Condorcet method: Difference between revisions

Deleting the WILDLY inaccurate #Connection to cardinal methods
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==Connection to cardinal methods==
 
See also [[Score voting#Connection to Condorcet methods]] and [[rated pairwise preference ballot]]. Essentially, some [[Rated method|rated methods]] can be considered possible parametrizations 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>
 
Note that the above schemes can make Score fail the logical property that a voter's strength of preference between any pair of candidates must equal the sum of the strengths of preference between all sequential pairs of candidates in a [[beat-or-tie path]] from the first candidate of the pair to the second; see [[Ranked voting#Strength of preference]] for an example. The failure of this property seems to be the major reason traditional Condorcet methods can have Condorcet cycles and one major reason for why they fail certain properties such as Favorite Betrayal and Independence of Irrelevant Alternatives.
 
[[Approval voting]] can be thought of as a Condorcet method where voters must rank every candidate either 1st or last. This can most clearly be seen by observing that, when voters are limited to ranking candidates in this way in a Condorcet method, then Condorcet methods can be counted in exactly the same way as Approval using the [[Pairwise counting#Negative vote-counting approach]], with the candidate being marked on the most ballots getting the most voters backing them in head-to-head matchups, and thus being the [[CW]].
 
==Demonstrating pairwise counting==