Quadratic voting

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Single-winner methods Single vote - plurality methods First preference plurality (FPP) Two-round (US: Jungle primary) Partisan primary Instant-runoff UK: Alternative vote (AV) US: Ranked-choice (RCV) Party block voting Plurality block voting Condorcet methods Condorcet-IRV Round-robin voting Minimax Schulze Ranked pairs Maximal lottery Positional voting Plurality (el. IRV) Borda count (el. Baldwin, Mdn. Bucklin) Antiplurality (el. Coombs) Cardinal voting Score voting Approval voting Majority judgment STAR voting
Proportional representation Party-list Apportionment Highest averages Largest remainders National remnant Biproportional List type Closed list Open list Panachage List-free PR Localized list Quota-remainder methods Hare STV Schulze STV CPO-STV Quota Borda Approval-based committees Thiele's method Phragmen's method Expanding approvals rule Method of equal shares Fractional social choice Direct representation Interactive representation Liquid democracy Fractional approval voting Maximal lottery Random ballot Semi-proportional representation Cumulative SNTV Limited voting
Mixed systems By results of combination Mixed-member majoritarian Mixed-member proportional By mechanism of combination Non-compensatory Parallel (superposition) Coexistence Conditional Fusion (majority bonus) Compensatory Seat linkage system UK: 'AMS' NZ: 'MMP' Vote linkage system Negative vote transfer Mixed ballot Supermixed systems Dual-member proportional Rural–urban proportional Majority jackpot By ballot type Single vote Double simultaneous vote Dual-vote
Paradoxes and pathologies Spoiler effects Spoiler effect Cloning paradox Frustrated majorities paradox Center squeeze Pathological response Perverse response Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting Exaggeration Truncation Turkey-raising Wasted vote Paradoxes of majority rule Tyranny of the majority Discursive dilemma Conflicting majorities paradox
Social and collective choice Impossibility theorems Arrow's theorem Majority impossibility Moulin's impossibility theorem McKelvey–Schofield chaos theorem Gibbard's theorem Positive results Median voter theorem Condorcet's jury theorem May's theorem Condorcet dominance theorems Harsanyi's utilitarian theorem VCG mechanism Quadratic voting
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Quadratic voting (QV) is a voting system that encourages voters to express their true relative intensity of preference (utility) between multiple options or elections.^[1] 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 failure mode by allowing voters to vote multiple times on any 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 / putting all votes on one issue (since additional votes require more and more sacrifice of influence over other issues).

Quadratic voting works by having voters allocate "credits" (usually distributed equally, although some proposals talk about using real money) to various issues. The number of votes to add is determined by a quadratic cost function, which simply means that the number of votes an individual 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).^[2] Because the quadratic cost function makes each additional vote more expensive (to go from 2-3 votes, you need to allocate 5 extra credits, but from 3-4, you would need to add 7), voters are incentivized to not over-allocate to a single issue and instead to spread their credits across multiple issues in order to make better use of their credits. This incentive 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 anyone other than their favorite, QV disincentivizes this behavior by giving voters who more accurately represent their preferences across multiple options more overall votes than those who don't.^[3]