Revision as of 09:44, 26 March 2022 (view source) Kristomun (talk \| contribs) (Add WDS nonmonotonicity probability figure for IRV) ← Older edit		Revision as of 08:56, 7 April 2022 (view source) Kristomun (talk \| contribs) m (Improve reference) Newer edit →
Line 5: == Details == 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">D{{cite Rjournal\| 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 ~~"Monotonicity and Single-Seat Election Rules"], ''[[Voting matters]]'', Issue 6, 1996~~}}</ref> 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.

Monotonicity: Difference between revisions

Monotonicity (view source)