This article is about the voting system criterion. For the mathematical notion of an order preserving mapping, see monotonic function. For the concept of population or voter monotonicity, see Participation criterion.
A 4-candidate Yee diagram under IRV. The diagram shows who would win an IRV election if the electorate is centered at a particular point. Moving the electorate to the left can cause a right-wing candidate to win, and vice versa. Black lines show the optimal solution (achieved by Condorcet or score voting).
The monotonicitycriterion, also called positive response[1] or positive vote weight,[2] is a principle of social choice theory that says that increasing a candidate's ranking or rating should not cause them to lose.[3] 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").
Systems that violate positive response (such as instant-runoff and the two-round system) 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 principle that increasing an option's popularity in a democratic election should only improve the chances of that option winning; as a result, German courts have previously struck down nonmonotonic systems for violating the right to equal and direct suffrage.[4][5]
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.
^Ornstein, Joseph T.; Norman, Robert Z. (2014-10-01). "Frequency of monotonicity failure under Instant Runoff Voting: estimates based on a spatial model of elections". Public Choice. 161 (1–2): 1–9. doi:10.1007/s11127-013-0118-2. ISSN0048-5829. S2CID30833409.
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