The sequential elimination methods are a class of
voting systems
An electoral or voting system is a set of rules used to determine the results of an election. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, nonprofit organizations and inf ...
that repeatedly eliminate the last-place finisher of another voting method until a single candidate remains.
The method used to determine the loser is called the ''base method''. Common are the
two-round system
The two-round system (TRS or 2RS), sometimes called ballotage, top-two runoff, or two-round plurality, is a single-winner electoral system which aims to elect a member who has support of the majority of voters. The two-round system involves one ...
,
instant-runoff voting
Instant-runoff voting (IRV; ranked-choice voting (RCV), preferential voting, alternative vote) is a single-winner ranked voting election system where Sequential loser method, one or more eliminations are used to simulate Runoff (election), ...
, and some
primary systems.
Instant-runoff voting
Instant-runoff voting (IRV; ranked-choice voting (RCV), preferential voting, alternative vote) is a single-winner ranked voting election system where Sequential loser method, one or more eliminations are used to simulate Runoff (election), ...
is a sequential loser method based on
plurality voting
Plurality voting refers to electoral systems in which the candidates in an electoral district who poll more than any other (that is, receive a plurality) are elected.
Under single-winner plurality voting, and in systems based on single-member ...
, while
Baldwin's method is a sequential loser method based on the
Borda count
The Borda method or order of merit is a positional voting rule that gives each candidate a number of points equal to the number of candidates ranked below them: the lowest-ranked candidate gets 0 points, the second-lowest gets 1 point, and so on ...
.
Properties
Proofs of criterion compliance for loser-elimination methods often use
mathematical induction
Mathematical induction is a method for mathematical proof, proving that a statement P(n) is true for every natural number n, that is, that the infinitely many cases P(0), P(1), P(2), P(3), \dots all hold. This is done by first proving a ...
, 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.
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.
If the base method passes
independence from the weakest alternative, the loser-elimination method is equivalent to the base method.
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
A Condorcet winner (, ) is a candidate who would receive the support of more than half of the electorate in a one-on-one race against any one of their opponents. Voting systems where a majority winner will always win are said to satisfy the Condo ...
), then a sequential loser method satisfies the corresponding set criterion (e.g. the
mutual majority criterion or the
Smith criterion
The Smith set, sometimes called the top-cycle or Condorcet winning set, generalizes the idea of a Condorcet winner to cases where no such winner exists. It does so by allowing cycles of candidates to be treated jointly, as if they were a single ...
), 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.
References
Further reading
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{{Voting systems
Electoral systems