Participation criterion

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The participation criterion, also called vote or population monotonicity, is a voting system criterion that says that a candidate should never lose an election as a result of receiving too many votes in support.^[1] It says that adding more voters who prefer Alice to Bob should not cause Alice to lose the election to Bob.^[2]

Voting systems that fail the participation criterion exhibit the no-show paradox, where a voter is effectively disenfranchised by the electoral system, because turning out to vote would make the outcome worse. In such a scenario, these voters' ballots are treated as "less than worthless", actively harming their own interests by reversing an otherwise-favorable outcome.^[3]

Positional methods and score voting satisfy the participation criterion. All methods satisfying paired majority-rule^[4][5] can fail in situations involving four-way cyclic ties, and the highest median methods^[6] can fail in some situations. Most notably, instant-runoff voting and the two-round system—the most commonly-used voting rules worldwide—often fail the participation criterion in competitive elections.^[7][8][9]