Participation criterion

The participation criterion, sometimes called join consistency, is a voting system criterion that says that a candidate should never lose an election because they have "too many supporters." In other words, adding a ballot that ranks A higher than B should not cause A to lose to B.

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.