Condorcet method: Difference between revisions
Citoid reference conversion
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See also [[Score voting#Connection to Condorcet methods]]. Essentially, [[Rated method|rated methods]] can be considered one possible parametrization of Condorcet methods.
Score Voting can be thought of as a Condorcet method where a voter is allowed to give a fraction of a vote to a candidate in a pairwise matchup against other candidates, rather than a full vote or nothing. Further, the amount of a vote the voter gives in one runoff directly alters the amount they give in another; if they arrange their scores such that they give 0.4 of a vote to help one candidate beat another, this automatically means they can at best arrange their scores such that they give up to 0.6 of their vote to help the second candidate beat someone else. Assuming a voter would vote the exact same way in a Score Voting runoff between all possible pairs of candidates as they did in the original Score election, Score elects the Condorcet winner using this modified definition.<ref>{{Cite web|url=https://rangevoting.org/CondDQ.html|title="Condorcet" definition quibble|last=|first=|date=|website=RangeVoting.org|url-status=live|archive-url=|archive-date=|access-date=2020-04-06}}</ref>
It's possible to modify Score to be more like a traditional Condorcet method by allowing voters to write the scores they would give to every possible pair of candidates in a Score runoff, and then using a Condorcet method to process this, treating a score of, say, A5 B3 (where the max score is 5) as 0.4 votes for A>B. As this would be utterly infeasible with just a few candidates running however, one way to accomplish most of the same objective is to allow voters to mark on their ballots that they want their vote strategically optimized, meaning that if their cardinally expressed preferences are A5 B3 Z2, instead of having their vote considered as B3 Z2 in an B vs. Z runoff, it would be considered as B5 Z0 (if the max score is 5), which is functionally equivalent to the Plurality voting runoffs that are used for the traditional Condorcet winner definition. This strategic optimization can be done fractionally to allow a voter to customize how much optimization they want to be done with their scores in each runoff. It is also possible for voters to indicate an approval threshold, meaning that for all approved candidates, no strategic optimization is applied to pairwise matchups between them, but all pairwise matchups between approved and disapproved candidates are strategically optimized. With this modification, if all voters use strategic optimization, Score becomes a traditional Condorcet method (which will need a cycle resolution method to be applied at times), but if no voters strategically optimize, it remains Score (which never needs cycle resolution methods to be applied).
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