Pairwise preference: Difference between revisions
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The interpretation of pairwise ties can conceptually link different concepts together sometimes. For example, the [[Smith set]] and [[Schwartz set]] are identical except that one treats a tie as counting against both tied candidates (i.e. it's as bad as a defeat) in terms of their deservingness to be in the set or not, while the other treats a tie as having no relevance to the quality of either of the tied candidates.
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:
26 B:5 A:5 (honest preference was A:4)
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Multi-winner methods that use pairwise counting, such as [[CPO-STV]] and [[Schulze STV]], instead of doing pairwise matchups between individual candidates, do pairwise matchups between sets of candidates (called [[winner set]]<nowiki/>s).
The nature of pairwise preferences prevents direct comparisons of candidates from two separate elections, unlike with [[rated method]]<nowiki/>s or other methods. For example, it is possible to compare Reagan's [[approval rating]] in polls from the 1980s to Obama's in the 2010s without having to ask voters about both in the same election/poll, but their pairwise matchup against each other can't be evaluated like that.
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.
Another criticism is that it can be harder to do [[pairwise counting]] than it is to count the vote in other methods, such as [[Approval voting]]. The [[Rated pairwise preference ballot#Rated or ranked preference]] implementation can potentially mitigate this criticism, because for every voter who indicates a rated preference, at most only one piece of information need be collected from their ballot for every candidate they marked (their score for the candidate), rather than several pairwise preferences.
<references />
[[Category:Condorcet-related concepts]]
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