Round-robin voting

Round-robin voting (also called paired/pairwise comparison or tournament voting) refers to a set of ranked voting systems that elect winners by comparing all candidates in a round-robin tournament. Every candidate is matched up against every other candidate, where their point total is equal to the number of votes they receive; the method then selects a winner based on the results of these paired matchups.

Round-robin methods are one of the four major categories of single-winner electoral methods, along with multi-stage methods (including instant-runoff voting and Baldwin's method), positional methods (including plurality and Borda), and graded methods (including score and STAR voting).

While most methods satisfying the Condorcet criterion are pairwise-counting methods, some are not, with the most notable example being the Tideman alternative method.

Summary
In paired voting, each voter ranks candidates from first to last (or rates them on a scale); candidates not ranked by voters are given the lowest rank or score.

For each pair of candidates (as in a round-robin tournament), we count how many votes rank each candidate over the other candidate. Thus each pair will have two totals, the size of its majority and the size of its minority.

Pairwise counting
In the pairwise-counting procedure, we compare each pair of candidates (as in a round-robin tournament), counting how many voters rank each candidate over the other.

Pairwise counts are often displayed in a pairwise comparison or outranking matrix. In these matrices, each row represents candidate as a 'runner,' while each column represents each candidate as an 'opponent'. The cells at the intersection of rows and columns each show the result of a particular pairwise comparison. Cells comparing a candidate to themselves are left blank.

Imagine there is an election between four candidates: A, B, C, and D. The first matrix below records the preferences expressed on a single ballot paper, in which the voter's preferences are (B, C, A, D); that is, the voter ranked B first, C second, A third, and D fourth. In the matrix a '1' indicates that the runner is preferred over the 'opponent', while a '0' indicates that the runner is defeated.

Alternatively, the margin matrix can be used for most methods. The margin matrix considers only the difference in the vote shares of the two candidates, making it antisymmetric (i.e. the top half is the negative of the bottom half).

Example
A pairwise-comparison matrix can be constructed as: