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Round-robin voting
Round-robin, paired comparison, or tournament voting methods, are a set of ranked voting systems that choose winners by comparing every pair of candidates one-on-one, similar to a round-robin tournament. In each paired matchup, the total number of voters who prefer each candidate is recorded in a beats matrix. Then, a majority-preferred (Condorcet) candidate is elected, if one exists. Otherwise, if there is a cyclic tie, the candidate "closest" to being a Condorcet winner is elected, based on the recorded beats matrix. How "closest" is defined varies by method.
Round-robin methods are one of the four major categories of single-winner electoral methods, along with multi-stage methods (like RCV-IRV), positional methods (like plurality and Borda), and graded methods (like score and STAR voting).
Most, but not all, election methods meeting the Condorcet criterion are based on pairwise counting.
In paired voting, each voter ranks candidates from first to last (or rates them on a scale). For each pair of candidates (as in a round-robin tournament), we count how many votes rank each candidate over the other.
Pairwise counts are often displayed in a pairwise comparison or outranking matrix such as those below. In these matrices, each row represents each 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 opponent is preferred over the runner.
In this matrix the number in each cell indicates either the number of votes for runner over opponent (runner,opponent) or the number of votes for opponent over runner (opponent, runner).
If pairwise counting is used in an election that has three candidates named A, B, and C, the following pairwise counts are produced:
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Round-robin voting AI simulator
(@Round-robin voting_simulator)
Round-robin voting
Round-robin, paired comparison, or tournament voting methods, are a set of ranked voting systems that choose winners by comparing every pair of candidates one-on-one, similar to a round-robin tournament. In each paired matchup, the total number of voters who prefer each candidate is recorded in a beats matrix. Then, a majority-preferred (Condorcet) candidate is elected, if one exists. Otherwise, if there is a cyclic tie, the candidate "closest" to being a Condorcet winner is elected, based on the recorded beats matrix. How "closest" is defined varies by method.
Round-robin methods are one of the four major categories of single-winner electoral methods, along with multi-stage methods (like RCV-IRV), positional methods (like plurality and Borda), and graded methods (like score and STAR voting).
Most, but not all, election methods meeting the Condorcet criterion are based on pairwise counting.
In paired voting, each voter ranks candidates from first to last (or rates them on a scale). For each pair of candidates (as in a round-robin tournament), we count how many votes rank each candidate over the other.
Pairwise counts are often displayed in a pairwise comparison or outranking matrix such as those below. In these matrices, each row represents each 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 opponent is preferred over the runner.
In this matrix the number in each cell indicates either the number of votes for runner over opponent (runner,opponent) or the number of votes for opponent over runner (opponent, runner).
If pairwise counting is used in an election that has three candidates named A, B, and C, the following pairwise counts are produced: