Participation criterion

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The participation criterion, sometimes called voter monotonicity, is a voting system criterion that says candidates 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 result.^[5]

The criterion can also be described as a weaker form of strategyproofness: while it is impossible for honesty to always be the perfect strategy (by Gibbard's theorem), the participation criterion guarantees honesty will always be an effective, rather than counterproductive, strategy (i.e. an honest vote will make the outcome better, not worse). Strategy in non-participatory systems can become highly complex, as casting an honest vote is not a potential fallback option for honest voters.

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 fail the participation criterion with high frequency in competitive elections, typically as a result of center squeeze.^[1][2][7]