Borda count: Difference between revisions
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== Notes == |
== Notes == |
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Borda can be thought of as a variant of [[Score voting]] where the scores for each candidate are chosen to some extent for the voter, rather than by the voter. Because of the way Borda chooses those scores, a [[Condorcet winner]] can never have the fewest points (i.e. be in last place) in Borda, while this can happen in Score voting (Simple example: if between two candidates, a majority of voters give the first candidate a 1 out of 5, and the minority give the second candidate a 5 out of 5, then the majority's 1st choice, who is the Condorcet winner, would have fewer points than the minority's preference and thus be in last place). As an extension of this property, the [[:Category:Sequential loser-elimination methods|instant-runoff]] form of Borda, [[Baldwin]], is a [[Smith-efficient]] [[Condorcet method]], whereas the same is not true for the instant-runoff form of Score, [[IRNR]]. |
Borda can be thought of as a variant of [[Score voting]] where the scores for each candidate are chosen to some extent for the voter, rather than by the voter. Because of the way Borda chooses those scores, a [[Condorcet winner]] can never have the fewest points (i.e. be in last place) in Borda, while this can happen in Score voting (Simple example: if between two candidates, a majority of voters give the first candidate a 1 out of 5, and the minority give the second candidate a 5 out of 5, then the majority's 1st choice, who is the Condorcet winner, would have fewer points than the minority's preference and thus be in last place). As an extension of this property, the [[:Category:Sequential loser-elimination methods|instant-runoff]] form of Borda, [[Baldwin]], is a [[Smith-efficient]] [[Condorcet method]], whereas the same is not true for the instant-runoff form of Score, [[IRNR]]. |
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The Borda count can be done in different ways depending on how points are assigned. For certain variants, it may be possible to find the Borda scores for the candidates using [[pairwise preference]]<nowiki/>s. <ref>https://rangevoting.org/Wright_Barry.pdf "We can also compute the Borda Count social preference order by summing the rows of the margin of victory matrix. To see why, consider this deconstruction of the Borda Count score. Since even a last place candidate gets 1 point, each candidate automatically gets n points, where n is the number of voters. Then for each pairwise victory, the candidate must be ranked one slot above another candidate on a particular ballot. Thus, the remaining points are exactly equal to the number of pairwise victories the candidate has. Since there is a clear bijection between the total number of pairwise victories and the sum of the entries in a candidate’s row of the margin of victory matrix, we can simply use this value"</ref><ref>https://web.stanford.edu/~jdlevin/Papers/Voting.pdf bottom of p.11-12 "Since every point a candidate receives may be considered a head-to-head vote against some other candidate, Borda scores are equal to the total number of head-to-head votes a candidate receives. This means we can count Borda scores by writing a paired-comparisons matrix and summing the rows to generate the candidates' scores."</ref> |
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==See also== |
==See also== |
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