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][2] More formally, it says that adding more voters who prefer Alice to Bob should not cause Alice to lose the election to Bob.^[3]

Voting systems that fail the participation criterion exhibit the no-show paradox,^[4] 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.^[5]

The criterion can also be thought of as a weak kind of strategyproofness: while it is impossible for honesty to always be the best strategy (by Gibbard's theorem), the participation criterion guarantees honesty will always "work" as a strategy (i.e. an honest vote will make the outcome better).

Positional methods and score voting satisfy the participation criterion. All methods satisfying paired majority-rule^[4][6] can fail in situations involving four-way cyclic ties, though such scenarios are empirically rare. Most notably, instant-runoff voting and the two-round system often fail the participation criterion in competitive elections, typically as a result of center squeeze.^[1][2][7]