Pairwise preference: Difference between revisions
→Pairwise matchups
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== Pairwise matchups ==
A pairwise matchup is when voters choose between two candidates, with there being a winner and loser, or a tie (the possibility of which will only intermittently be discussed throughout this article). The idea is that when there are only two options to choose from, it's always possible to get a [[majority]] in favor of one of them, because any votes that don't go to one must have gone to the other. A major argument in favor of analyzing pairwise preferences is that it minimizes the ability of [[strategic nomination]] to affect the race, that is, [[Independence of irrelevant alternatives]] is maximally satisfied (though not completely, if using [[majority rule]]) by ensuring candidates who enter or drop out of the race play less of a role in deciding which of the remaining candidates wins.
The most direct way to conduct a pairwise comparison is to ask voters "Who do you prefer between these two candidates" for every pair of candidates. However, this would be rather onerous when there are more candidates running, and could even result in violations of [[transitivity]]: a voter could say they prefer A>B (A over B in the A vs B matchup), B>C, and C>A, which means that if these were the only 3 candidates in the election, and the voter had total power to decide which of them won, then they'd be unable to make up their mind, since for whichever one they choose, they'd want to pick someone else (in fact, when voters express these cyclical preferences on their ballots, the common approaches to making their preferences "rational"/acyclical are to either ignore the last or lowest part of the cycle, such that A>B>C>A becomes A>B>C, or to treat all candidates as equally preferred, i.e. A=B=C, though the noncyclical preferences the voter expressed in regard to these candidates versus other candidates are still respected).
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