Pairwise preference: Difference between revisions
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If every voter indicates the same rated preference for each pair of candidates, then the Smith set is always full of candidates who are at least weak Condorcet winners i.e. tied for having the most points/approvals. (Note that this is not the case if voters are allowed to have preferences that wouldn't be writable on a cardinal ballot i.e. if the max score is 5, and a voter indicates their 1st choice is 5 points better than their 2nd choice, and that their 2nd choice is 5 points better than their 3rd choice, then this would not be an allowed preference in cardinal methods, and thus it would be possible for a Condorcet cycle to occur. Also, if a voter indicates their 1st choice is 2 points better than their 2nd choice, that this likely automatically implies their 1st choice must be at least 2 points better than their 3rd choice, etc. So there seems to be a [[transitivity]] of strength of preference, just as there is a transitivity of preference for rankings.)<ref>{{Cite web|url=https://www.reddit.com/r/EndFPTP/comments/fcexg4/score_but_for_every_pairwise_matchup/|title=r/EndFPTP - Score but for every pairwise matchup|website=reddit|language=en-US|access-date=2020-04-24}}</ref>
== Uses ==
Pairwise preferences can be used to find the [[order of finish]] of any [[Condorcet method]] when there is a [[Condorcet ranking]], and can always be used to calculate a complete result in [[:Category:Defeat-dropping Condorcet methods|Category:Defeat-dropping Condorcet methods]]. They can sometimes be used in [[:Category:Runoff-based voting methods|Category:Runoff-based voting methods]] to avoid having to do additional rounds of counting (i.e. because no matter which candidates enter the runoff, the result is already known).
When combined with rated information, it is possible to surmise some additional information about how voters scored the candidates. For example, if 2/3rds of the voters prefer A>B, yet B has a higher points total than A, then the A>B voters must have received less than half the [[utility]] gain of going from their less-preferred candidate in the matchup to their more-preferred candidate as the B>A voters.
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== Criticism ==
One major criticism of pairwise preferences is that they are harder to understand and think about because a candidate's quality can't be completely summed up into one number, like in [[cardinal method]]<nowiki/>s.
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