Reversal symmetry

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Reversal symmetry" – news · newspapers · books · scholar · JSTOR (November 2007) (Learn how and when to remove this message)

Part of the Politics and Economics series
Electoral systems
Comparison of electoral systems Social choice theory Mechanism design List (By country)
Single-winner methods Single vote-runoff methods Plurality (FPP) Two-round (US: Jungle primary) Partisan primary Alternative vote (US: Ranked-choice/RCV) Condorcet methods Ranked pairs Schulze Minimax Kemeny–Young Nanson Condorcet-IRV Maximal lottery Positional voting Plurality Borda count Antiplurality Cardinal voting Score voting Approval voting Majority judgment STAR voting Quadratic voting
Proportional representation Party-list List type Open list Closed list Localized list Panachage Mixed single vote Apportionment Highest averages Largest remainders National remnant Biproportional Quota-remainder methods Hare STV Schulze STV CPO-STV Quota Borda Cumulative 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
Mixed systems By type of representation Mixed-member majoritarian Mixed-member proportional Non-compensatory mixed systems Parallel voting Majority bonus Compensatory mixed systems Additional member system Majority jackpot Scorporo Mixed ballot transferable vote Alternative Vote Plus Dual-member proportional Rural–urban proportional
Voting system criteria Spoiler-resistance Condorcet criterion Smith independence Spoiler independence Clone independence Strategy-resistance No lesser evil voting Binary independence Maskin monotonicity Later-no-harm Later-no-help Rational response Participation criterion Positive response Reinforcement criterion Reversal symmetry
Social and collective choice Impossibility theorems Arrow's theorem Majority impossibility Moulin's impossibility theorem McKelvey–Schofield chaos theorem Gibbard's theorem Fishburn's example Positive results Median voter theorem Condorcet's jury theorem May's theorem Campbell-Kelly theorem Harsanyi's utilitarian theorem Tournament sets Smith set Landau set Copeland set Split-cycle set Bipartisan set
Politics portal Economics portal
v t e

The reversal criterion is a voting system criterion which says that if every voter's opinions on each of the candidates is perfectly reversed (i.e. they rank candidates in order from worst to best), the outcome of the election should be reversed as well, i.e. the first- and last- place finishers should switch places.^[1] In other words, the results of the election should not depend arbitrarily on whether voters rank candidates from best to worst (and then select the best candidate), or whether we ask them to rank candidates from worst to best (and then select the least-bad candidate).

Another, equivalent way to motivate the criterion is to say that a voting system should never elect the worst candidate, according to the method itself (as doing so suggests the method is, in some sense, self-contradictory). The worst candidate can be identified by reversing all ballots (to rank candidates from worst-to-best) and then running the algorithm to find a single worst candidate.^[2]

Situations where the same candidate is elected when all ballots are reversed are sometimes called best-is-worst paradoxes, and can occur in ranked-choice runoff voting (RCV) and minimax. Methods that satisfy reversal symmetry include the Borda count, ranked pairs, Kemeny–Young, and Schulze. Most rated voting systems, including approval and score voting, satisfy the criterion as well.