Pairwise counting: Difference between revisions

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== Election examples ==
Here is an example of a pairwise victory table for the [https://en.wikipedia.org/wiki/2009_Burlington_mayoral_election Burlington 2009] election:
Here is an example of a pairwise victory table for the [https://en.wikipedia.org/wiki/2009_Burlington_mayoral_election Burlington 2009] election:
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The following terms are often used when discussing pairwise counting:
The following terms are often used when discussing pairwise counting:


'''Pairwise win/beat''' and '''pairwise lose''': When one candidate receives more votes in a pairwise matchup/comparison against another candidate, they "pairwise beat" that candidate, with the other candidate in the matchup pairwise losing.
'''Pairwise win/beat''' and '''pairwise lose''': When one candidate receives more votes in a pairwise matchup/comparison against another candidate, the former candidate "pairwise beats" the latter candidate, and the latter candidate "pairwise loses."


'''Pairwise winner''' and '''pairwise loser''': the candidate who pairwise wins is the pairwise winner of the matchup, with the other candidate being the pairwise loser of the matchup.
'''Pairwise winner''' and '''pairwise loser''': The candidate who pairwise wins is the pairwise winner of the matchup. The other candidate is the pairwise loser of the matchup.


'''Pairwise tie''': When two candidates receive the same number of votes in their pairwise matchup.
'''Pairwise tie''': Occurs when two candidates receive the same number of votes in their pairwise matchup.


'''Pairwise order/ranking''': Also known as a [[Condorcet ranking]], it is a ranking of candidates such that each candidate is ranked above all candidates they pairwise beat. One does not always exist due to the [[Condorcet paradox]], though there is always a [[Smith set ranking|Smith ranking]] which more generally holds instead for groups of candidates.
'''Pairwise order/ranking''': Also known as a [[Condorcet ranking]], is the ranking of candidates such that each candidate is ranked above all candidates they pairwise beat. Sometimes such a ranking does not exist due to the [[Condorcet paradox]]. As a related concept, there is always a [[Smith set ranking|Smith ranking]] that applies to groups of candidates.


==Notes==
==Notes==
Retrieved from "https://electowiki.org/wiki/Pairwise_counting"