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 some primary systems.
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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
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