What is Quadratic Voting?

Quadratic Voting is a method of collective decision-making in which a participant votes not just for or against an issue, but also expresses how strongly they feel about it. It can help protect the interests of small groups of voters that care deeply about particular issues. Quadratic Voting can be used in democratic institutions, in corporate governance, and blockchain-enabled collective decision-making.

Why ‘Quadratic’?

In Quadratic Voting, each participant is given a number of credits that can be used to vote for an issue. However, the cost of casting more than one vote for an issue is quadratic, not linear. So, the marginal cost of each additional vote is far higher than of the previous vote.

Here is the Quadratic Voting formula: Cost to the voter = (Number of votes) to the power of 2.

Imagine that a vote generally costs $1 to put toward an issue, and you have $100 of voting credits. You want to cast your vote toward protecting endangered species. Casting one vote will cost you $1. However, casting two votes for the same issue will cost you $4, casting three votes for the same issue will cost you $9 and casting 10 votes for the same issue will cost you your entire $100 of credits.

So, while you are increasing the chances of victory for your issue with each
additional vote, the quadratic nature of the voting ensures that only those who care deeply about issues will cast additional votes for them.

Use in Colorado

After Democrats won Colorado’s Governorship and both of the state’s houses in 2018, they used Quadratic Voting to decide which appropriations bills to fund first. Since legislators were likely to sponsor their own bills and vote for them, the Democratic caucus sought a method to gauge which bills had everyone’s support.

Initially, the Colorado Democrats assigned 15 tokens for each legislator to use on their preferred 15 bills. After this didn’t work well, they talked to Microsoft economist Glen Weyl, who explained how Quadratic Voting could provide a solution.

Weyl saw Quadratic Voting as a solution to the ‘tyranny of the majority’ issue. Regular voting assumes that everyone cares for an issue equally, which is rarely the case. The reality is that some legislators do not care about certain issues, care moderately about others and care deeply about a few.

So, instead, each legislator was given 100 tokens. If a legislator cast one vote each for several issues, it would cost them one token each. However, a legislator could cast more than one vote for an issue, at the following cost in tokens:

Colorado’s experiment with Quadratic Voting was largely successful.

How is quadratic voting different from traditional voting
systems?

First-Past-the-Post: In the first-past-the-post system used in most democracies, a candidate can win without getting the votes of a majority of people. Let’s say Candidate A gets 35% of votes, B, 30%, C, 24%, and D, 11%. A wins, but we know that a majority of people voted for someone other than A.

Proportional Voting: To address this, some jurisdictions have adopted proportional voting systems. Here, if 35% of the electorate votes for a given party, then 35% of seats in the legislature given to that party, and so on. Though these systems can be seen as an ‘evolved’ version of the first-past-the-post system, they do not work when a binary (yes or no) decision has to be made.

Ranked Choice Voting: In Ranked Choice Voting (which is used by several jurisdictions in California), each voter ranks their favorite candidates. The candidate with the lowest number of votes is eliminated in each round, and that candidate’s votes are redistributed to the candidates next in each vote’s preference order ahead of the next round. Though Ranked Choice Voting has its strengths, it is a complex and time-consuming system.

Quadratic Voting: Though Quadratic Voting is also complex, it arguably better protects the interests of small groups of voters that care deeply about particular issues. By increasing the cost of each additional vote, it disincentivizes voters that don’t care about issues from casting several votes for them. It also allows voters to show the intensity of their support for a given issue by casting several votes for it – at the expense of their ability to vote on other issues.

Conclusion

Modern democracies have generally used one person, one vote in their elections and legislative processes. Corporations have often adopted more sophisticated voting mechanisms (for example, allowing a shareholder to designate someone else to vote on their behalf). Complicated but arguably more democratic voting systems, such as Proportional Voting and Ranked Choice Voting, have not found widespread acceptance due to their complexity.

Now that blockchain-enabled collective decision making allows
votes to be tracked in a transparent, public way, more complicated voting
systems can be adopted. By allowing voters to express not just their
preferences but also the intensity of these preferences, Quadratic Voting
protects the interests of small groups of voters that care deeply about certain issues.

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Shaan Ray