Participation criterion
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.
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 Criterion
For deterministic single-winner methods, the criterion is defined as follows:
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:[1]
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.
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: "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 Methods
This criterion is important in the context of the Balinski–Young theorem. Failing the participation criterion is an an example of failing Population monotonicity.
Plurality voting, Approval voting, Cardinal Ratings, Borda count, and Woodall's DAC and DSC methods all pass the Participation Criterion. Condorcet methods, Majority Choice Approval, and IRV fail.
All Monroe type multi-member systems fail participation.
Some parts of this article are derived with permission from text at http://electionmethods.org
Notes
The Participation criterion offers one way of justifying Score voting being no worse than FPTP: voters can never be hurt by casting an FPTP-style vote (bullet voting) relative to not voting. Many other voting methods, such as IRV and STAR (and possibly Condorcet fail even this weaker version of Participation. Example for IRV:
30+2 A>B 31 B 49 C
If 2 of the 32 A>B voters show up and bullet vote A, then B is eliminated and then C wins. But if they don't vote, then A is eliminated and then B wins.
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
References
- ↑ D R Woodall, "Monotonicity and Single-Seat Election Rules", Voting matters, Issue 6, 1996