Instant-runoff voting: Difference between revisions
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== Notes ==
Though IRV is often praised for passing [[later-no-harm]], which is claimed to encourage voters to rank all of their preferences, it doesn't tend to use as much of the information provided by the voters as other ranked methods, such as [[Condorcet methods]]. So there may be a tradeoff between collecting more information and using more information that has to be evaluated when choosing between IRV and other voting methods.
IRV always elects a Condorcet winner who receives over [[Dominant mutual third|1/3rd]] of 1st choice votes. More generally, a candidate who at any point when they are uneliminated receives over 1/3rd of all active votes and [[Pairwise counting|pairwise beats]] (is preferred by more voters than) all other uneliminated candidates is guaranteed to win. This is because when all but two candidates are eliminated, the one preferred by more voters is guaranteed to win in IRV, and a candidate with over 1/3rd of active votes is guaranteed to be one of the final two remaining candidates, because at most only one other candidate can get more active votes than the over-1/3rd pairwise victor.
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, since at every point in IRV a voter's ballot is transferred to their highest-ranked candidate among the uneliminated candidates, 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
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