Pairwise counting: Difference between revisions

'''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.

 

==Negative vote-counting approach==

[[File:Negative vote-counting approach to pairwise counting.png|thumb|1114x1114px|Negative vote-counting approach for pairwise counting (Note: Regular approach may be better in some use cases; see cited discussions in text to the left).]]

The usual approach to pairwise counting is for the precinct vote-counters to mark all of the voter's preferences in each head-to-head matchup. This can be slow, and also can make it difficult to accommodate write-in candidates, since the vote-counters won't know ahead of time who those candidates are, and thus won't be able to indicate preferences in those matchups. An alternative method of pairwise counting is the "negative votes/counting" approach: the precinct vote-counters simply indicate how many voters ranked/rated/marked a candidate on their ballot, and which candidates the voter ranked above (and equal to, depending on implementation; see below) the candidates they marked. In other words, instead of a candidate being assumed to be preferred only in the matchups where the vote-counters mark them as being so, the vote-counters assume a voter prefers a candidate they marked in all matchups against other candidates, and then work to indicate which matchups this is not true for.