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User:BetterVotingAdvocacy/Self-referential Smith-efficient Condorcet method: Difference between revisions
User:BetterVotingAdvocacy/Self-referential Smith-efficient Condorcet method (view source)
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Self-referential Condorcet methods (SR-Condorcet methods) guarantee the election of a candidate, the SR-Condorcet winner, who would win within the voting method if it was just them and any other candidate, when one exists (related to a [[Condorcet winner]]). More broadly, if there are a smallest set of candidates, the SR-Smith set, who would each win if it was just them and any other candidate not in the set, some voting methods always elect someone from this set of candidates (related to the [[Smith set]]).
(Note that an underlying assumption is that a voter would cast the same ballot no matter which candidates are added or removed; if voters change their preferences, then most likely no voting method can be an SR-Condorcet method.)
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[[Pairwise counting]] can generally be adapted in some way (not necessarily using majority rule) to determine if there is an SR-Condorcet winner or SR-Smith set in a particular voting method.
In some sense, SR methods are the natural result of making [[Majority rule|majority rule]] and [[utilitarianism]] maximally satisfy [[Independence of irrelevant alternatives|Independence of irrelevant alternative]]<nowiki/>s. Indeed, one could define SR methods with reference to 3-candidste matchups, 4-candidate, etc. With majority rule, since there won't necessarily be a majority or a tie when there are more than 2 candidates, defining this is tricky.
It is possible to fuse Score voting and Condorcet methods by allowing voters to cast either rated or ranked ballots (or submit a rated ballot with the option to request it be counted as either a rated or a ranked ballot; see the [[ballot]] article for how to do this) and then counting those voters who cast rated ballots as having weak preferences in each runoff (i.e. a voter who scored one candidate a 1 and the other a 0.8 would be counted as giving 0.2 votes to help the first candidate pairwise beat the latter) and counting the voters who cast ranked ballots as having maximally strong preferences in each runoff (i.e. the previously mentioned voter would be counted as giving 1 vote to help the first candidate pairwise beat the latter).
Generally, the idea of SR methods is that voters indicate a "global" (i.e. their entire ballot is used to determine this) margin of preference between each candidate, with the candidate that has a positive margin (i.e. that's in their favor) against all other candidates winning. This is in contrast to something like [[IRV]], which only focuses on the [[FPTP]]-based "local" margin at the top of each voter's ballot, and changes dynamically (i.e. operates sequentially and shifts its opinion of how good or bad each candidate is over time, as it goes down each voter's ballot).
[[Category:Binary relations theory]]
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