Pairwise counting: Difference between revisions
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'''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 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|choose-one voting]], though see the [[Pairwise counting#Cardinal methods|Cardinal methods]] 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; see above.
'''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 (or the former 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 winner''' and '''pairwise loser''': The candidate who pairwise wins a matchup is the pairwise winner of the matchup (not to be confused with the pairwise champion; see the definition two spots below). The other candidate is the pairwise loser of the matchup. (Note that sometimes "pairwise loser" is also used to refer to a [[Condorcet loser]], which is a candidate who is pairwise defeated in all of their matchups).
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