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.
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{{wikipedia}}
The '''participation criterion''' is a [[voting system criterion]] applicable to both single and multiple winner [[ranked voting]] systems. A method that passes this criterion ensures a voter that it's always better to cast a full honest vote than to not show up for the election at all. It does this by guaranteeing that adding a ballot can never change the winner from someone who is ranked higher on that ballot to someone who is ranked lower.
{{definition|Adding one or more ballots that vote X over Y should never change▼
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.
== Definition ==
For deterministic single-winner methods, the criterion is defined as follows:
▲{{definition|Adding one or more ballots that vote X over Y should never change the winner from X to Y.}}
== Complying Methods ==▼
For multi-winner methods and methods that involve an element of chance, the definition is:<ref name="Woodall-Monotonicity">{{cite journal| title = Monotonicity and single-seat election rules| last = Woodall| first = Douglas R.| journal = Voting matters| volume = 6| pages = 9–14| year = 1996|url=http://www.votingmatters.org.uk/ISSUE6/P4.HTM}}</ref>
{{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.}}
''Some parts of this article are derived with permission from text at http://electionmethods.org''▼
== Variants ==
== 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. ▼
▲=== Semi-honest participation criterion ===
▲This is a weaker form of the
This criterion is important in the context of the [[Balinski–Young theorem]]. Failing the participation criterion is an an example of failing [[population 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.
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.
== Notes ==
See [[Truncation]] for a Participation-like criterion for [[bullet voting]].
Note that the Participation criterion doesn't say a voter should be able to benefit in some circumstances by voting, nor does it quantify such a thing. For example, a voting method which randomly chooses one of the candidates regardless of the votes would pass Participation, despite not giving voters any power. Voting methods like [[Score]] and [[FPTP]] can have this quantified because they are based on similar systems of increasing a candidate's "quality number", with each voter only being able to increase the number for a given candidate to a certain maximal amount.
== See also ==
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*[[Voting system]]
*[[Monotonicity criterion]]
*[[Independence of Irrelevant Ballots]]
*[[Condorcet Criterion]]
*[[Generalized Condorcet criterion]]
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*[[Favorite Betrayal criterion]]
*[[Summability criterion]]
== References ==
<references/>
▲''Some parts of this article are derived with permission from text at http://electionmethods.org''
== External links ==
* [http://electionmethods.org/ Election Methods Education and Research Group]
[[Category:Voting system criteria]]
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