Smith//Minimax: Difference between revisions
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To determine the winner of an election, use the following algorithm:
* Determine the smallest set of candidates in a particular election who, when paired off in pairwise elections, can beat all other candidates outside the set. This is known as the ''Smith set'' This set might consist of only one candidate, the [[Condorcet winner]]. However, when the electorate is conflicted (as in [[Voting paradox|Condorcet's paradox]]), the set usually has at least one [[Condorcet cycle|cycle]] of candidates for whom A beats B, B beats C, and C beats A.
* If there is more than one candidate remaining, determine the winner using one of the two following methods (see the [[defeat strength]] article):
** "winning votes": elects the candidate whose greatest pairwise loss to another candidate is the least, when the strength of a pairwise loss is measured as the number of voters who voted for the winning side.
** "margins": elects the candidate whose greatest pairwise loss is measured as the number of votes for the winning side ''minus'' the number of votes for the losing side.
Example using winning votes:
{{ballots|
19: C>A>B>D
17: D>C>A>B
17: B>C>A>D
16: D>B>C>A
16: A>B>C>D
15: D>A>B>C}}
A beats B (67 to 33) beats C (64 to 36) beats A (69 to 31), but all three beat D (all 52 to 48), so the three are in the Smith set. Smith//Minimax first eliminates D, and then C wins for having the fewest winning votes against them in any of their defeats (C was beaten only by someone with 64 winning votes, whereas the others are beaten by 67 and 69 wv respectively). Regular Minimax would elect D for having the weakest defeat here (only 52 wv against them), resulting in a failure of the [[mutual majority criterion]].
==Notes==
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[[Category:Smith-efficient Condorcet methods]]
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