Concept
The participation criterion is a voting system criterion. Voting systems that fail the participation criterion are said to exhibit the no show paradox and allow a particularly unusual strategy of tactical voting: abstaining from an election can help a voter's preferred choice win. The criterion has been defined as follows: In a deterministic framework, the participation criterion says that the addition of a ballot, where candidate A is strictly preferred to candidate B, to an existing tally of votes should not change the winner from candidate A to candidate B. In a probabilistic framework, the participation criterion says that the addition of a ballot, where each candidate of the set X is strictly preferred to each other candidate, to an existing tally of votes should not reduce the probability that the winner is chosen from the set X. Plurality voting, approval voting, range voting, and the Borda count all satisfy the participation criterion. All Condorcet methods, Bucklin voting, and IRV fail. The participation criterion for voting systems is one example of a rational participation constraint for social choice mechanisms in general. The most common failure of the participation criterion is not in the use of particular voting systems, but in simple yes or no measures that place quorum requirements. A public referendum, for example, if it required majority approval and a certain number of voters to participate in order to pass, would fail the participation criterion, as a minority of voters preferring the "no" option could cause the measure to fail by simply not voting rather than voting no. In other words, the addition of a "no" vote may make the measure more likely to pass. A referendum that required a minimum number of yes votes (not counting no votes), by contrast, would pass the participation criterion. Hervé Moulin showed in 1988 that whenever there are at least four candidates and at least 25 voters, no resolute (single-valued) Condorcet consistent voting rule satisfies the participation criterion.
