Condorcet winner criterion: Difference between revisions
Improved references by filling in more information.
(Cleaned up the initial paragraph a bit.) |
(Improved references by filling in more information.) |
||
Line 100:
===Independence of Irrelevant Alternatives===
Note that the Condorcet criterion also implies the following criterion which is somewhat related to Independence of Irrelevant Alternatives: removing losing candidates can't change the result of an election if there is a Condorcet winner.
===Weak Condorcet winners===
Line 120:
3 B1(>A)</blockquote>Now both of A and B1 are weak CWs, because they both pairwise tie each other. In this particular example, since there is nothing that distinguishes either candidate from the other, the neutrality criterion requires that both A and B1 must have an equal probability of winning i.e. both must have a 50% chance. This means that removing clones of B1 increased B1's chances of winning (which were originally at 0%, since A was guaranteed to win earlier i.e. had a 100% chance of winning.) <ref name="Schulze 2018 p206">
Weak CWs have also been called Condorcet non-losers, with the requirement that they always win when they exist being called Exclusive-Condorcet. <ref>{{Cite web|url=http://www.votingmatters.org.uk/ISSUE3/P5.HTM#r2|title=Voting matters, Issue 3: pp 8-15|last=|first=|date=|website=www.votingmatters.org.uk|url-status=live|archive-url=|archive-date=|access-date=2020-05-09|quote=Exclusive-Condorcet (see Fishburn[2]). If there is a Condorcet non-loser, then at least one Condorcet non-loser should be elected.}}</ref>
==Multi-winner generalizations==
Schulze has proposed a generalization of the Condorcet criterion for multi-winner methods:<ref name="Schulze 2018">{{cite
A method passes the M-seat Condorcet criterion if its M-seat election outcome always contains such a ''b'' when he exists, and passes the multi-winner Condorcet criterion if it passes the M-seat Condorcet criterion for all M.
Line 133:
Note that Bloc Ranked Pairs and Bloc Score voting (if scored methods are considered) would pass this criterion, though they are not proportional, and the latter is not a Condorcet method in the single-winner case. So it may make more sense to consider Schulze's criterion as one of several that a multi-winner method ought to pass to be considered a Condorcet multi-winner or Condorcet PR method, rather than the definitive one.
In addition to Schulze's generalization, Gehrein, and Aziz ''et al.'' have proposed different multi-winner generalizations, based on the concept of stability.<ref name="Aziz">{{cite arXiv | last1=Aziz | first1=Haris | last2=Elkind | first2=Edith | last3=Faliszewski | first3=Piotr | last4=Lackner | first4=Martin | last5=Skowron | first5=Piotr | title=The Condorcet Principle for Multiwinner Elections: From Shortlisting to Proportionality | date=2017-01-27 | eprint=1701.08023 | class=cs.GT}}</ref>
==Abstract Condorcet Criterion==
Line 228:
==Outside of voting theory==
Analogues to the Condorcet criterion have been proposed in non-voting contexts; it appears in many places when discussing how to aggregate ranked information. It has been used to discuss search engine rankings <ref name="Dwork Kumar Naor Sivakumar 2001 p. ">{{
==References==
|