Instant-runoff voting: Difference between revisions
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== Notes ==
IRV always elects a Condorcet winner who receives
The number of votes a candidate has in any round of an IRV election is guaranteed to be equal to or less than the number of votes they receive in a [[Pairwise counting|pairwise matchup]] against all other candidates who are uneliminated during that round. This is because it is guaranteed that the candidate who a voter's vote is supporting in any round was ranked higher than any of the other uneliminated candidates by that voter, thus that candidate receives that voter's vote in all pairwise matchups against those lower-ranked candidates. This means that when the IRV winner receives a majority of active votes, they guaranteeably pairwise beat all other uneliminated candidates, and that when there are only two candidates remaining, the number of votes each candidate has is exactly the number of votes they each receive in their pairwise matchup (if equal ranking is allowed, the exact number of votes may differ; for example: <blockquote>40 A
40 B
20 A=B </blockquote>If fractional equal-ranking is allowed, the number of votes each candidate has is 50, while if whole-votes equal-ranking is used instead, each candidate has 60 votes. However, they each have only 40 votes in their pairwise matchup.)Several variations of IRV have been proposed to meet the [[Condorcet]] and [[Smith criterion|Smith]] criteria. The simplest of these are to (either (elect the [[Condorcet winner]] if one exists), or (eliminate all candidates not in the [[Smith set]])), and then run IRV.
==See also==
*[[Australian electoral system]]
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