Participation criterion: Difference between revisions

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.
m (Move derivation credit to the references section.)
(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.)
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While the criterion ensures that a voter can't benefit from staying home rather than voting honestly, a voter may do even better by engaging in [[tactical voting]]; participation does not imply that the method is strategy-proof.
 
== Statement of CriterionDefinition ==
 
For deterministic single-winner methods, the criterion is defined as follows:
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== Variants ==
 
=== Weak Participation criterion===
 
By voting, you cannot cause X to be elected instead of Y (with all other winners staying the same) if you scored Y higher than X. One consequence of this criteria, is that by voting, you can never get a result that is less desirable according to your ballot then a result that is more desirable according to your ballot. The difference between this criterion and the strong Strong Participation criterion is that because unless there was an infinite range for you to score candidates on (you are scoring candidates on infinite sliding bars), due to the approximations you make when expressing your utilities on a finite number of scores, your ballot can disagree with you about whether outcome X is better than outcome Y.
 
(Described here: [https://rangevoting.org/QualityMulti.html#faildesid "Optimal proportional representation" multiwinner voting systems I: methods, algorithms, advantages, and inherent flaws])
 
=== Semi-honest participation criterion ===
This is a weaker form of the [[participation criterion]]. It states that for any set of ballots, an extra voter with a given preference set must be able to cast a ballot which is semi-honest and meaningfully expressive, without making the result worse. Meaningfully expressive means that if the voter prefers some set of candidates to the winner, the non-harmful ballot must be able to express that preference.
 
== Complying Methodsmethods ==
 
This criterion is important in the context of the [[Balinski–Young theorem]]. Failing the participation criterion is an an example of failing [[Populationpopulation monotonicity]].
 
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.
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