Participation criterion

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:

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 4 candidates and at least 25 voters, no resolute (single-valued) Condorcet consistent voting rule satisfies the participation criterion. However, when there are at most 3 candidates, the minimax method (with some fixed tie-breaking) satisfies both the Condorcet and the participation criterion. Similarly, when there are 4 candidates and at most 11 voters, there is a voting rule that satisfies both criteria, but no such rule exists for 4 candidates and 12 voters. Similar incompatibilities have also been proven for set-valued voting rules.

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