Pairwise preference: Difference between revisions
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==== Collecting pairwise information from ranked ballots ====
Thus, in the context of voting, it's more common to ask voters to indicate their preference using a [[Ballot types|ballot type]] that automatically imposes transitivity, usually with a [[ranked ballot]] (though [[rated ballot]]<nowiki/>s are also sometimes used; theoretically, any ballot type that allows a voter to indicate at least one pairwise preference works for this purpose). The use of a transitive ballot type has the further advantage that, because it is usually assumed a voter prefers every candidate they mark a preference for over every unmarked candidate, voters don't have to explicitly mark all of their preferences.
=== Identifying the winner of the matchup ===
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The following terms are often used when discussing pairwise preferences:
* '''Pairwise matchup''': Also known as a head-to-head matchup, it is when voters are asked to indicate their preference between two candidates or winner sets, with the one that voters prefer (i.e. give more votes to) winning. It is usually done on the basis of majority rule (i.e. if more voters prefer one candidate over the other than the number of voters who have the opposing preference, then the candidate preferred by more voters wins the matchup) using [[choose-one voting]], though see the [[Strength of preference]] section for alternative ways. Pairwise matchups can be simulated from ranked or rated ballots and then assembled into a table to show all of the matchups simultaneously.
* '''Pairwise win/beat''' and '''pairwise lose/defeated''': When one candidate receives more votes in a pairwise matchup/comparison against another candidate, the former candidate "pairwise beats" the latter candidate (is "pairwise preferred" to the latter candidate), and the latter candidate "pairwise loses." Often this is represented by writing "Pairwise winner>Pairwise loser"; this can be extended to show a [[beatpath]] by showing, for example, "A>B>C>D", which means A pairwise beats B, B pairwise beats C, and C pairwise beats D (though it may or may not be the case, depending on the context, that, for example, A pairwise beats C).
* '''Pairwise
* '''Pairwise tie''': Occurs when two candidates receive the same number of votes in their pairwise matchup. (Note that sometimes it is also called a tie when there is pairwise cycling, though this is different; see the definition two spots below.) Note that some cycles can be symmetrical ties i.e. you can swap the candidates' names without changing the result. (See the [[Condorcet paradox]] article for an example, and the [[neutrality criterion]] and [[tie]] for more information). ▼
* '''Pairwise
* '''Pairwise cycling:''' Also known as a [[Condorcet cycle]], it is when within a set of candidates, each candidate has at least one pairwise defeat (when looking only at the matchups between the candidates in the set). ▼
* '''Minimal pairwise dominant set''': Also known as the [[Smith set]], it is the smallest '''dominating set''', which is any group of candidates who
▲'''Pairwise tie''': Occurs when two candidates receive the same number of votes in their pairwise matchup. (Note that sometimes it is also called a tie when there is pairwise cycling, though this is different; see the definition two spots below.) Note that some cycles can be symmetrical ties i.e. you can swap the candidates' names without changing the result. (See the [[Condorcet paradox]] article for an example, and the [[neutrality criterion]] and [[tie]] for more information).
** Note that the terms '''dominating/dominant''' are often used as shorter versions of pairwise-dominant.
* '''Pairwise
▲'''Pairwise cycling:''' Also known as a [[Condorcet cycle]], it is when within a set of candidates, each candidate has at least one pairwise defeat (when looking only at the matchups between the candidates in the set).
▲'''Minimal pairwise dominant set''': Also known as the [[Smith set]], it is the smallest group of candidates who pairwise beat all others. The [[pairwise champion]] will always be the only member of this set when they exist.
== Presentation ==
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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.
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.
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.
== Notes ==
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