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Monotonicity criterion
Property of electoral systems / From Wikipedia, the free encyclopedia
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 called perverse.[5]
![A diagram showing who would win an IRV election for different electorates. The win region for each candidate is erratic, with random pixels dotting the image and jagged, star-shaped (convex) regions occupying much of the image. Moving the electorate to the left can cause a right-wing candidate to win, and vice versa.](http://upload.wikimedia.org/wikipedia/commons/thumb/1/1f/IRV_Yee.svg/640px-IRV_Yee.svg.png)
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.[2][6]
Most voting systems (including Borda and all common tournament solutions) satisfy positive response,[4] as do all commonly-used rated voting methods (including approval, score, and their proportional counterparts).[note 1]
However, the criterion is violated by instant-runoff voting,[7] the single transferable vote,[8] 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.