Quadratic voting

Quadratic voting (QV) is a voting system that encourages voters to express their true relative intensity of preference (utility) between multiple options or elections. By doing so, quadratic voting seeks to mitigate tyranny of the majority—where minority preferences are by default repressed since under majority rule, majority cooperation is needed to make any change. Quadratic voting prevents this by allowing voters to vote multiple times on one option at the cost of not being able to vote as much on other options. This enables minority issues to be addressed where the minority has a sufficiently strong preference relative to the majority (since motivated minorities can vote multiple times) while also disincentivizing extremism or putting all votes on one issue (since additional votes require increasing sacrifice of influence over other issues).

In quadratic voting, voters allocate "credits" (usually distributed equally, though some suggest using real money) to various issues. The number of votes to add is determined by a quadratic cost function, which means that the number of votes a person casts for a given issue is equal to the square root of the number of credits they allocate (put another way, to add 3 votes requires allocating the square or quadratic of the number of votes, i.e., 9 credits). Because the quadratic cost function makes each additional vote more expensive (to go from 2 votes to 3, you must allocate 5 extra credits, but to go from 3 to 4, you must add 7), voters are incentivized not to over-allocate to a single issue and instead to spread their credits across multiple issues to make better use of them. This creates voting outcomes more closely aligned with a voter's true relative expected utility between options. Compared to score voting or cumulative voting, where voters may simply not vote for any option other than their favorite, QV gives voters who more accurately represent their preferences across multiple options more overall votes than those who don't.