, 1957. URL https://api.semanticscholar.org/CorpusID:121527283. [20] Fei Mi and Dit-Yan Yeung. Probabilistic graphical models for boosting cardinal and ordinal peer grading in moocs. In AAAI Conference on Artificial Intelligence, 2015. [21] Chris Piech, Jonathan Huang, Zhenghao Chen, Chuong Do, Andrew Ng, and Daphne Koller. Tuned models of peer assessment in moocs. In Proceedings of The 6th International Conference on Educational Data Mining (EDM), 2013. [22] R. L. Plackett. The Analysis of Permutations. Journal of the Royal Statistical Society Series C, 24(2):193–202, June 1975. doi: 10.2307/2346567. URL https://ideas.repec.org/a/bla/jorssc/v24y1975i2p193-202.html. [23] Karthik Raman and Thorsten Joachims. Methods for ordinal peer grading. In International Conference on Knowledge Discovery and Data Mining (KDD), 2014. [24] Karthik Raman and Thorsten Joachims. Bayesian ordinal peer grading. In Proceedings of the ACM Conference on Learning at Scale, 2015. [25] Vikas C Raykar, Shipeng Yu, Linda H Zhao, Gerardo Hermosillo Valadez, Charles Florin, Luca Bogoni, and Linda Moy. Learning from crowds. Journal of machine learning research, 11(4), 2010. [26] Nihar Shah, Sivaraman Balakrishnan, Joseph Bradley, Abhay Parekh, Kannan Ramchandran, and Martin Wainwright. Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependence. In International Conference on Artificial Intelligence and Statistics (AISTATS), 2015. [27] Nihar B Shah, Joseph K Bradley, Abhay Parekh, Martin Wainwright, and Kannan Ramchandran. A case for ordinal peer-evaluation in moocs. In NIPS Workshop on Data-Driven Education, 2013. [28] Louis Leon Thurstone. The method of paired comparisons for social values. The Journal of Abnormal and Social Psychology, 21:384–400, 1927. URL https://api.semanticscholar.org/CorpusID:144595330. [29] Markus Triska. Solution Methods for the Social Golfer Problem. PhD thesis, Vienna University of Technology, March 2008. Available from https://www.metalevel.at/mst.pdf. [30] Kristi Tsukida, Maya R Gupta, et al. How to analyze paired comparison data. Department of Electrical Engineering University of Washington, Tech. Rep. UWEETR-2011-0004, 1, 2011. [31] Bo Waggoner and Yiling Chen. Output agreement mechanisms and common knowledge. Proceedings of the AAAI Conference on Human Computation and Crowdsourcing, 2(1): 220–226, Sep. 2014. doi: 10.1609/hcomp.v2i1.13151. URL https://ojs.aaai.org/index.php/HCOMP/article/view/13151. [32] Banghua Zhu, Stephen Bates, Zhuoran Yang, Yixin Wang, Jiantao Jiao, and Michael I. Jordan. The sample complexity of online contract design. In ACM Conference on Economics and Computation (EC), 2023. This paper is available on Arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. Authors: (1) Kiriaki Frangias; (2) Andrew Lin; (3) Ellen Vitercik; (4) Manolis Zampetakis. This paper is available on arxiv under CC 4.0 license. Authors : Authors (1) Kiriaki Frangias; (2) Andrew Lin; (3) Ellen Vitercik; (4) Manolis Zampetakis. Table of Links Abstract and Introduction Abstract and Introduction Warm-up: Agents with known equal disutility Warm-up: Agents with known equal disutility Agents with unknown disutilites Agents with unknown disutilites Experiments Experiments Conclusions and future directions, References Conclusions and future directions, References A Summary of notation A Summary of notation B Omitted proofs from Section 2 B Omitted proofs from Section 2 C Omitted proofs from Section 3 C Omitted proofs from Section 3 D Additional Information about Experiments D Additional Information about Experiments 5 Conclusions and future directions We studied the multifaceted problem of designing a crowdsourcing mechanism that efficiently and accurately ranks a set of items using pairwise comparisons from rational agents. We based our approach on the classic principal-agent model from contract theory. To distribute comparisons among agents, we used an unexpected connection to the social golfer problem which allowed us to simultaneously minimize the agents’ workload and ensure enough agents evaluate each comparison. We showed that by optimizing the payment mechanisms, the principal can incentivize enough agents to exert effort, ensuring our algorithm recovers the ground-truth ranking. Our experiments showed that even when noise is added to our original model, our method consistently aids the principal in retrieving the accurate ground-truth ordering. llude, which allowed us to assign the same set of verified comparisons to all agents. How should our mechanism change if agents can collude? Moreover, we assumed that agents who do not exert effort will return comparisons consistent with a uniformly-random permutation of the items. What other models of agent behavior can we study under this framework? Finally, as is standard in contract theory, we assumed that the principal knows the probability π that an effortful agent is good. How should we handle the case where π is unknown? References [1] Abolfazl Asudeh, Gensheng Zhang, Naeemul Hassan, Chengkai Li, and Gergely V. Zaruba. Crowdsourcing pareto-optimal object finding by pairwise comparisons. In Proceedings of the 24th ACM International on Conference on Information and Knowledge Management (CIKM), 2015. [2] Ralph Allan Bradley and Milton E Terry. Rank analysis of incomplete block designs: I. the method of paired comparisons. Biometrika, 39(3/4):324–345, 1952. [3] Yang Cai, Constantinos Daskalakis, and Christos Papadimitriou. Optimum statistical estimation with strategic data sources. In Conference on Learning Theory (COLT), 2015. [4] Xi Chen, Paul N Bennett, Kevyn Collins-Thompson, and Eric Horvitz. Pairwise ranking aggregation in a crowdsourced setting. In Proceedings of the International Conference on Web Search and Data Mining, pages 193–202, 2013. [5] Yuxin Chen and Changho Suh. Spectral MLE: Top-k rank aggregation from pairwise comparisons. In International Conference on Machine Learning (ICML), 2015. [6] Paul Duetting, Tomer Ezra, Michal Feldman, and Thomas Kesselheim. Combinatorial contracts. In Symposium on Foundations of Computer Science (FOCS), 2022. [7] Anindya Ghose, Panagiotis G Ipeirotis, and Beibei Li. Designing ranking systems for hotels on travel search engines by mining user-generated and crowdsourced content. Marketing Science, 31(3):493–520, 2012. [8] John Guiver and Edward Snelson. Bayesian inference for plackett-luce ranking models. In International Conference on Machine Learning (ICML), 2009. [9] Stephen Guo, Aditya Parameswaran, and Hector Garcia-Molina. So who won? dynamic max discovery with the crowd. In Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data, SIGMOD ’12, page 385–396, New York, NY, USA, 2012. Association for Computing Machinery. ISBN 9781450312479. doi: 10.1145/2213836.2213880. URL https://doi.org/10.1145/2213836.2213880. [10] Guru Guruganesh, Jon Schneider, and Joshua Wang. Contracts under moral hazard and adverse selection. In ACM Conference on Economics and Computation (EC), 2021. [11] R. Jurca and B. Faltings. Mechanisms for making crowds truthful. Journal of Artificial Intelligence Research, 34:209–253, mar 2009. doi: 10.1613/jair.2621. URL https://doi.org/10.1613%2Fjair.2621. [12] Radu Jurca and Boi Faltings. Robust incentive-compatible feedback payments. In Workshop on Trading Agent Design and Analysis, 2006. [13] Radu Jurca and Boi Faltings. Minimum payments that reward honest reputation feedback. In ACM Conference on Economics and Computation (EC), 2006. [14] Jiawen Kang, Zehui Xiong, Dusit Niyato, Dongdong Ye, Dong In Kim, and Jun Zhao. Toward secure blockchain-enabled internet of vehicles: Optimizing consensus management using reputation and contract theory. IEEE Transactions on Vehicular Technology, 68(3):2906–2920, 2019. [15] Ngai Meng Kou, Yan Li, Hao Wang, Leong Hou U, and Zhiguo Gong. Crowdsourced top-k queries by confidence-aware pairwise judgments. Proceedings of the 2017 ACM International Conference on Management of Data, 2017. URL https://api.semanticscholar.org/CorpusID:36647621. [16] Jean-Jacques Laffont and David Martimort. Moral Hazard: The Basic Trade-Offs, pages 145–186. Princeton University Press, 2002. URL http://www.jstor.org/stable/j.ctv7h0rwr.8. [17] Shili Lin. Rank aggregation methods. Wiley Interdisciplinary Reviews: Computational Statistics, 2(5):555–570, 2010. [18] Tyler Lu and Craig Boutilier. Learning mallows models with pairwise preferences. In International Conference on Machine Learning (ICML), 2011. [19] C. L. Mallows. Non-null ranking models. i. Biometrika, 44:114–130, 1957. URL https://api.semanticscholar.org/CorpusID:121527283. [20] Fei Mi and Dit-Yan Yeung. Probabilistic graphical models for boosting cardinal and ordinal peer grading in moocs. In AAAI Conference on Artificial Intelligence, 2015. [21] Chris Piech, Jonathan Huang, Zhenghao Chen, Chuong Do, Andrew Ng, and Daphne Koller. Tuned models of peer assessment in moocs. In Proceedings of The 6th International Conference on Educational Data Mining (EDM), 2013. [22] R. L. Plackett. The Analysis of Permutations. Journal of the Royal Statistical Society Series C, 24(2):193–202, June 1975. doi: 10.2307/2346567. URL https://ideas.repec.org/a/bla/jorssc/v24y1975i2p193-202.html. [23] Karthik Raman and Thorsten Joachims. Methods for ordinal peer grading. In International Conference on Knowledge Discovery and Data Mining (KDD), 2014. [24] Karthik Raman and Thorsten Joachims. Bayesian ordinal peer grading. In Proceedings of the ACM Conference on Learning at Scale, 2015. [25] Vikas C Raykar, Shipeng Yu, Linda H Zhao, Gerardo Hermosillo Valadez, Charles Florin, Luca Bogoni, and Linda Moy. Learning from crowds. Journal of machine learning research, 11(4), 2010. [26] Nihar Shah, Sivaraman Balakrishnan, Joseph Bradley, Abhay Parekh, Kannan Ramchandran, and Martin Wainwright. Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependence. In International Conference on Artificial Intelligence and Statistics (AISTATS), 2015. [27] Nihar B Shah, Joseph K Bradley, Abhay Parekh, Martin Wainwright, and Kannan Ramchandran. A case for ordinal peer-evaluation in moocs. In NIPS Workshop on Data-Driven Education, 2013. [28] Louis Leon Thurstone. The method of paired comparisons for social values. The Journal of Abnormal and Social Psychology, 21:384–400, 1927. URL https://api.semanticscholar.org/CorpusID:144595330. [29] Markus Triska. Solution Methods for the Social Golfer Problem. PhD thesis, Vienna University of Technology, March 2008. Available from https://www.metalevel.at/mst.pdf. [30] Kristi Tsukida, Maya R Gupta, et al. How to analyze paired comparison data. Department of Electrical Engineering University of Washington, Tech. Rep. UWEETR-2011-0004, 1, 2011. [31] Bo Waggoner and Yiling Chen. Output agreement mechanisms and common knowledge. Proceedings of the AAAI Conference on Human Computation and Crowdsourcing, 2(1): 220–226, Sep. 2014. doi: 10.1609/hcomp.v2i1.13151. URL https://ojs.aaai.org/index.php/HCOMP/article/view/13151. [32] Banghua Zhu, Stephen Bates, Zhuoran Yang, Yixin Wang, Jiantao Jiao, and Michael I. Jordan. The sample complexity of online contract design. In ACM Conference on Economics and Computation (EC), 2023. This paper is available on Arxiv under CC 4.0 license. This paper is available on Arxiv under CC 4.0 license. Arxiv

Algorithmic Contract Design for Crowdsourced Ranking: Conclusions, Future Directions, and References

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Kiriaki Frangias;
(2) Andrew Lin;
(3) Ellen Vitercik;
(4) Manolis Zampetakis. Table of Links Abstract and Introduction Warm-up: Agents with known equal disutility Agents with unknown disutilites Experiments Conclusions and future directions, References A Summary of notation B Omitted proofs from Section 2 C Omitted proofs from Section 3 D Additional Information about Experiments 4 Experiments In the following section, we present experiments that test our models and algorithm. We evaluate the impact of our algorithm on the principal’s utility compared to when she chooses not to incentivize agents, the efficacy of our algorithm in returning correct pairwise comparisons, and the robustness of our model to noisy values of ψ and π. Experimental procedure. Unless otherwise specified, we keep the following set of hyperparameter values across our experiments: π = 0.8, δ = 0.01, s = 100, n = 100, ψ¯ = 2, and ψ = 0.01. Peer grading is an example of a setting where s = n since the number of assignments is the same as the number of students. In Appendix D, we include experiments with a broad variety of parameter settings. Since we add noise to our model in these experiments, CrowdSort may not catch all bad agents and thus may return conflicting comparisons. We discard all conflicting comparisons (see Algorithm 4 in Appendix D). Despite this pessimistic post-processing strategy, our experiments show that we can recover most comparisons even under noise. 4.1 Principal’s utility The empirical utilities are calculated as follows. Let m be the number of agents not identified as “bad” by CrowdSort and k be the number of comparisons after post-processing. We set λ = 2 to be the principal’s per-comparison utility and define to be her empirical utility for running CrowdSort with p∗, v∗ , and r∗ defined in Equations (1) and (2). Similarly is her expected utility for performing all comparisons herself, where 2n log n is the expected number of comparisons required by quicksort (this value could easily be adjusted for any sorting algorithm). For ease of comparison, the y-axis is scaled by dividing all values by the baseline utility U0. We note that the size of the confidence interval decreases with π. For small values of π, a small number of agents are “good”, even though all agents exert effort. Then with higher probability, k will be small. This corresponds to higher variance in the principal’s utility across trials. In Figure 1b, we add noise to the parameter ψ and analyze the effect on the principal’s utility. We sample the disutility of each agent independently and identically from the distribution Uniform(ψ − 0.5ψ, ψ + 0.5ψ). However, we still calculate p∗, v∗, and r∗ from Equations (1) and (2) using ψ itself instead of the noisy version. The blue shading corresponds to a 90% confidence interval across 50 trials. Discussion. Comparing Figures 1a and 1b, we can see that even when noise is added to our model, our theoretical threshold is close to the point at which the principal’s utility from running CrowdSort dips below their utility from performing all comparisons herself. This demonstrates that our theoretical results are robust to noise in the model. When adding noise to ψ, the principal must pay fewer agents because fewer are incentivized to exert effort. Thus, we see a steeper decline in Figure 1a compared to 1b. 4.2 Number of pairwise comparisons returned Discussion. These experiments show that our algorithm retrieves all comparisons in the absence of noise. Moreover, even when a large amount of noise is added to ψ or π, our algorithm returns almost all of the comparisons with sufficient payment, despite the postprocessing phase excluding any conflicting comparison, again illustrating our algorithm’s robustness. 4.3 Optimization problem Discussion. For suitable values of g, approximately 40 samples are required for the utility of the principal under our model to surpass the utility she would get, if she were to perform all pairwise comparisons herself. We also notice that the principal’s utility increases as we increase either g or the number of samples. This result is shown in the multi-colored plots in Figure 3. Therefore, even for a small number of samples, the principal’s utility when implementing CrowdSort is well above her utility if she performed all comparisons on her own. This paper is available on Arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. Authors: (1) Kiriaki Frangias; (2) Andrew Lin; (3) Ellen Vitercik; (4) Manolis Zampetakis. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Kiriaki Frangias; (2) Andrew Lin; (3) Ellen Vitercik; (4) Manolis Zampetakis. Table of Links Abstract and Introduction Abstract and Introduction Warm-up: Agents with known equal disutility Warm-up: Agents with known equal disutility Agents with unknown disutilites Agents with unknown disutilites Experiments Experiments Conclusions and future directions, References Conclusions and future directions, References A Summary of notation A Summary of notation B Omitted proofs from Section 2 B Omitted proofs from Section 2 C Omitted proofs from Section 3 C Omitted proofs from Section 3 D Additional Information about Experiments D Additional Information about Experiments 4 Experiments In the following section, we present experiments that test our models and algorithm. We evaluate the impact of our algorithm on the principal’s utility compared to when she chooses not to incentivize agents, the efficacy of our algorithm in returning correct pairwise comparisons, and the robustness of our model to noisy values of ψ and π. Experimental procedure. Unless otherwise specified, we keep the following set of hyperparameter values across our experiments: π = 0.8, δ = 0.01, s = 100, n = 100, ψ¯ = 2, and ψ = 0.01. Peer grading is an example of a setting where s = n since the number of assignments is the same as the number of students. In Appendix D, we include experiments with a broad variety of parameter settings. Experimental procedure. Since we add noise to our model in these experiments, CrowdSort may not catch all bad agents and thus may return conflicting comparisons. We discard all conflicting comparisons (see Algorithm 4 in Appendix D). Despite this pessimistic post-processing strategy, our experiments show that we can recover most comparisons even under noise. 4.1 Principal’s utility The empirical utilities are calculated as follows. Let m be the number of agents not identified as “bad” by CrowdSort and k be the number of comparisons after post-processing. We set λ = 2 to be the principal’s per-comparison utility and define to be her empirical utility for running CrowdSort with p∗, v∗ , and r∗ defined in Equations (1) and (2). Similarly is her expected utility for performing all comparisons herself, where 2n log n is the expected number of comparisons required by quicksort (this value could easily be adjusted for any sorting algorithm). For ease of comparison, the y-axis is scaled by dividing all values by the baseline utility U0. We note that the size of the confidence interval decreases with π. For small values of π, a small number of agents are “good”, even though all agents exert effort. Then with higher probability, k will be small. This corresponds to higher variance in the principal’s utility across trials. In Figure 1b, we add noise to the parameter ψ and analyze the effect on the principal’s utility. We sample the disutility of each agent independently and identically from the distribution Uniform(ψ − 0.5ψ, ψ + 0.5ψ). However, we still calculate p∗, v∗, and r∗ from Equations (1) and (2) using ψ itself instead of the noisy version. The blue shading corresponds to a 90% confidence interval across 50 trials. Discussion . Comparing Figures 1a and 1b, we can see that even when noise is added to our model, our theoretical threshold is close to the point at which the principal’s utility from running CrowdSort dips below their utility from performing all comparisons herself. This demonstrates that our theoretical results are robust to noise in the model. Discussion When adding noise to ψ, the principal must pay fewer agents because fewer are incentivized to exert effort. Thus, we see a steeper decline in Figure 1a compared to 1b. 4.2 Number of pairwise comparisons returned Discussion . These experiments show that our algorithm retrieves all comparisons in the absence of noise. Moreover, even when a large amount of noise is added to ψ or π, our algorithm returns almost all of the comparisons with sufficient payment, despite the postprocessing phase excluding any conflicting comparison, again illustrating our algorithm’s robustness. Discussion 4.3 Optimization problem Discussion . For suitable values of g, approximately 40 samples are required for the utility of the principal under our model to surpass the utility she would get, if she were to perform all pairwise comparisons herself. We also notice that the principal’s utility increases as we increase either g or the number of samples. This result is shown in the multi-colored plots in Figure 3. Therefore, even for a small number of samples, the principal’s utility when implementing CrowdSort is well above her utility if she performed all comparisons on her own. Discussion This paper is available on Arxiv under CC 4.0 license. This paper is available on Arxiv under CC 4.0 license. Arxiv

Algorithmic Contract Design for Crowdsourced Ranking: A Deeper Look at Our Experiments

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Kiriaki Frangias;
(2) Andrew Lin;
(3) Ellen Vitercik;
(4) Manolis Zampetakis. Table of Links Abstract and Introduction Warm-up: Agents with known equal disutility Agents with unknown disutilites Experiments Conclusions and future directions, References A Summary of notation B Omitted proofs from Section 2 C Omitted proofs from Section 3 D Additional Information about Experiments 3 Agents with unknown disutilites We now significantly expand our model to study heterogeneous agents with differing, unknown disutilities. The full proofs of all results in this section are in Appendix C. 3.1 Model and notation Some agents might experience high disutility when exerting effort, so it may not be in the principal’s best interest to incentivize all agents to exert effort. Therefore, the principal must set the payment so that the number of agents incentivized is utility maximizing for the principal. For the rest of this section, we denote by g the number of agents that the principal aims to incentivize; in Theorem 3.6, we describe an efficient optimization problem that solves for the optimal value of g, denoted g∗. The principal controls the number of incentivized agents only through the payment function. Hence, the realized number of agents that exert effort, denoted ˆg, is a random variable with a distribution that depends on the payment. Under this model, the principal will: 1. Calculate g∗, the optimal number of agents to incentivize. 2. Announce the payment pg∗ ∈ R+ (based on g∗). 3. Verify a subset of comparisons assigned to the agents. 4. Assign each comparison to a total of r agents. 5. Pay pg∗ to all agents not identified as “bad.” 3.2 Payment function 3.3 Correctness of CrowdSort Next, we bound the redundancy required to ensure that CrowdSort returns the groundtruth ordering. Proof. We know from Lemma 3.4 that if then with high probability, the algorithm CrowdSort(T, s, v, r, δ) identifies all “bad” agents. Therefore, it suffices to assign each comparison to at least one “good” agent for the true value of the comparison to be returned. By Remark 3.3, we know that for any agent ai, So the probability that all r agents assigned to a single comparison are “bad” is at most: Taking the union bound over all comparisons, we have that the probability there exists a comparison such that all agents assigned to it are “bad” is at most Upper-bounding the above probability by δ/2, we get that: Finally, notice that the above inequality and Inequality (6) hold simultaneously with probability at least 1 − δ/2. 3.4 Principal’s incentive We combine the results presented above in the following theorem, in which we additionally prove that it is possible for the principal to efficiently compute the optimal number of agents to incentivize. Based on Lemma 3.5, we use the notation and This paper is available on Arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. Authors: (1) Kiriaki Frangias; (2) Andrew Lin; (3) Ellen Vitercik; (4) Manolis Zampetakis. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Kiriaki Frangias; (2) Andrew Lin; (3) Ellen Vitercik; (4) Manolis Zampetakis. Table of Links Abstract and Introduction Abstract and Introduction Warm-up: Agents with known equal disutility Warm-up: Agents with known equal disutility Agents with unknown disutilites Agents with unknown disutilites Experiments Experiments Conclusions and future directions, References Conclusions and future directions, References A Summary of notation A Summary of notation B Omitted proofs from Section 2 B Omitted proofs from Section 2 C Omitted proofs from Section 3 C Omitted proofs from Section 3 D Additional Information about Experiments D Additional Information about Experiments 3 Agents with unknown disutilites We now significantly expand our model to study heterogeneous agents with differing, unknown disutilities. The full proofs of all results in this section are in Appendix C. 3.1 Model and notation Some agents might experience high disutility when exerting effort, so it may not be in the principal’s best interest to incentivize all agents to exert effort. Therefore, the principal must set the payment so that the number of agents incentivized is utility maximizing for the principal. For the rest of this section, we denote by g the number of agents that the principal aims to incentivize; in Theorem 3.6, we describe an efficient optimization problem that solves for the optimal value of g, denoted g∗. The principal controls the number of incentivized agents only through the payment function. Hence, the realized number of agents that exert effort, denoted ˆg, is a random variable with a distribution that depends on the payment. Under this model, the principal will: 1. Calculate g∗, the optimal number of agents to incentivize. 2. Announce the payment pg∗ ∈ R+ (based on g∗). 3. Verify a subset of comparisons assigned to the agents. 4. Assign each comparison to a total of r agents. 5. Pay pg∗ to all agents not identified as “bad.” 3.2 Payment function 3.3 Correctness of CrowdSort Next, we bound the redundancy required to ensure that CrowdSort returns the groundtruth ordering. Proof. We know from Lemma 3.4 that if then with high probability, the algorithm CrowdSort(T, s, v, r, δ) identifies all “bad” agents. Therefore, it suffices to assign each comparison to at least one “good” agent for the true value of the comparison to be returned. By Remark 3.3, we know that for any agent ai, So the probability that all r agents assigned to a single comparison are “bad” is at most: r Taking the union bound over all comparisons, we have that the probability there exists a comparison such that all agents assigned to it are “bad” is at most Upper-bounding the above probability by δ/2, we get that: Finally, notice that the above inequality and Inequality (6) hold simultaneously with probability at least 1 − δ/2. 3.4 Principal’s incentive We combine the results presented above in the following theorem, in which we additionally prove that it is possible for the principal to efficiently compute the optimal number of agents to incentivize. Based on Lemma 3.5, we use the notation and This paper is available on Arxiv under CC 4.0 license. This paper is available on Arxiv under CC 4.0 license. Arxiv Arxiv

Algorithmic Contract Design: What to Know About Agents With Unknown Disutilites 

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Kiriaki Frangias;
(2) Andrew Lin;
(3) Ellen Vitercik;
(4) Manolis Zampetakis. Table of Links Abstract and Introduction Warm-up: Agents with known equal disutility Agents with unknown disutilites Experiments Conclusions and future directions, References A Summary of notation B Omitted proofs from Section 2 C Omitted proofs from Section 3 D Additional Information about Experiments 2 Warm-up: Agents with known equal disutility As a warm up to our main result, in this section, we propose a contract assuming that (a) the principal knows the agents’ disutilites and (b) every agent experiences the same value of per-comparison disutility (assumptions we relax in Section 3). We begin with a formal model in Section 2.1 and define the optimal payment in Section 2.2. In Sections 2.3 and 2.4, we present our main algorithm CrowdSort for computing the correct sorting. Section 2.5 identifies conditions under which the principal gets higher utility when implementing our proposed contract than when performing all pairwise comparisons herself. The full proofs of all results in this section are in Appendix B. 2.1 Model and notation The interaction proceeds as follows: 1. The principal fixes a payment p∗ ∈ R+ that she will pay agents in order to incentivize them to exert effort. 2. The principal verifies a subset of the comparisons and announces the size of this set to the agents. 3. Agents choose whether to exert effort, which fixes their type upfront. 4. Agents are assigned verified and unverified comparisons. 2.2 Agents’ incentives 2.3 Peer grading algorithm 2.4 Allocation of items 2.4.1 Assigning verified comparisons. Lemma 2.3. If each item in V appears in exactly one pair, then no pair in V is redundant. 2.4.2 Assigning unverified comparisons. We now define findWset. First, we bound the number of agents each comparison must be assigned to in order to retrieve the ground-truth sorting. Details about the social golfer problem. In the social golfer problem, the goal is to determine whether m golfers can play together in g groups of p (where m = gp) for w days in such a way that (1) no two golfers play in the same group more than once, and (2) each golfer plays exactly once each day. Thus, an instance of this problem is defined by integers (g, p, w). For us, the golfers correspond to the items, the days correspond to the partitions, and the groups of golfers correspond to the sets in the partitions. Thus, we aim to solve this problem with g, p, and w all approximately equal to √n. 2.5 Principal’s incentives We synthesize our results in the following theorem, in which we additionally prove that if the principal’s disutility ψ¯ is sufficiently larger than the agents’ disuility ψ, then it is in the principal’s best interest to use our mechanism rather than perform all pairwise comparisons herself. This is a natural assumption, which implies that the principal would have to be compensated sufficiently more per comparison than the agents for their work to be profitable to the principal. This paper is available on Arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. Authors: (1) Kiriaki Frangias; (2) Andrew Lin; (3) Ellen Vitercik; (4) Manolis Zampetakis. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Kiriaki Frangias; (2) Andrew Lin; (3) Ellen Vitercik; (4) Manolis Zampetakis. Table of Links Abstract and Introduction Abstract and Introduction Warm-up: Agents with known equal disutility Warm-up: Agents with known equal disutility Agents with unknown disutilites Agents with unknown disutilites Experiments Experiments Conclusions and future directions, References Conclusions and future directions, References A Summary of notation A Summary of notation B Omitted proofs from Section 2 B Omitted proofs from Section 2 C Omitted proofs from Section 3 C Omitted proofs from Section 3 D Additional Information about Experiments D Additional Information about Experiments 2 Warm-up: Agents with known equal disutility As a warm up to our main result, in this section, we propose a contract assuming that (a) the principal knows the agents’ disutilites and (b) every agent experiences the same value of per-comparison disutility (assumptions we relax in Section 3). We begin with a formal model in Section 2.1 and define the optimal payment in Section 2.2. In Sections 2.3 and 2.4, we present our main algorithm CrowdSort for computing the correct sorting. Section 2.5 identifies conditions under which the principal gets higher utility when implementing our proposed contract than when performing all pairwise comparisons herself. The full proofs of all results in this section are in Appendix B. 2.1 Model and notation The interaction proceeds as follows: 1. The principal fixes a payment p∗ ∈ R+ that she will pay agents in order to incentivize them to exert effort. 2. The principal verifies a subset of the comparisons and announces the size of this set to the agents. 3. Agents choose whether to exert effort, which fixes their type upfront. 4. Agents are assigned verified and unverified comparisons. 2.2 Agents’ incentives 2.3 Peer grading algorithm 2.4 Allocation of items 2.4.1 Assigning verified comparisons. Lemma 2.3. If each item in V appears in exactly one pair, then no pair in V is redundant. Lemma 2.3. If each item in V appears in exactly one pair, then no pair in V is redundant. 2.4.2 Assigning unverified comparisons. We now define findWset. First, we bound the number of agents each comparison must be assigned to in order to retrieve the ground-truth sorting. Details about the social golfer problem. In the social golfer problem, the goal is to determine whether m golfers can play together in g groups of p (where m = gp) for w days in such a way that (1) no two golfers play in the same group more than once, and (2) each golfer plays exactly once each day. Thus, an instance of this problem is defined by integers (g, p, w). For us, the golfers correspond to the items, the days correspond to the partitions, and the groups of golfers correspond to the sets in the partitions. Thus, we aim to solve this problem with g, p, and w all approximately equal to √n. Details about the social golfer problem. 2.5 Principal’s incentives We synthesize our results in the following theorem, in which we additionally prove that if the principal’s disutility ψ¯ is sufficiently larger than the agents’ disuility ψ, then it is in the principal’s best interest to use our mechanism rather than perform all pairwise comparisons herself. This is a natural assumption, which implies that the principal would have to be compensated sufficiently more per comparison than the agents for their work to be profitable to the principal. This paper is available on Arxiv under CC 4.0 license. Arxiv Arxiv

Algorithmic Contract Design for Crowdsourced Ranking: Warm-up: Agents With Known Equal Disutility

This paper is available on Arxiv under CC 4.0 license.
Authors:
(1) Kiriaki Frangias;
(2) Andrew Lin;
(3) Ellen Vitercik;
(4) Manolis Zampetakis. Table of Links Abstract and Introduction Warm-up: Agents with known equal disutility Agents with unknown disutilites Experiments Conclusions and future directions, References A Summary of notation B Omitted proofs from Section 2 C Omitted proofs from Section 3 D Additional Information about Experiments Abstract Ranking is fundamental to many areas, such as search engine and recommender system optimization, as well as peer grading. Crowdsourcing, which is often used for these tasks, requires proper incentivization to ensure accurate inputs. In this work, we draw on the field of contract theory from Economics to propose a novel mechanism that enables a principal to accurately rank a set of items by incentivizing agents to provide pairwise comparisons of the items. Our mechanism implements these incentives by verifying a subset of each agent’s comparisons with a ground-truth ordering, a task we assume to be costly. The agent is compensated (for example, monetarily or with class credit) based on the accuracy of these comparisons. Our mechanism achieves the following guarantees: (1) it only requires the principal to verify O(log s) comparisons, where s is the total number of agents, and (2) it provably achieves higher total utility for principal compared to ranking the items herself with no crowdsourcing. 1 Introduction Ranking is a central task across a wide range of applications including search engine optimization, recommender systems, and peer grading: search engines rank pages by relevance, recommender systems rank content by entertainment value, and peer graders rank submissions by quality. Platforms often use crowdsourcing to determine rankings [7, 9, 15], especially when ranking many alternatives. In many such cases, it is often more feasible and accurate for agents to provide pairwise comparisons than cardinal evaluations [26, 27]. However, rational agents will only invest the effort necessary to provide accurate comparisons when properly incentivized. In many real world scenarios, such as peer grading, these incentives involve a principal (the ranking’s end-user) verifying a selection of an agent’s comparisons against a ground-truth sorting. The agent’s payment depends on these verified comparisons’ accuracy. We propose a novel mechanism that enables a principal to rank a set of items from pairwise comparisons while minimizing the requisite payments and number of verifications, which are costly for the principal. To model the principal and agents, we draw on contract theory, a classical field in economics [16] that has become increasingly relevant in computer science [e.g., 6, 10, 14, 32]. The principal assigns comparisons to each agent and verifies a subset of these comparisons against a ground-truth ordering. The agent does not know the subset’s identity. The principal will compensate each agent for correctly evaluating all verified pairs. Given the principal’s offered payment, the agent decides whether they will exert effort. As in the standard model of contract theory, if the agent exerts effort, they will be “good” at the task with some probability and “bad” at the task with some smaller probability. If they decide not to exert effort, they will be “bad” with certainty. A “good” agent will return the correct comparisons, but a “bad” agent will not. When modeling the agents, we introduce heterogeneity through differing values of the per-comparison disutility that they experience. We therefore assume that every agent can potentially be “good”, but might require more or less compensation to be incentivized to exert effort. As we show, this also allows the principal to incentivize and pay only agents with small disutilities, even though these values are not a priori known to the principal. Key challenges. The primary obstacle we face in designing a mechanism for this problem lies in determining how to distribute the comparisons among the agents while satisfying several critical requirements: (a) The number of items assigned to each agent (i.e., the subset of items that make up their pairwise comparisons) should be small, minimizing the agent’s workload. (b) Every comparison must be evaluated by at least one “good” agent with high probability. In other words, we want each agent’s comparisons to cover as few items as possible to satisfy (a). However, we need the union of all agents’ comparisons to have sufficiently high redundancy to satisfy (b). These conditions are fundamentally at odds, so satisfying both requires care. 1.1 Our contributions We summarize our four primary contributions below. 2. Aggregating the noisy comparisons. Next, we present an algorithm for identifying “bad” agents and aggregating comparisons from “good” agents. Our algorithm returns the correct ranking with high probability. 3. Determining payments. We identify the payments necessary to ensure enough agents are “good” to recover the ground-truth sorting. This depends on the disutility it costs agents to make comparisons. We study a range of settings, from a warm-up where the principal knows the disutilities (as is typical in contract theory), to a setting where the disutilities are drawn from a distribution about which the principal has limited information. 4. Principal’s utility. We show that it suffices for the principal to verify O(log s) comparisons to ensure that the ground-truth sorting is recovered. We also identify natural conditions under which, by implementing our proposed contract, the principal achieves higher total utility than she would if she performed all pairwise comparisons herself. 5. Experiments. In experiments, we stress-test our results by relaxing our model along several axes. We demonstrate that even when the assumed model is inaccurate, with a sufficient increase in the payment the principal can recover the ground-truth ranking. 1.2 Related work Rank Aggregation. Ranking via pairwise comparisons can be considered as a subfield of rank aggregation [2, 19, 22, 28]. Recent work on rank aggregation with pairwise comparisons has built upon and extended these techniques [4, 5, 8, 18, 30]. Lin [17] provides an extensive introduction. Rank aggregation differs from our work, which models the data sources as agents with differing reliability. Crowdsourcing. Crowdsourcing offers a cost-effective and efficient way to consolidate feedback from a large number of non-experts. With the rise of crowdsourcing platforms, such as Amazon Mechanical Turk, crowdsourcing has been commonly used in a variety of applications, including sorting [1, 4, 25]. A central task in crowdsourcing is modeling the reliability of annotators [4, 25]. Chen et al. [4], for example, use the Bradley-Terry model for ranking aggregation, assuming that annotators are either perfect or spammers (comparisons are correct with probability 0.5). In contrast, we study a dynamic setting in which annotators can be incentivized to exert effort and therefore increase the accuracy of their work. Ordinal peer grading. This area is most related to our work. With the rise of massive online open courses (MOOCs), it has become increasingly important to decentralize the grading process in an efficient manner that comes at a low cost to teaching staff [21]. Peer grading can be a solution to this technical hurdle. Ordinal peer grading (in which students are asked to rank other students’ work) is an inexpensive, accurate, and robust way to assess performance [27]. However, many works on ordinal peer grading draw on probabilistic methods to estimate grader reliability and lack perspective on strategic interactions [20, 23, 24]. In contrast, works relating to aggregating feedback from strategic data sources focus mostly on regression or cardinal evaluations of items [3, 11–13, 31]. Our work aims to bridge this gap using a contract between the principal and the agents. The contract structures their interaction and leverages their strategic behavior by incentivizing agents to perform accurate comparisons. It also comes at a low cost to the principal while provably retrieving the correct ranking of items. This paper is available on Arxiv under CC 4.0 license. This paper is available on Arxiv under CC 4.0 license. Authors: (1) Kiriaki Frangias; (2) Andrew Lin; (3) Ellen Vitercik; (4) Manolis Zampetakis. This paper is available on Arxiv under CC 4.0 license. Arxiv Authors: Authors: (1) Kiriaki Frangias; (2) Andrew Lin; (3) Ellen Vitercik; (4) Manolis Zampetakis. Table of Links Abstract and Introduction Abstract and Introduction Warm-up: Agents with known equal disutility Warm-up: Agents with known equal disutility Agents with unknown disutilites Agents with unknown disutilites Experiments Experiments Conclusions and future directions, References Conclusions and future directions, References A Summary of notation A Summary of notation B Omitted proofs from Section 2 B Omitted proofs from Section 2 C Omitted proofs from Section 3 C Omitted proofs from Section 3 D Additional Information about Experiments D Additional Information about Experiments Abstract Ranking is fundamental to many areas, such as search engine and recommender system optimization, as well as peer grading. Crowdsourcing, which is often used for these tasks, requires proper incentivization to ensure accurate inputs. In this work, we draw on the field of contract theory from Economics to propose a novel mechanism that enables a principal to accurately rank a set of items by incentivizing agents to provide pairwise comparisons of the items. Our mechanism implements these incentives by verifying a subset of each agent’s comparisons with a ground-truth ordering, a task we assume to be costly. The agent is compensated (for example, monetarily or with class credit) based on the accuracy of these comparisons. Our mechanism achieves the following guarantees: (1) it only requires the principal to verify O(log s) comparisons, where s is the total number of agents, and (2) it provably achieves higher total utility for principal compared to ranking the items herself with no crowdsourcing. 1 Introduction Ranking is a central task across a wide range of applications including search engine optimization, recommender systems, and peer grading: search engines rank pages by relevance, recommender systems rank content by entertainment value, and peer graders rank submissions by quality. Platforms often use crowdsourcing to determine rankings [7, 9, 15], especially when ranking many alternatives. In many such cases, it is often more feasible and accurate for agents to provide pairwise comparisons than cardinal evaluations [26, 27]. However, rational agents will only invest the effort necessary to provide accurate comparisons when properly incentivized. In many real world scenarios, such as peer grading, these incentives involve a principal (the ranking’s end-user) verifying a selection of an agent’s comparisons against a ground-truth sorting. The agent’s payment depends on these verified comparisons’ accuracy. We propose a novel mechanism that enables a principal to rank a set of items from pairwise comparisons while minimizing the requisite payments and number of verifications, which are costly for the principal. To model the principal and agents, we draw on contract theory, a classical field in economics [16] that has become increasingly relevant in computer science [e.g., 6, 10, 14, 32]. The principal assigns comparisons to each agent and verifies a subset of these comparisons against a ground-truth ordering. The agent does not know the subset’s identity. The principal will compensate each agent for correctly evaluating all verified pairs. Given the principal’s offered payment, the agent decides whether they will exert effort. As in the standard model of contract theory, if the agent exerts effort, they will be “good” at the task with some probability and “bad” at the task with some smaller probability. If they decide not to exert effort, they will be “bad” with certainty. A “good” agent will return the correct comparisons, but a “bad” agent will not. When modeling the agents, we introduce heterogeneity through differing values of the per-comparison disutility that they experience. We therefore assume that every agent can potentially be “good”, but might require more or less compensation to be incentivized to exert effort. As we show, this also allows the principal to incentivize and pay only agents with small disutilities, even though these values are not a priori known to the principal. Key challenges. The primary obstacle we face in designing a mechanism for this problem lies in determining how to distribute the comparisons among the agents while satisfying several critical requirements: Key challenges. (a) The number of items assigned to each agent (i.e., the subset of items that make up their pairwise comparisons) should be small, minimizing the agent’s workload. (b) Every comparison must be evaluated by at least one “good” agent with high probability. In other words, we want each agent’s comparisons to cover as few items as possible to satisfy (a). However, we need the union of all agents’ comparisons to have sufficiently high redundancy to satisfy (b). These conditions are fundamentally at odds, so satisfying both requires care. 1.1 Our contributions We summarize our four primary contributions below. 2. Aggregating the noisy comparisons. Next, we present an algorithm for identifying “bad” agents and aggregating comparisons from “good” agents. Our algorithm returns the correct ranking with high probability. 2. Aggregating the noisy comparisons. 3. Determining payments. We identify the payments necessary to ensure enough agents are “good” to recover the ground-truth sorting. This depends on the disutility it costs agents to make comparisons. We study a range of settings, from a warm-up where the principal knows the disutilities (as is typical in contract theory), to a setting where the disutilities are drawn from a distribution about which the principal has limited information. 3. Determining payments. 4. Principal’s utility. We show that it suffices for the principal to verify O(log s) comparisons to ensure that the ground-truth sorting is recovered. We also identify natural conditions under which, by implementing our proposed contract, the principal achieves higher total utility than she would if she performed all pairwise comparisons herself. 4. Principal’s utility. 5. Experiments. In experiments, we stress-test our results by relaxing our model along several axes. We demonstrate that even when the assumed model is inaccurate, with a sufficient increase in the payment the principal can recover the ground-truth ranking. 5. Experiments. 1.2 Related work Rank Aggregation. Ranking via pairwise comparisons can be considered as a subfield of rank aggregation [2, 19, 22, 28]. Recent work on rank aggregation with pairwise comparisons has built upon and extended these techniques [4, 5, 8, 18, 30]. Lin [17] provides an extensive introduction. Rank aggregation differs from our work, which models the data sources as agents with differing reliability. Rank Aggregation. Crowdsourcing . Crowdsourcing offers a cost-effective and efficient way to consolidate feedback from a large number of non-experts. With the rise of crowdsourcing platforms, such as Amazon Mechanical Turk, crowdsourcing has been commonly used in a variety of applications, including sorting [1, 4, 25]. A central task in crowdsourcing is modeling the reliability of annotators [4, 25]. Chen et al. [4], for example, use the Bradley-Terry model for ranking aggregation, assuming that annotators are either perfect or spammers (comparisons are correct with probability 0.5). In contrast, we study a dynamic setting in which annotators can be incentivized to exert effort and therefore increase the accuracy of their work. Crowdsourcing Ordinal peer grading. This area is most related to our work. With the rise of massive online open courses (MOOCs), it has become increasingly important to decentralize the grading process in an efficient manner that comes at a low cost to teaching staff [21]. Peer grading can be a solution to this technical hurdle. Ordinal peer grading (in which students are asked to rank other students’ work) is an inexpensive, accurate, and robust way to assess performance [27]. Ordinal peer grading. However, many works on ordinal peer grading draw on probabilistic methods to estimate grader reliability and lack perspective on strategic interactions [20, 23, 24]. In contrast, works relating to aggregating feedback from strategic data sources focus mostly on regression or cardinal evaluations of items [3, 11–13, 31]. Our work aims to bridge this gap using a contract between the principal and the agents. The contract structures their interaction and leverages their strategic behavior by incentivizing agents to perform accurate comparisons. It also comes at a low cost to the principal while provably retrieving the correct ranking of items. This paper is available on Arxiv under CC 4.0 license. This paper is available on Arxiv under CC 4.0 license. Arxiv

Algorithmic Contract Design for Crowdsourced Ranking: An Introduction to Get You Started

These days, social media plays an integral part in life, influencing how we communicate, obtain information, and share information with each other. Although less than 30 years old [1], we have seen a huge evolution of platforms like Facebook, Twitter, TikTok, and LinkedIn: Facebook is now Meta and owns WhatsApp, Instagram, and Threads; Twitter is X. Both are owned by billionaires who have anticipated technological trends, capitalized on these opportunities and pioneered the way for a rapidly innovative industry. The biggest driving success of social media, from a business point of view, is consumer data. A large majority of social media platforms are free of charge and are able to operate this way because you’re allowing them access to your data in return. With this, companies like Meta have been able to shape social media content and interactions. This is something that can be viewed as beneficial or unethical depending on the intent and use case, with issues like privacy and manipulation far from uncommon now. In this article, we will be delving into the ethics of using and algorithms in social media, examining how they help personalize content, potentially leading to bias and echo chambers, and the future of AI in social media platforms. AI A Brief History of Algorithms and Their Increasing Use Cases in Social Media ‘An algorithm is a series of instructions designed to solve specific problems, perform tasks, or make decisions’ [2]. In social media, these instructions govern user experiences such as content ranking, filtering, and personalization, typically based on trends for different consumer groups. This allows you as the user to find content that will interest you much faster, as it is likely to appear on For You Pages without you having to search for it. Algorithms haven’t always been used in social media. It was in 2009 that Tumblr and Facebook introduced ranking metrics and personalized feeds. In 2012, more followed suit. Facebook upped its algorithmic use in its news feed and introduced sponsored content [3]. began a “semi-structured feed,” and YouTube introduced a ranking algorithm, prioritizing watch time over quantity [4]. Since then, algorithms’ roles in such social media have only continued to increase. By 2015, machine learning was starting to play a role in sorting and filtering algorithms, underpinned by developments in Big Data efforts. 2016’s political events like the Trump election and Brexit referendum (and a pivotal year in the Cambridge Analytica scandal) then brought to public attention some of the ethical dilemmas surrounding such heavy and increasing use of algorithms and user data collection in social media. LinkedIn These days, AI-powered algorithms are built so precisely they recommend content based on your specific previous interactions on the platform, with growing user data allowing social media companies to eliminate a significant majority of any guesswork. Documentaries like The Social Dilemma [5] and The Great Hack [6] give some insight into just how engineered some of these algorithms are, often with the end goal of keeping a user on their platform for longer and driving interaction with the platform. While increased user interaction means more data for social media companies to collect, tweak, and repeat this process, this goal does not take into consideration what’s best for the user and wider society with regard to social media consumption. Ethical Issues Stemming from Algorithmic Bias Algorithms can perpetuate harmful biases, and in the context of social media, this often manifests as the reinforcement of stereotypes and limited exposure to diverse viewpoints. Culminated over time, this can fuel discrimination, polarise electorates, and even contribute to extremism and right-wing/autocratic populism, which exploit societal divisions. At a low level of impact, examples of algorithmic bias could include job postings for certain industries, e.g., LinkedIn being shown more to men than women, because the training data sets the algorithms were modeled on predict that more men are likely to work in those roles. While this doesn’t necessarily have an immediately obvious harmful impact, it creates a negative feedback loop that works against society’s goals to improve equality and representation across workplaces and specific industries. In this way, gender bias is perpetuated as a result of algorithmic bias by limiting opportunities for women to see those ads. Now, to delve deeper into the higher-level implications of algorithmic bias, we will examine the 2016 Trump election as a case study. Case Study: How Algorithms Affected Polarization/Echo Chambers in Trump 2016 Election Throughout the course of the 2016 US presidential election, research has shown that algorithms may have exacerbated political polarization by amplifying echo chambers and limiting the electorate’s exposure to diverse viewpoints. Many think it was this mechanism that allowed Trumpism to run rampant and also why so few people predicted his victory [7], as these dynamics were not fully understood nor visible during the election period. Even on social media, therefore, it seems true that ‘birds of a feather flock together’ [8]. Algorithms tailor content to align with users' preferences, shielding them from opposing views and opinions, and creating ‘filter bubbles’. In turn, some individuals within these filter bubbles continue the positive reinforcement of their views by further isolating themselves within digital environments where their beliefs and opinions are echoed and even more so reinforced. These are called ‘echo chambers’. Essentially, social media fosters an environment in which we all ingest such extremely personalized news and content feeds that we become blind to others’ differing perspectives. Currently, it is not clear from research whether social media only serves as a platform allowing echo chambers to emerge or whether its use of algorithms goes so far as to play a role in creating these echo chambers[8]. The 2016 Trump win shows how social media companies’ agendas can have widespread consequences affecting millions of people, which, while unintended, are still hugely impactful and also unethical. We know that social media algorithms are designed to maximize user engagement and retention by serving content tailored to individual preferences. Now, though, we also see how this applies even to political conversations, leveraging users’ political leanings and vulnerabilities. Who knows how the election would have played out if algorithms weren’t impacting people’s personal political beliefs? And how does this affect democracy and political stability? If people are not aware of these manipulations, can the outcomes be considered fair and valid? The Future of AI in Social Media The role of algorithms and AI in social media is only continuing to evolve alongside our innovations within those fields. From AI-generated content to AI-powered algorithms allowing the precision we touched on earlier, the ethical challenges that come with its integration into social media will similarly need to be increasingly considered. This needs to start with addressing algorithmic biases and promoting algorithmic transparency in social media platforms. Future policy considerations and regulations will play a crucial role in shaping the trajectory of AI use in social media. There is already growing attention being given to the need for algorithmic regulation and protection from the harm these invisible biases can cause, especially in the US. So far, initiatives include[9]: The “Algorithmic Accountability Act of 2022” The “Eliminating Bias in Algorithmic Systems Act of 2023” The “AI Bill of Rights” While there are more frameworks currently being drawn up in the proposal stages, there is still insufficient regulation of such powerful technologies when we consider the impact they already have. Striking a delicate balance between innovation and safeguarding user interests will require a collaborative approach involving technology companies, policymakers, and users alike. Social media does have the power to be a force for good, uniting communities and fostering inclusivity; however, without adequate frameworks and regulations protecting user rights, its use of AI and algorithms also has the power to be destructive to individuals and wider society. References [1] . The Evolution of Social Media: How Did It Begin, and Where Could It Go Next? | Maryville Online [2] Everything You Need to Know About Social Media Algorithms [3] Facebook's News Feed is 10 years old. This is how the site has changed | World Economic Forum [4] a history of - social media algorithms [5] Watch The Social Dilemma | Netflix Official Site [6] Watch The Great Hack | Netflix Official Site [7] The 'Filter Bubble' Explains Why Trump Won and You Didn't See It Coming [8] How social media echo chambers emerge (and why all your friends think Trump will lose) [9] Eliminating Bias in Algorithmic Systems Act of 2023

AI in Social Media: Ethical Considerations of AI and Algorithms in Shaping Social Media Interactions

সোশ্যাল মিডিয়াতে এআই: সোশ্যাল মিডিয়া ইন্টারঅ্যাকশন গঠনে এআই এবং অ্যালগরিদমের নৈতিক বিবেচনা

KI in sozialen Medien: Ethische Überlegungen zu KI und Algorithmen bei der Gestaltung von Interaktionen in sozialen Medien

IA en las redes sociales: consideraciones éticas de la IA y los algoritmos para dar forma a las interacciones en las redes sociales

L'IA dans les médias sociaux : considérations éthiques sur l'IA et les algorithmes pour façonner les interactions avec les médias sociaux

सोशल मीडिया में एआई: सोशल मीडिया इंटरैक्शन को आकार देने में एआई और एल्गोरिदम के नैतिक विचार

ソーシャルメディアにおける AI: ソーシャルメディアのインタラクションの形成における AI とアルゴリズムの倫理的考慮

소셜 미디어의 AI: 소셜 미디어 상호 작용 형성 시 AI 및 알고리즘에 대한 윤리적 고려 사항

IA nas mídias sociais: considerações éticas de IA e algoritmos na formação de interações nas mídias sociais

ИИ в социальных сетях: этические аспекты ИИ и алгоритмы формирования взаимодействия в социальных сетях

Sosyal Medyada Yapay Zeka: Sosyal Medya Etkileşimlerini Şekillendirmede Yapay Zeka ve Algoritmalara İlişkin Etik Hususlar

AI trong truyền thông xã hội: Những cân nhắc về mặt đạo đức đối với AI và thuật toán trong việc định hình các tương tác trên truyền thông xã hội

社交媒体中的人工智能：人工智能和算法在塑造社交媒体互动方面的伦理考量

Backpropagation - The Most Fundamental Training Systems Algorithm in Modern Generative AI

A Comparative Algorithm Audit of Conspiracies on the Net: Conclusion and Bibliography

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Aleksandra Urman, She is a corresponding author from Department of Informatics, University of Zurich, Switzerland;
(2) Mykola Makhortykh, Institute of Communication and Media Studies, University of Bern, Switzerland;
(3) Roberto Ulloa, GESIS - Leibniz-Institut für Sozialwissenschaften, Germany;
(4) Juhi Kulshrestha, Department of Politics and Public Administration, University of Konstanz, Germany. Table of Links Abstract and Introduction
Web search results: biases, inaccuracies and their consequences
Conspiracy theories in the online environments
Research questions
Methodology
Results
Discussion
Limitations
Conclusion and Bibliography Methodology Data collection Agent-based audit setup. To collect the data we used agent-based algorithm impact auditing (see Ulloa et al., 2021). This type of auditing relies on automated agents, i.e., software that simulates user browsing behavior (e.g. scrolling web pages) and records the outputs. The benefit of this approach is that it allows controlling for search personalization (Hannak et al., 2013) and randomization (Makhortykh et al., 2020). Unlike human agents, automated agents can be easily synchronized (i.e., to isolate the effect of time at which the search actions are conducted) and deployed in a controlled environment (e.g., a network of virtual machines using the same IP range, the same type of operating system (OS) and the same browsing software) to limit the effects of personalization based on user-specific factors (e.g. location or OS type). Our approach is comparative in the sense that we assess the outputs of several SEs across multiple locations, time periods, and queries. To increase the robustness of our observations, the data were collected over two collection rounds: March 18-19 and May 8-9 2021. From the technical standpoint, the data collection was organized as follows: each agent was made of two browser plugins (for either Chrome or Firefox desktop browsers). The first plugin (the bot) simulated human activity in the browser, in our case opening the search engine page, entering a query and scrolling down the first page of search outputs. The second plugin (the tracker) recorded html content appearing in the browser and sent it to the remote server. The agents were deployed via Amazon Elastic Compute Cloud (EC2). We focused our exploration to the five biggest SEs by market share on desktop devices worldwide: Google, Bing, Yahoo, Yandex and DuckDuckGo (Desktop Search Engine Market Share Worldwide, n.d.). During the first round of data collection (March), we deployed 60 agents per location (see below), whereas for the second round we decreased this number to 30 agents per location because of budgetary limitations. The agents were equally distributed between the SEs (i.e., 12 agents per engine for the first round and 6 agents per engine for the second round). The majority of agents were able to perform their planned routine; the only major exception was Yandex, where multiple agents were blocked because of the aggressive bot detection mechanisms (e.g., frequent captchas) utilized by the search engine (hence, the absence of results for Yandex for some search queries). Search query selection. We have collected search results for six queries that correspond to specific conspiracy theories (“flat earth”, “new world order”, “qanon”) or to subjects related to conspiracy theories (“9/11”, “illuminati”, “george soros”). We specifically included these two groups of queries, because we suggest that they might be entered by users with two different intentions: those corresponding to the names of conspiracies are more likely to be entered by people already interested in a given theory, while the latter - by people merely interested in a certain topic. Thus if conspiratorial content is returned for the latter queries, it might lead to users’ incidental exposure to conspiracies. Further, we expect to observe discrepancies between the two groups of queries with more conspiratorial content returned for the queries corresponding to specific theories and less for the subjects which are surrounded by conspiracy theories. Location selection. We analyze the data collected for the five SEs, across three locations: two in the US (Ohio and California) and one in the UK (London). Our selection of locations is determined in part by the availability of different EC2 servers (see the description of technical implementation of the data collection below). Also, we utilized locations where English is the official language for the purposes of comparability - e.g., to make sure that any results we retrieve are due to the differences in the location, not to data voids in a specific language. Finally, we selected Ohio and California due to the differences in the ideological orientations of the two states (while California is a solid “blue” (Democratic) state in the US, Ohio is a “swing” state; we included it since there are no solid “red” states where EC2 servers are located); the inclusion of the UK server allows us to check whether our observations are country-specific. This comparative approach allows us to go beyond single-country observations that are common for algorithm audit studies (e.g., Haim et al., 2018; Puschmann, 2019; Urman et al., 2021a). Data analysis After the data were collected, we extracted all unique URLs that appeared on the first page of search results for each engine and search query. We have focused on the first page of search results since people tend to perceive top search results as more credible and rarely look at/click on the results beyond the first page (Pan et al., 2007; Schultheiß et al., 2018; Unkel and Haas, 2017; Urman and Makhortykh, 2021). In total, there were 375 such unique URLs collected. The content under these URLs was then manually coded by two trained coders with the disagreements between the two resolved through consensus coding. The coding involved two variables, broadly corresponding to the RQs: conspiracy-related stance and type of source. The conspiracy-related stance variable included the following categories: ● Debunks conspiracy: the content under the URL lists argument(s) why a conspiracy theory is not  true ● No mention of conspiracy: there are no mentions of conspiracy theories in the source at all ● Promotes conspiracy: the content under the URL lists argument(s) why a conspiracy theory is true ● Mentions conspiracy: a conspiracy theory is mentioned, but there is no clear stance associated - e.g., no arguments for it being true or false OR arguments for it being true or false are presented in equal shares. The type of source variable included the following categories: ● Reference website: e.g., online encyclopedias such as Wikipedia or Britannica ● Media: any media organization regardless of its ideological position or themes, except purely scientific news-focused sites (see the next category ● Science: scientific repositories such as JSTOR or news sites devoted exclusively to science such as Science News ● Social media: e.g., Facebook pages, YouTube videos or Twitter accounts ● Conspiracy website: a website dedicated to the promotion of one specific conspiracy or of an array of conspiracy theories, such as a website of the Flat Earth Society ● Other: all other websites that do not fit into any of the previous categories To assess the prevalence of conspiratorial content in search results (RQ1), we calculated the share of results for each stance towards conspiracy theories per condition (i.e., query, engine, location and collection round). To assess the prioritization of source types in relation to conspiracy content (RQ2), we first calculated the shares of results for each type per condition, and then the share of results with different stances towards conspiracy theories for each source type per location-round pair. This paper is available on arxiv under CC 4.0 license. Authors: (1) Aleksandra Urman, She is a corresponding author from Department of Informatics, University of Zurich, Switzerland; (2) Mykola Makhortykh, Institute of Communication and Media Studies, University of Bern, Switzerland; (3) Roberto Ulloa, GESIS - Leibniz-Institut für Sozialwissenschaften, Germany; (4) Juhi Kulshrestha, Department of Politics and Public Administration, University of Konstanz, Germany. This paper is available on arxiv under CC 4.0 license. Authors: (1) Aleksandra Urman, She is a corresponding author from Department of Informatics, University of Zurich, Switzerland; (2) Mykola Makhortykh, Institute of Communication and Media Studies, University of Bern, Switzerland; (3) Roberto Ulloa, GESIS - Leibniz-Institut für Sozialwissenschaften, Germany; (4) Juhi Kulshrestha, Department of Politics and Public Administration, University of Konstanz, Germany. Table of Links Abstract and Introduction Web search results: biases, inaccuracies and their consequences Conspiracy theories in the online environments Research questions Methodology Results Discussion Limitations Conclusion and Bibliography Abstract and Introduction Abstract and Introduction Web search results: biases, inaccuracies and their consequences Web search results: biases, inaccuracies and their consequences Conspiracy theories in the online environments Conspiracy theories in the online environments Research questions Research questions Methodology Methodology Results Results Discussion Discussion Limitations Limitations Conclusion and Bibliography Conclusion and Bibliography Methodology Data collection Data collection Agent-based audit setup. To collect the data we used agent-based algorithm impact auditing (see Ulloa et al., 2021). This type of auditing relies on automated agents, i.e., software that simulates user browsing behavior (e.g. scrolling web pages) and records the outputs. The benefit of this approach is that it allows controlling for search personalization (Hannak et al., 2013) and randomization (Makhortykh et al., 2020). Unlike human agents, automated agents can be easily synchronized (i.e., to isolate the effect of time at which the search actions are conducted) and deployed in a controlled environment (e.g., a network of virtual machines using the same IP range, the same type of operating system (OS) and the same browsing software) to limit the effects of personalization based on user-specific factors (e.g. location or OS type). Our approach is comparative in the sense that we assess the outputs of several SEs across multiple locations, time periods, and queries. Agent-based audit setup. To increase the robustness of our observations, the data were collected over two collection rounds: March 18-19 and May 8-9 2021. From the technical standpoint, the data collection was organized as follows: each agent was made of two browser plugins (for either Chrome or Firefox desktop browsers). The first plugin (the bot) simulated human activity in the browser, in our case opening the search engine page, entering a query and scrolling down the first page of search outputs. The second plugin (the tracker) recorded html content appearing in the browser and sent it to the remote server. The agents were deployed via Amazon Elastic Compute Cloud (EC2). We focused our exploration to the five biggest SEs by market share on desktop devices worldwide: Google, Bing, Yahoo, Yandex and DuckDuckGo (Desktop Search Engine Market Share Worldwide, n.d.). During the first round of data collection (March), we deployed 60 agents per location (see below), whereas for the second round we decreased this number to 30 agents per location because of budgetary limitations. The agents were equally distributed between the SEs (i.e., 12 agents per engine for the first round and 6 agents per engine for the second round). The majority of agents were able to perform their planned routine; the only major exception was Yandex, where multiple agents were blocked because of the aggressive bot detection mechanisms (e.g., frequent captchas) utilized by the search engine (hence, the absence of results for Yandex for some search queries). Search query selection. We have collected search results for six queries that correspond to specific conspiracy theories (“flat earth”, “new world order”, “qanon”) or to subjects related to conspiracy theories (“9/11”, “illuminati”, “george soros”). We specifically included these two groups of queries, because we suggest that they might be entered by users with two different intentions: those corresponding to the names of conspiracies are more likely to be entered by people already interested in a given theory, while the latter - by people merely interested in a certain topic. Thus if conspiratorial content is returned for the latter queries, it might lead to users’ incidental exposure to conspiracies. Further, we expect to observe discrepancies between the two groups of queries with more conspiratorial content returned for the queries corresponding to specific theories and less for the subjects which are surrounded by conspiracy theories. Search query selection. Location selection. We analyze the data collected for the five SEs, across three locations: two in the US (Ohio and California) and one in the UK (London). Our selection of locations is determined in part by the availability of different EC2 servers (see the description of technical implementation of the data collection below). Also, we utilized locations where English is the official language for the purposes of comparability - e.g., to make sure that any results we retrieve are due to the differences in the location, not to data voids in a specific language. Finally, we selected Ohio and California due to the differences in the ideological orientations of the two states (while California is a solid “blue” (Democratic) state in the US, Ohio is a “swing” state; we included it since there are no solid “red” states where EC2 servers are located); the inclusion of the UK server allows us to check whether our observations are country-specific. This comparative approach allows us to go beyond single-country observations that are common for algorithm audit studies (e.g., Haim et al., 2018; Puschmann, 2019; Urman et al., 2021a). Location selection. Data analysis Data analysis After the data were collected, we extracted all unique URLs that appeared on the first page of search results for each engine and search query. We have focused on the first page of search results since people tend to perceive top search results as more credible and rarely look at/click on the results beyond the first page (Pan et al., 2007; Schultheiß et al., 2018; Unkel and Haas, 2017; Urman and Makhortykh, 2021). In total, there were 375 such unique URLs collected. The content under these URLs was then manually coded by two trained coders with the disagreements between the two resolved through consensus coding. The coding involved two variables, broadly corresponding to the RQs: conspiracy-related stance and type of source. The conspiracy-related stance variable included the following categories: ● Debunks conspiracy: the content under the URL lists argument(s) why a conspiracy theory is not  true ● No mention of conspiracy: there are no mentions of conspiracy theories in the source at all ● Promotes conspiracy: the content under the URL lists argument(s) why a conspiracy theory is true ● Mentions conspiracy: a conspiracy theory is mentioned, but there is no clear stance associated - e.g., no arguments for it being true or false OR arguments for it being true or false are presented in equal shares. The type of source variable included the following categories: ● Reference website: e.g., online encyclopedias such as Wikipedia or Britannica ● Media: any media organization regardless of its ideological position or themes, except purely scientific news-focused sites (see the next category ● Science: scientific repositories such as JSTOR or news sites devoted exclusively to science such as Science News ● Social media: e.g., Facebook pages, YouTube videos or Twitter accounts ● Conspiracy website: a website dedicated to the promotion of one specific conspiracy or of an array of conspiracy theories, such as a website of the Flat Earth Society ● Other: all other websites that do not fit into any of the previous categories To assess the prevalence of conspiratorial content in search results (RQ1), we calculated the share of results for each stance towards conspiracy theories per condition (i.e., query, engine, location and collection round). To assess the prioritization of source types in relation to conspiracy content (RQ2), we first calculated the shares of results for each type per condition, and then the share of results with different stances towards conspiracy theories for each source type per location-round pair.

A Comparative Algorithm Audit of Conspiracies on the Net: Methodology

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Aleksandra Urman, She is a corresponding author from Department of Informatics, University of Zurich, Switzerland;
(2) Mykola Makhortykh, Institute of Communication and Media Studies, University of Bern, Switzerland;
(3) Roberto Ulloa, GESIS - Leibniz-Institut für Sozialwissenschaften, Germany;
(4) Juhi Kulshrestha, Department of Politics and Public Administration, University of Konstanz, Germany. Table of Links Abstract and Introduction
Web search results: biases, inaccuracies and their consequences
Conspiracy theories in the online environments
Research questions
Methodology
Results
Discussion
Limitations
Conclusion and Bibliography Limitations One limitation of the present study is that our selection of queries does not cover the whole range of existing conspiracy theories (Douglas et al., 2019) or all possible queries regarding a specific conspiracy theory, however, encompassing all theories or queries is arguably impossible, and our study should be treated as a first step towards more comprehensive analyses of conspiratorial information spread via SEs. Though the number of included theories is limited, we suggest that our approach is already more comprehensive than that of the majority of studies that focus on the spread of one specific theory online (with notable exceptions such as Mahl et al., 2021). As there is no established resource regarding the popularity of certain theories worldwide, our selection of queries was based on the internal discussions between authors, during which we tried to select the theories that are, first, in broad circulation and, second, that are “popular” worldwide, not within a single country. Another limitation of the present study is our focus on just three anglophone Western locations and on one language - English. This makes our analysis Western- and English-centric. We aim to address this in future work by conducting studies on the topic with broader linguistic and geographic focus. Finally, while we collected the data over two collection rounds to increase the robustness of the findings, these rounds were relatively close to each other. In the future, research infrastructure that enables more longitudinal data collection will be established to trace long-term changes (or their lack) in SEs’ outputs. This paper is available on arxiv under CC 4.0 license. Authors: (1) Aleksandra Urman, She is a corresponding author from Department of Informatics, University of Zurich, Switzerland; (2) Mykola Makhortykh, Institute of Communication and Media Studies, University of Bern, Switzerland; (3) Roberto Ulloa, GESIS - Leibniz-Institut für Sozialwissenschaften, Germany; (4) Juhi Kulshrestha, Department of Politics and Public Administration, University of Konstanz, Germany. This paper is available on arxiv under CC 4.0 license. Authors: (1) Aleksandra Urman, She is a corresponding author from Department of Informatics, University of Zurich, Switzerland; (2) Mykola Makhortykh, Institute of Communication and Media Studies, University of Bern, Switzerland; (3) Roberto Ulloa, GESIS - Leibniz-Institut für Sozialwissenschaften, Germany; (4) Juhi Kulshrestha, Department of Politics and Public Administration, University of Konstanz, Germany. Table of Links Abstract and Introduction Web search results: biases, inaccuracies and their consequences Conspiracy theories in the online environments Research questions Methodology Results Discussion Limitations Conclusion and Bibliography Abstract and Introduction Abstract and Introduction Web search results: biases, inaccuracies and their consequences Web search results: biases, inaccuracies and their consequences Conspiracy theories in the online environments Conspiracy theories in the online environments Research questions Research questions Methodology Methodology Results Results Discussion Discussion Limitations Limitations Conclusion and Bibliography Conclusion and Bibliography Limitations One limitation of the present study is that our selection of queries does not cover the whole range of existing conspiracy theories (Douglas et al., 2019) or all possible queries regarding a specific conspiracy theory, however, encompassing all theories or queries is arguably impossible, and our study should be treated as a first step towards more comprehensive analyses of conspiratorial information spread via SEs. Though the number of included theories is limited, we suggest that our approach is already more comprehensive than that of the majority of studies that focus on the spread of one specific theory online (with notable exceptions such as Mahl et al., 2021). As there is no established resource regarding the popularity of certain theories worldwide, our selection of queries was based on the internal discussions between authors, during which we tried to select the theories that are, first, in broad circulation and, second, that are “popular” worldwide, not within a single country. Another limitation of the present study is our focus on just three anglophone Western locations and on one language - English. This makes our analysis Western- and English-centric. We aim to address this in future work by conducting studies on the topic with broader linguistic and geographic focus. Finally, while we collected the data over two collection rounds to increase the robustness of the findings, these rounds were relatively close to each other. In the future, research infrastructure that enables more longitudinal data collection will be established to trace long-term changes (or their lack) in SEs’ outputs.

A Comparative Algorithm Audit of Conspiracies on the Net: Limitations

A Comparative Algorithm Audit of Conspiracies on the Net: Results

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Aleksandra Urman, She is a corresponding author from Department of Informatics, University of Zurich, Switzerland;
(2) Mykola Makhortykh, Institute of Communication and Media Studies, University of Bern, Switzerland;
(3) Roberto Ulloa, GESIS - Leibniz-Institut für Sozialwissenschaften, Germany;
(4) Juhi Kulshrestha, Department of Politics and Public Administration, University of Konstanz, Germany. Table of Links Abstract and Introduction
Web search results: biases, inaccuracies and their consequences
Conspiracy theories in the online environments
Research questions
Methodology
Results
Discussion
Limitations
Conclusion and Bibliography Discussion We have analyzed the presence of conspiratorial content in top (desktop) web search results across the five most popular SEs, three locations and two time periods for six conspiracy-related queries. Our findings contribute to both, the scholarship on inaccuracies and bias in web search, and research on the spread of conspiracy theories online. We also expect our observations to be robust considering there were only minor differences between locations and observation rounds. Our analysis demonstrates that while there are large query-based differences, conspiracy-promoting content routinely resurfaces in the first page of results on all SEs except Google. Furthermore, Google’s results also contain the highest proportion of scientific sources debunking the conspiracy theories. We suggest that the absence of conspiratorial information in Google’s results is attributed to the company actively trying to reduce the share of misinformation and bias in its search outputs (Kayser-Bril, 2020). The company even explicitly covers the issue of conspiratorial content (including a specific example related to the 9/11 conspiracies) in its guidelines for search results’ quality raters (Google, 2021). Another finding concerns the types of web resources prioritized by different search engines. Besides Google, all other search engines we examined link to conspiracy theory-dedicated websites with Yandex being the engine with the highest share of links to conspiratorial content. At the same time, most content on all engines (except Yandex) comes from media and reference websites which tend to contain little conspiracy-promoting content. In line with the previous findings (e.g., Douglas et al., 2019), we observe that conspiratorial content is found mainly on dedicated niche websites or social media, but is rare on broad-reaching sites such as media, scientific and reference websites. The latter observation highlights that one of the ways to cull dissemination of conspiratorial information on search engines can be to implement domain-based filters de-prioritizing resources known to be involved in promoting such information, even though the long-term resilience of this solution can be questioned. Filtering out conspiracy-promoting websites from the top search outputs is important for (at least) two reasons. While it can be assumed that only users who are already interested in conspiratorial content purposefully navigate to the dedicated niche websites (Douglas et al., 2019), their appearance in top search results, especially for queries that do not denote conspiracy theories per se (e.g., “9/11” or “george soros”) can potentially lead to incidental exposure to conspiracy theories. This is troubling: given people’s high trust in search results (2021 Edelman Trust Barometer | Edelman, n.d.), conspiratorial information found by users merely exploring the topic in top search results can induce the formation of conspiratorial beliefs. This might be especially the case if users have limited knowledge on a given topic - which is partially implied by them turning to SEs to explore it - as lower knowledge on a subject is associated with higher beliefs in related conspiracy theories (Sallam et al., 2020). In the cases when the exposure to conspiratorial content via search engines is not incidental - i.e., if a person already interested in a conspiracy theory searches for related content online (e.g., “flat earth” or “illuminati”) - the appearance of conspiracy-promoting information in top search results is also concerning. If such a person is simply interested - but not yet believing - in conspiracy theories, conspiratorial content coming from a highly trusted source can foster conspiratorial belief development. If that person already, at least partially, believes in a conspiracy theory, their belief can be reinforced by conspiracy-promoting web search results due to high public trust in SE results coupled with confirmation bias (Knobloch-Westerwick et al., 2015; Nichols, 2017; Suzuki and Yamamoto, 2020). Due to the latter, the presence of even a single conspiracy-promoting result in top results might be enough to reinforce conspiracy beliefs. This paper is available on arxiv under CC 4.0 license. Authors: (1) Aleksandra Urman, She is a corresponding author from Department of Informatics, University of Zurich, Switzerland; (2) Mykola Makhortykh, Institute of Communication and Media Studies, University of Bern, Switzerland; (3) Roberto Ulloa, GESIS - Leibniz-Institut für Sozialwissenschaften, Germany; (4) Juhi Kulshrestha, Department of Politics and Public Administration, University of Konstanz, Germany. This paper is available on arxiv under CC 4.0 license. Authors: (1) Aleksandra Urman, She is a corresponding author from Department of Informatics, University of Zurich, Switzerland; (2) Mykola Makhortykh, Institute of Communication and Media Studies, University of Bern, Switzerland; (3) Roberto Ulloa, GESIS - Leibniz-Institut für Sozialwissenschaften, Germany; (4) Juhi Kulshrestha, Department of Politics and Public Administration, University of Konstanz, Germany. Table of Links Abstract and Introduction Web search results: biases, inaccuracies and their consequences Conspiracy theories in the online environments Research questions Methodology Results Discussion Limitations Conclusion and Bibliography Abstract and Introduction Abstract and Introduction Web search results: biases, inaccuracies and their consequences Web search results: biases, inaccuracies and their consequences Conspiracy theories in the online environments Conspiracy theories in the online environments Research questions Research questions Methodology Methodology Results Results Discussion Discussion Limitations Limitations Conclusion and Bibliography Conclusion and Bibliography Discussion We have analyzed the presence of conspiratorial content in top (desktop) web search results across the five most popular SEs, three locations and two time periods for six conspiracy-related queries. Our findings contribute to both, the scholarship on inaccuracies and bias in web search, and research on the spread of conspiracy theories online. We also expect our observations to be robust considering there were only minor differences between locations and observation rounds. Our analysis demonstrates that while there are large query-based differences, conspiracy-promoting content routinely resurfaces in the first page of results on all SEs except Google. Furthermore, Google’s results also contain the highest proportion of scientific sources debunking the conspiracy theories. We suggest that the absence of conspiratorial information in Google’s results is attributed to the company actively trying to reduce the share of misinformation and bias in its search outputs (Kayser-Bril, 2020). The company even explicitly covers the issue of conspiratorial content (including a specific example related to the 9/11 conspiracies) in its guidelines for search results’ quality raters (Google, 2021). Another finding concerns the types of web resources prioritized by different search engines. Besides Google, all other search engines we examined link to conspiracy theory-dedicated websites with Yandex being the engine with the highest share of links to conspiratorial content. At the same time, most content on all engines (except Yandex) comes from media and reference websites which tend to contain little conspiracy-promoting content. In line with the previous findings (e.g., Douglas et al., 2019), we observe that conspiratorial content is found mainly on dedicated niche websites or social media, but is rare on broad-reaching sites such as media, scientific and reference websites. The latter observation highlights that one of the ways to cull dissemination of conspiratorial information on search engines can be to implement domain-based filters de-prioritizing resources known to be involved in promoting such information, even though the long-term resilience of this solution can be questioned. Filtering out conspiracy-promoting websites from the top search outputs is important for (at least) two reasons. While it can be assumed that only users who are already interested in conspiratorial content purposefully navigate to the dedicated niche websites (Douglas et al., 2019), their appearance in top search results, especially for queries that do not denote conspiracy theories per se (e.g., “9/11” or “george soros”) can potentially lead to incidental exposure to conspiracy theories. This is troubling: given people’s high trust in search results (2021 Edelman Trust Barometer | Edelman, n.d.), conspiratorial information found by users merely exploring the topic in top search results can induce the formation of conspiratorial beliefs. This might be especially the case if users have limited knowledge on a given topic - which is partially implied by them turning to SEs to explore it - as lower knowledge on a subject is associated with higher beliefs in related conspiracy theories (Sallam et al., 2020). In the cases when the exposure to conspiratorial content via search engines is not incidental - i.e., if a person already interested in a conspiracy theory searches for related content online (e.g., “flat earth” or “illuminati”) - the appearance of conspiracy-promoting information in top search results is also concerning. If such a person is simply interested - but not yet believing - in conspiracy theories, conspiratorial content coming from a highly trusted source can foster conspiratorial belief development. If that person already, at least partially, believes in a conspiracy theory, their belief can be reinforced by conspiracy-promoting web search results due to high public trust in SE results coupled with confirmation bias (Knobloch-Westerwick et al., 2015; Nichols, 2017; Suzuki and Yamamoto, 2020). Due to the latter, the presence of even a single conspiracy-promoting result in top results might be enough to reinforce conspiracy beliefs.

A Comparative Algorithm Audit of Conspiracies on the Net: Discussion

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Aleksandra Urman, She is a corresponding author from Department of Informatics, University of Zurich, Switzerland;
(2) Mykola Makhortykh, Institute of Communication and Media Studies, University of Bern, Switzerland;
(3) Roberto Ulloa, GESIS - Leibniz-Institut für Sozialwissenschaften, Germany;
(4) Juhi Kulshrestha, Department of Politics and Public Administration, University of Konstanz, Germany. Table of Links Abstract and Introduction
Web search results: biases, inaccuracies and their consequences
Conspiracy theories in the online environments
Research questions
Methodology
Results
Discussion
Limitations
Conclusion and Bibliography Research questions Based on the research findings outlined in the previous section, we suggest that SEs can be conducive to the distribution of conspiratorial information and formation of conspiracy beliefs should such information appear in top search results. Unlike social media or online blogs, web search results have not been examined in the context of the distribution of conspiratorial information - despite numerous analyses showing that biased or not fully accurate results are not uncommon there. With this paper, we strive to partially fill the identified gaps in both - research focused on the presence of inaccurate information in web search and research on the spread of conspiracy theories online. Hence, our first research question concerns the general prevalence of conspiratorial information in top search results. RQ1: How prevalent is conspiratorial information in web search results? Because there are major discrepancies in the information provided by different SEs (e.g., Kravets and Toepfl, 2021; Makhortykh et al., 2020; Paramita et al., 2021), and in the results retrieved from different locations (Kliman-Silver et al., 2015), we find it worthwhile to address RQ1 from a comparative perspective to increase the robustness of the findings. Specifically, we compare the observations across different locations and on different search engines using the data collected at two different points in time. Further, we select two groups of conspiracy-related search queries, and expect to observe differences between the results retrieved for them, adding another comparative dimension to the analysis. Thus, we pose three sub-RQs in relation to RQ1: RQ1a: Does the prevalence of conspiratorial information in search results vary across different locations and time periods? RQ1b: Does the prevalence of conspiratorial information in search results vary across SEs, and how? RQ1c: Does the prevalence of conspiratorial information in search results vary across search queries, and how? Research, on one hand, demonstrates that SEs tend to over-represent certain source types while under-representing others (e.g., Puschmann, 2019; Haim et al., 2018), and, on another hand, suggests that conspiracy theories are mainly propagated on social media or small conspiracy-related websites (Douglas et al., 2019; Stano, 2020). Hence, we juxtapose the presence of conspiracies in web search with the prioritization of different sources and pose the following RQ: RQ2: What types of sources are prioritized by web SEs in relation to conspiracy theories? In the case of RQ2, we will also adopt a comparative approach similar to that of RQ1 - comparing the results for different engines, locations, waves and queries: RQ2a: Does the prevalence of sources of different types in search results vary across different locations and time periods? RQ2b: Does the prevalence of sources of different types in search results vary across SEs, and how? RQ2c: Does the prevalence of sources of different types in search results vary across search queries, and how? Additionally, we examine the relationship between the source type and the stance towards conspiracy theories. To do it, we formulate the last research question: RQ3: Are there differences in the share of conspiracy-promoting or conspiracy-debunking content coming from sources of different types? This paper is available on arxiv under CC 4.0 license. Authors: (1) Aleksandra Urman, She is a corresponding author from Department of Informatics, University of Zurich, Switzerland; (2) Mykola Makhortykh, Institute of Communication and Media Studies, University of Bern, Switzerland; (3) Roberto Ulloa, GESIS - Leibniz-Institut für Sozialwissenschaften, Germany; (4) Juhi Kulshrestha, Department of Politics and Public Administration, University of Konstanz, Germany. This paper is available on arxiv under CC 4.0 license. Authors: (1) Aleksandra Urman, She is a corresponding author from Department of Informatics, University of Zurich, Switzerland; (2) Mykola Makhortykh, Institute of Communication and Media Studies, University of Bern, Switzerland; (3) Roberto Ulloa, GESIS - Leibniz-Institut für Sozialwissenschaften, Germany; (4) Juhi Kulshrestha, Department of Politics and Public Administration, University of Konstanz, Germany. Table of Links Abstract and Introduction Web search results: biases, inaccuracies and their consequences Conspiracy theories in the online environments Research questions Methodology Results Discussion Limitations Conclusion and Bibliography Abstract and Introduction Abstract and Introduction Web search results: biases, inaccuracies and their consequences Web search results: biases, inaccuracies and their consequences Conspiracy theories in the online environments Conspiracy theories in the online environments Research questions Research questions Methodology Methodology Results Results Discussion Discussion Limitations Limitations Conclusion and Bibliography Conclusion and Bibliography Research questions Based on the research findings outlined in the previous section, we suggest that SEs can be conducive to the distribution of conspiratorial information and formation of conspiracy beliefs should such information appear in top search results. Unlike social media or online blogs, web search results have not been examined in the context of the distribution of conspiratorial information - despite numerous analyses showing that biased or not fully accurate results are not uncommon there. With this paper, we strive to partially fill the identified gaps in both - research focused on the presence of inaccurate information in web search and research on the spread of conspiracy theories online. Hence, our first research question concerns the general prevalence of conspiratorial information in top search results. RQ1: How prevalent is conspiratorial information in web search results? RQ1: How prevalent is conspiratorial information in web search results? Because there are major discrepancies in the information provided by different SEs (e.g., Kravets and Toepfl, 2021; Makhortykh et al., 2020; Paramita et al., 2021), and in the results retrieved from different locations (Kliman-Silver et al., 2015), we find it worthwhile to address RQ1 from a comparative perspective to increase the robustness of the findings. Specifically, we compare the observations across different locations and on different search engines using the data collected at two different points in time. Further, we select two groups of conspiracy-related search queries, and expect to observe differences between the results retrieved for them, adding another comparative dimension to the analysis. Thus, we pose three sub-RQs in relation to RQ1: RQ1a: Does the prevalence of conspiratorial information in search results vary across different locations and time periods? RQ1a: Does the prevalence of conspiratorial information in search results vary across different locations and time periods? RQ1b: Does the prevalence of conspiratorial information in search results vary across SEs, and how? RQ1b: Does the prevalence of conspiratorial information in search results vary across SEs, and how? RQ1c: Does the prevalence of conspiratorial information in search results vary across search queries, and how? RQ1c: Does the prevalence of conspiratorial information in search results vary across search queries, and how? Research, on one hand, demonstrates that SEs tend to over-represent certain source types while under-representing others (e.g., Puschmann, 2019; Haim et al., 2018), and, on another hand, suggests that conspiracy theories are mainly propagated on social media or small conspiracy-related websites (Douglas et al., 2019; Stano, 2020). Hence, we juxtapose the presence of conspiracies in web search with the prioritization of different sources and pose the following RQ: RQ2: What types of sources are prioritized by web SEs in relation to conspiracy theories? RQ2: What types of sources are prioritized by web SEs in relation to conspiracy theories? In the case of RQ2, we will also adopt a comparative approach similar to that of RQ1 - comparing the results for different engines, locations, waves and queries: RQ2a: Does the prevalence of sources of different types in search results vary across different locations and time periods? RQ2a: Does the prevalence of sources of different types in search results vary across different locations and time periods? RQ2b: Does the prevalence of sources of different types in search results vary across SEs, and how? RQ2b: Does the prevalence of sources of different types in search results vary across SEs, and how? RQ2c: Does the prevalence of sources of different types in search results vary across search queries, and how? RQ2c: Does the prevalence of sources of different types in search results vary across search queries, and how? Additionally, we examine the relationship between the source type and the stance towards conspiracy theories. To do it, we formulate the last research question: RQ3: Are there differences in the share of conspiracy-promoting or conspiracy-debunking content coming from sources of different types? RQ3: Are there differences in the share of conspiracy-promoting or conspiracy-debunking content coming from sources of different types?

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