Ranked Pairs: Difference between revisions
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(It's my understanding that Dr. Tideman prefers calling this method "Ranked Pairs".) |
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{{Wikipedia|Ranked pairs}}
The "'''Ranked Pairs'''" method (sometimes abbreviated as "RP") was created in 1987 by [[Nicolaus Tideman]].<ref name="Tideman2">{{Cite journal |last=Tideman |first=T. N. |date=1987-09-01 |title=Independence of clones as a criterion for voting rules |url=https://doi.org/10.1007/BF00433944 |journal=Social Choice and Welfare |language=en |volume=4 |issue=3 |pages=185–206 |doi=10.1007/BF00433944 |issn=1432-217X}}</ref> It is a [[voting system]] that selects a single winner using votes that express preferences. The ranked-pairs method can also be used to create a sorted list of winners. Ranked Pairs passes the [[Smith criterion]] and the [[Condorcet winner criterion]] (thus making it a "[[Condorcet method]]"). The ranked-pairs method has many variations such as the "[[Maximize Affirmed Majorities]]" (or "MAM") and "[[Maximum Majority Voting]]" (or "MMV") voting methods.
== Procedure ==
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Therefore, A is the winner.
=== A Limit case ===
We assume 48% of voters vote A>B>C, 3% votes B>C>A, 49% votes C>A>B. A>B in 97% (locked), C>A in 52% (locked) and B>C in 51% (not locked since there is a cycle). Thus, we have C>A>B and C is the winner. However, if we make a [[Borda count]] (2 points for first place 1 point for second place) A has 145 points and C has only 101 points and thus one could think that A deserves more to win.
== Advantages and disadvantages ==
Ranked Pairs is [[Smith-efficient]], because every Smith set member pairwise beats everybody outside the set. As a result, every defeat by a Smith set member over a non-Smith candidate is locked before any opposite-direction defeat, so a non-Smith candidate can never win.
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.
While Ranked Pairs behaves similarly to [[Schulze]], Ranked Pairs passes [[local independence of irrelevant alternatives]] whereas Schulze does not. Some authors argue that the Ranked Pairs method is more intuitive and easier to understand than Schulze as well.<ref name="Munger 2023 pp. 434–444">{{cite journal | last=Munger | first=Charles T. | title=The best Condorcet-compatible election method: Ranked Pairs | journal=Constitutional Political Economy | volume=34 | issue=3 | date=2023 | issn=1043-4062 | doi=10.1007/s10602-022-09382-w | pages=434–444}}</ref>
One disadvantage of Ranked Pairs is there's no easy way to detect ties for first place, as 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> However, ties can still be broken fairly and efficiently using some secondary method that doesn't compromise Ranked Pairs' properties. The most common such tiebreaker is [[random voter hierarchy]], a generalization of [[random ballot]]. Cardinal methods like [[Graduated Majority Judgment|highest medians]] can also be used, at the cost of slightly weakening properties like ranked [[clone independence]].
== Notes ==
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When ignoring struckthrough (non-locked in) pairwise victories, C is the only candidate with no pairwise defeats, and thus is the RP winner. The RP ranking is C>A>B, since C pairwise beats all others, A pairwise beats everyone except C, and B pairwise loses to everyone (when ignoring the defeats ignored by the RP procedure).
== References ==
<references />
▲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.
== External Resources ==
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[[Category:Monotonic_electoral_systems]]
[[Category:Ranked voting methods]]
[[Category:Condorcet methods]]
[[Category:Clone-independent electoral systems]]
{{fromwikipedia}}
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