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Monotonicity: Difference between revisions
Created new #Details section, moving most of the introduction into that section
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{{wikipedia|Monotonicity criterion}}
The '''monotonicity criterion''' is a [[voting system criterion]] used to evaluate both single and multiple winner [[
<ref name="Woodall-Monotonicity">D R Woodall, [http://www.votingmatters.org.uk/ISSUE6/P4.HTM "Monotonicity and Single-Seat Election Rules"], ''[[Voting matters]]'', Issue 6, 1996</ref> In deterministic single winner elections that is to say no winner is harmed by up-ranking and no loser can win by down-ranking. If the method relies on chance, then up-ranking a candidate can not decrease that candidate's chance of winning, nor can down-ranking the candidate increase it. Douglas R. Woodall called the criterion '''mono-raise'''.▼
== Details ==
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Raising a candidate {{math|''x''}} on some ballots ''while changing'' the orders of other candidates does ''not'' constitute a failure of monotonicity. E.g., harming candidate {{math|''x''}} by changing some ballots from {{math|''z'' > ''x'' > ''y''}} to {{math|''x'' > ''y'' > ''z''}} isn't a violation of the monotonicity criterion.
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