Pairwise counting: Difference between revisions
Reintroduced Condorcet loser as e.g. STAR passes it and uses pairwise counting. Summable contingent vote would also use it.
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(Reintroduced Condorcet loser as e.g. STAR passes it and uses pairwise counting. Summable contingent vote would also use it.) |
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'''Pairwise counting''' is the process of considering a set of items, comparing one pair of items at a time, and for each pair counting the comparison results. In the context of voting theory, it involves comparing pairs of candidates or winner sets (usually using majority rule) to determine the winner and loser of the [[Pairwise matchup|pairwise matchup]]. This is done by looking at voters' (usually [[Ranked ballot|ranked]] or [[Rated ballot|rated]]) ballots to count, for each pair of candidates, which one they indicated a preference for, if they did. The [[pairwise preference]] article discusses how pairwise comparison information can be used.
Most, but not all, election methods that meet the [[Condorcet criterion]] or the [[Condorcet loser criterion]] use pairwise counting.<ref group="nb">
== Procedure ==
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=== Dealing with write-in candidates ===
[[File:Approaches for handling write-in candidates in pairwise counting.png|thumb|837x837px]]
The difficulty of handling [[Write-in candidate|write-in candidat]]<nowiki/>es depends on how a voter's preference between ranked and unranked candidates is counted.
# If the voter is treated as preferring ranked candidates over unranked candidates (which is the near-universal approach), then write-ins can be difficult to count using pairwise counting, because the vote-counters don't know who they are and thus can't directly record voter preferences in matchups between on-ballot mainstream candidates and write-in candidates.
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==Count complexity==
==== Sequentially examining each rank on a voter's ballot ====
[[File:Pairwise counting with ranked ballot GIF.gif|thumb|576x576px|A GIF for pairwise counting with a [[ranked ballot]], which shows how to sequentially count it one rank at a time. Click on the image and then the thumbnail of the image to see the animation.]]The naive way of counting pairwise preferences implies determining, for each pair of candidates, and for each voter, if that voter prefers the first candidate of the pair to the second or vice versa. This requires looking at ballots <math>O(Vc^2)</math> times.
If reading a ballot takes a lot of time, it's possible to reduce the number of times a ballot has to be consulted by noting that:
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===Notes===
Image to right shows interpretation of ranked ballot.
==References==
<references />
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<references group="nb" />
[[Category:
[[Category:Condorcet-related concepts]]
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