Participation criterion: Difference between revisions
Add limit on how many voters can be present for there to exist a voting rule passing both Condorcet and participation.
(Removed weak participation as it seems to be the same as ordinary participation - both this page and the one on Wikipedia refers to cast ballots. Fix some Initial Capitalization as well.) |
(Add limit on how many voters can be present for there to exist a voting rule passing both Condorcet and participation.) |
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{{definition|Adding one or more ballots that vote X over Y should never change the winner from X to Y.}}
For multi-winner methods and methods that involve an element of chance, the definition is:<ref name="Woodall-Monotonicity">
{{definition|The addition of a further ballot should not, for any positive whole number k, reduce the probability that at least one candidate is elected out of the first k candidates listed on that ballot.}}
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Every [[weighted positional method]] that gives higher ranked candidates higher scores passes the participation criterion. In particular, [[Plurality voting]] and the [[Borda count]] both pass. Furthermore, [[Approval voting]], [[Cardinal Ratings]], and Woodall's [[Descending Acquiescing Coalitions|DAC]] and [[Descending Solid Coalitions|DSC]] methods all pass the participation criterion. All [[Condorcet method]]s,<ref name=":0">{{Cite journal|last=Moulin|first=Hervé|date=1988-06-01|title=Condorcet's principle implies the no show paradox|journal=Journal of Economic Theory|volume=45|issue=1|pages=53–64|doi=10.1016/0022-0531(88)90253-0}}</ref><ref>{{cite web|url=http://rangevoting.org/CondPF.html|title=Participation failure" is forced in Condorcet methods with at least 4 candidates|accessdate=2014-12-24}}</ref> [[Bucklin voting]],<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/1998-June/001727.html|title=Regretted Turnout. Insincere = ranking.|author=Markus Schulze|accessdate=2011-05-14|date=1998-06-12}}</ref> and [[instant-runoff voting|IRV]]<ref name="WDSParticipationReversalSymmetry">{{cite web|author=Warren D. Smith|url=http://rangevoting.org/TBlecture.html#partic|title=Lecture "Mathematics and Democracy"|accessdate=2011-05-12}}</ref> fail.
It's possible to pass both Condorcet and Participation for three candidates and any number of voters, or for four candidates up to 11 voters inclusive.<ref name="Brandt Geist Peters 2016">{{cite arXiv | last=Brandt | first=Felix | last2=Geist | first2=Christian | last3=Peters | first3=Dominik | title=Optimal Bounds for the No-Show Paradox via SAT Solving | date=2016-02-25 | eprint=1602.08063 | class=cs.GT }}</ref> This result also holds for certain probabilistic extensions of the Condorcet criterion.
All Monroe type multi-member systems fail participation.
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