# Sequential loser-elimination method

A **sequential loser-elimination method** is a method that works by repeatedly eliminating the loser of another voting method until a single candidate remains, and then electing that candidate. The method that is used to determine the loser is called the *base method*.

Proving criterion compliances for loser-elimination methods often use inductive proofs, and can thus be easier than proving such compliances 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).

When the base method passes local independence of irrelevant alternatives, the loser-elimination method is equivalent to the base method.

Instant runoff voting is a sequential loser-elimination method based on First past the post (note that IRV with whole-votes equal-ranking may not be a sequential-loser elimination method depending on which rules are used to determine the winner; see the STV#Ways of dealing with equal rankings section), and Baldwin is a sequential loser-elimination method based on the Borda count.

## Notes[edit | edit source]

Note that though a voting method may be a sequential loser-elimination method in its single-winner case, it may not be so under certain generalizations of the criterion to the multi-winner case. Consider the following 2-winner example for STV with Droop quotas:

99 A>B 1 C

A and B would win. However, if the criterion for a multi-winner sequential loser-elimination method is that it must repeatedly eliminate until only (# of winners) candidates remain, with no surplus distribution being done, and with those remaining candidates winning, then A and C would win, since B is the candidate with the fewest 1st choices here. So for the multi-winner or proportional case, it may be required to allow surplus distribution or other steps in order to best generalize the sequential loser-elimination criterion for the multi-winner case.

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