Sequential elimination method

This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations. (March 2024) (Learn how and when to remove this message)

Part of the Politics series
Electoral systems
Single-winner/majoritarian Plurality First-past-the-post Plurality at-large (plurality block voting) General ticket (party block voting) Multi-round voting Two-round Exhaustive ballot Primary election Nonpartisan unified top-four Majority at-large (two-round block voting) Ranked / preferential systems Instant-runoff (alternative vote) Contingent vote Coombs' method Condorcet methods (Copeland's, Dodgson's, Kemeny–Young, Minimax, Nanson's, ranked pairs, Schulze, Alternative Smith) Positional voting (Borda count, Nauru/Dowdall method) Bucklin voting Oklahoma primary electoral system Preferential block voting Cardinal / graded systems Score voting Approval voting Combined approval voting Unified primary Usual judgment Satisfaction approval voting Majority judgment STAR voting
Proportional representation Party-list Electoral list open list closed list local lists Apportionment Sainte-Laguë D'Hondt Huntington–Hill Hare Droop Imperiali Hagenbach-Bischoff National remnant Highest averages Largest remainder Proportional forms of ranked voting Single transferable vote Gregory Wright Schulze STV CPO-STV Ranked party list PR Spare vote Proportional forms of cardinal voting Proportional approval voting Sequential proportional approval voting Method of Equal Shares Phragmen's voting rules Biproportional apportionment Fair majority voting Weighted voting Direct representation Interactive representation Liquid democracy
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 Mixed single vote (positive vote transfer) Scorporo (negative vote transfer) Mixed ballot transferable vote Alternative Vote Plus Dual-member proportional Rural–urban proportional
Other systems and related theory Semi-proportional representation Single non-transferable vote Limited voting Cumulative voting Binomial voting Other systems Multiple non-transferable vote Double simultaneous vote Proxy voting Delegated voting Indirect STV Liquid democracy Random selection (sortition, random ballot) Supermajority Social choice theory Arrow's theorem Gibbard–Satterthwaite theorem Public choice theory Veto Players List of electoral systems List of electoral systems by country Comparison of electoral systems Effects of electoral systems Political fragmentation Political efficacy Voter turnout
Politics portal
v t e

The sequential elimination methods are a class of voting systems that repeatedly eliminate the last-place finisher of another voting method until a single candidate remains.^[1] The method used to determine the loser is called the base method. Common are the two-round system, instant-runoff voting, and systems where parties nominate candidates in partisan primaries.

Instant-runoff voting is a sequential loser method based on plurality voting, while Baldwin's method is a sequential loser method based on the Borda count.^[2]

Properties

Proofs of criterion compliance for loser-elimination methods often use mathematical induction, and so can be easier than proving such compliance for other method types. For instance, if the base method passes the majority criterion, a sequential loser-elimination method based on it will pass mutual majority. Loser-elimination methods are also not much harder to explain than their base methods.^[2]

However, loser-elimination methods often fail monotonicity due to chaotic effects (sensitivity to initial conditions): the order in which candidates are eliminated can create erratic behavior.^[1]

If the base method passes independence from the weakest alternative, the loser-elimination method is equivalent to the base method.^[1] In other words, methods that are immune to weak spoilers are already "their own" elimination methods, because eliminating the weakest candidate does not affect the winner.

If the base method satisfies a criterion for a single candidate (e.g. the majority criterion or the Condorcet criterion), then a sequential loser method satisfies the corresponding set criterion (e.g. the mutual majority criterion or the Smith criterion), so long as eliminating a candidate can't remove another candidate from the set in question. This is because when all but one of the candidates of the set have been eliminated, the single-candidate criterion applies to the remaining candidate.^[1]

References

Further reading

• Chowdhury, Subhasish M.; Kim, Sang-Hyun (July 2017). "'Small, yet Beautiful': Reconsidering the optimal design of multi-winner contests" (PDF). Games and Economic Behavior. 104: 486–493. doi:10.1016/j.geb.2017.05.012. S2CID 43411835.
• Klunover, Doron (December 2023). "Bureaucracy and labor market inefficiency: A contest model". European Journal of Political Economy. 80: 102472. doi:10.1016/j.ejpoleco.2023.102472. S2CID 262024392.