Ranked Pairs: Difference between revisions

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(Moved some of the Notes to an advantages and disadvantages section, and added Munger paper advocating for RP.)
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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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== Advantages and disadvantages ==
 
Ranked Pairs is [[Smith-efficient]], because noevery Smith set member canpairwise bebeats beateneverybody by a candidate not inoutside the Smith set,. andAs thereforea anyresult, candidateevery notdefeat inby thea Smith set can'tmember haveover their defeats toa non-Smith setcandidate membersis discardedlocked duringbefore theany RPopposite-direction proceduredefeat, so theya can'tnon-Smith becomecandidate thecan Condorcetnever winnerwin.
 
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.
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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 that 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>. WhileHowever, itties iscan possiblestill tobe breakbroken pairwisefairly tiesand fairly,efficiently doingusing sosome leadssecondary method that doesn't compromise Ranked Pairs' toproperties. declareThe onemost ofcommon thesuch winnerstiebreaker theis [[random solevoter winnerhierarchy]], withouta givinggeneralization informationof about[[random whetherballot]]. otherCardinal candidatesmethods couldlike have[[Graduated wonMajority wereJudgment|highest medians]] can also be used, at the tiescost brokenof slightly weakening properties like ranked [[clone differentlyindependence]].
 
 
== Notes ==
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