Pairwise preference: Difference between revisions
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Most pairwise criteria ([[Condorcet criterion]], [[Smith]], etc.) assume a voter may indicate as many transitive pairwise preferences as desired i.e. they may place each candidate in a separate rank. Some [[:Category:Pairwise counting-based voting methods|Category:Pairwise counting-based voting methods]] actually violate this by limiting the number of [[slot]]<nowiki/>s voters have, such as common implementations of [[Smith//Score]]. This can be done for practical reasons (to keep the ballot smaller, potentially), or for more philosophical reasons; some object to the idea that a voter should be able to put a full vote "between" every transitive pair of candidates (because it may be unlikely for voters to honestly feel such maximally strong preferences), and so wish to limit the number of available ranks. Indeed, when a voter can only indicate two ranks (or also give candidates partial support between these two ranks), then you get [[Score voting]], because if you give 1 vote to help A beat B, then you must give 0 votes for B>C (or if you give 0.6 votes A>B, then you can't give 0.5 votes B>C). The [[Rated pairwise preference ballot]] can be implemented with fewer ranks than candidates in this manner, which then forces [[preference compression]] (or, more complexly, no, or a less strict, limitation on ranks might be imposed, but the voter might be required to indicate a weak preference between at least some of the ranks).
Because of [[preference compression]], which can happen also for [[strategic voting]] purposes i.e. [[Min-max voting]], it's not always possible to get accurate pairwise data from [[rated ballot]]<nowiki/>s. Thus, it is often useful to differentiate between a candidate who gets at least half of all voters to prefer them over their opponents in head-to-head matchups, rather than only at least half of all voters ''with preferences in the relevant matchups'' (i.e. they tie or [[Majority-beat]] their opponents), since no matter what preferences preference-compressing voters have in those matchups, the candidate in question will at least tie or win the matchup no matter what. Example: <blockquote>25 A:5 B:4
26 B:5 A:5 (honest preference was A:4)
49 C:5 D:5 </blockquote>Here, the [[CW]] based on honest pairwise preferences is B, but because of min-max voting (potentially done to ensure at least one of A or B enter the runoff rather than both C and D), it looks like A is the CW.
It may help to interpret pairwise data by putting the % of the votes a candidate got in the pairwise matchup. So, for example:
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