Monotonicity: Difference between revisions
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== Details == |
== Details == |
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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'''.<ref name="Woodall-Monotonicity"> |
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'''.<ref name="Woodall-Monotonicity">{{cite journal| title = Monotonicity and single-seat election rules| last = Woodall| first = Douglas R.| journal = Voting matters| volume = 6| pages = 9–14| year = 1996|url=http://www.votingmatters.org.uk/ISSUE6/P4.HTM}}</ref> |
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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. |
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. |