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).
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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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. For example, it is possible to compare Reagan's [[approval rating]] to Obama's 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.
<references />
[[Category:Condorcet-related concepts]]
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