Ranked Pairs: Difference between revisions
Add information about neutrality vs tie-breaking, per EM discussion
(It's my understanding that Dr. Tideman prefers calling this method "Ranked Pairs".) |
(Add information about neutrality vs tie-breaking, per EM discussion) |
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Ranked Pairs is [[Smith-efficient]], because no Smith set member can be beaten by a candidate not in the Smith set, and therefore any candidate not in the Smith set can't have their defeats to Smith set members discarded during the RP procedure, so they can't become the Condorcet winner.
Ranked Pairs passes the [[Independence of Smith-dominated Alternatives]] criterion, because the only cycles for RP to potentially resolve will always be between Smith set members. Because of this, all candidates not in the Smith set can be eliminated before starting the procedure, reducing the number of operations needed to be done to find the winner. In addition, Ranked Pairs, like [[Schulze]], is equivalent to [[Minimax]] when there are 3 or fewer candidates with no pairwise ties between them, so if the Smith set has 3 or fewer candidates in it with no pairwise ties between them, [[Smith//Minimax]] can be run instead to find/demonstrate the RP winner.
One disadvantage of Ranked Pairs is that there's no easy way to detect ties for first place: determining whether there exists a way to break ties between pairwise victories so that a given candidate wins is NP-complete.<ref name="Brill">{{cite journal | last=Brill | first=Markus | last2=Fischer | first2=Felix | title=The Price of Neutrality for the Ranked Pairs Method | journal=Proceedings of the AAAI Conference on Artificial Intelligence | publisher=Association for the Advancement of Artificial Intelligence (AAAI) | volume=26 | issue=1 | date=2012-07-26 | issn=2374-3468 | doi=10.1609/aaai.v26i1.8250 | pages=1299–1305}}</ref>. While it is possible to break pairwise ties fairly, doing so leads Ranked Pairs to declare one of the winners the sole winner, without giving information about whether other candidates could have won were the ties broken differently.
== References ==
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== External Resources ==
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