Round-robin voting

[1] In each paired matchup, we record the total number of voters who prefer each candidate in a beats matrix.

Otherwise, if there is a cyclic tie, the candidate "closest" to being a Condorcet winner is elected, based on the recorded beats matrix.

Most, but not all, election methods meeting the Condorcet criterion are based on pairwise counting.

The cells at the intersection of rows and columns each show the result of a particular pairwise comparison.

If pairwise counting is used in an election that has three candidates named A, B, and C, the following pairwise counts are produced: If the number of voters who have no preference between two candidates is not supplied, it can be calculated using the supplied numbers.

Suppose that this imaginary election has two additional voters, and their preferences are D > A > C > B and A > C > B > D. Added to the first voter, these ballots yield the following sum matrix: In the sum matrix above, A is the Condorcet winner, because they beat every other candidate one-on-one.

For N candidates, there are N · (N − 1) pairwise matchups, assuming it is necessary to keep track of tied ranks.

When working with margins, only half of these are necessary because storing both candidates' percentages becomes redundant.