First preference Copeland: Difference between revisions
Add monotonicity failure.
(Added and linkified names, as well as a link to the WDS proof that FPC is not cloneproof.) |
(Add monotonicity failure.) |
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First preference Copeland passes [[Smith criterion|Smith]] because supposing otherwise, that some candidate Y not in the Smith set wins; then for a candidate X in the Smith set, Y is beaten by every candidate X is beaten by, and some more. Thus Y's penalty must be higher than X's, so Y couldn't have been the winner.
However, FPC fails both [[independence of clone alternatives]]<ref>{{cite web|url=https://munsterhjelm.no/km/yahoo_lists_archive/RangeVoting/web/2006-December/msg00040.html|title=Wait a minute - Simmons' "cloneproof" method is not really cloneproof!|date=2006-12-31|last=Smith|first=W.|website=RangeVoting Yahoo list mirror}}</ref> and the [[monotonicity criterion]]. One example of monotonicity failure is as follows:
{{ballots|
8: A>B>C
2: A>C>B
9: B>C>A
12: C>A>B}} and C wins. Then raise C on the two A>C>B ballots:
{{ballots|
8: A>B>C
9: B>C>A
14: C>A>B}} and A wins.
{{stub}}
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