Monotonicity criterion

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The positive response,^[1][2] monotonicity, or nonperversity criterion^[3] is a principle of social choice theory that says that increasing a candidate's ranking or rating should not cause them to lose.^[4] Positive response rules out cases where a candidate loses an election as a result of receiving too much support from voters (i.e. being "too popular to win"). Rules that violate positive response are also called perverse^[5] and are said to suffer the more-is-less paradox. Such paradoxes are especially common in ranked-choice voting (RCV-IRV),^[6] a behavior which often leads to the elimination of moderate candidates and the election of extremists.^[7]

Systems that violate positive response can create situations where a voter's ballot has a reversed effect on the election, making it "less than worthless". This runs counter to the basic democratic principle that increasing an option's popularity in a democratic election should only improve their chances of winning; as a result, German courts have previously struck down nonmonotonic systems for violating the right to equal and direct suffrage.^[2][8]

Most ranked methods (including Borda and all common tournament solutions) satisfy positive response,^[4] as do all commonly-used rated voting methods (including approval, highest medians, and score).^{[note 1]}

However, the criterion is violated by instant-runoff voting,^[9] the single transferable vote,^[10] and Hamilton's apportionment method.^[2]

The participation criterion is a closely-related, but different, concept. While positive responsiveness deals with a voter changing their opinion (or vote), participation deals with situations where a voter choosing to cast a ballot can have a reversed effect on the election.

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