Minimax Condorcet method: Difference between revisions

In [[voting system]]s, the '''MinmaxMinimax Condorcet method''' or(often referred to as "'''the Minimax method,'''" alsoand sometimes as "'''minmax'''" or "'''min-max'''") is one of several [[Condorcet method]]s used for tabulating votes and determining a winner when using [[Ranked voting systems|ranked voting]] in a [[single-member district|single-winner]] election. It is sometimes referred to as the '''Simpson-KramerSimpson–Kramer method''',<ref name="Caplin Nalebuff 1988 pp. 787–814">{{cite journal | last=Caplin | first=Andrew | last2=Nalebuff | first2=Barry | title=On 64%-Majority Rule | journal=Econometrica | publisher=[Wiley, Econometric Society] | volume=56 | issue=4 | year=1988 | issn=00129682 | jstor=1912699 | pages=787–814 | url=https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=c10e05dc6ea7cfa1ba1b28aa6c54e7abbf96eccc | access-date=2023-05-27}}</ref> is the name of a class of election methods based on electing the candidate with the most consistently high performance in pairwise contests with other candidates. It is sometimes also calledand the '''leastsuccessive reversal''' or method'''successive reversal''' method,.<ref name="Green-Armytage">{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-August/075781.html|title=the name of the rose|website=Election-methods mailing list archives|date=2003-08-04|last=Green-Armytage|first=J. }}</ref> although this term is ambiguous.

* x: '''A'''>B=C

* 1: '''A=C'''>B

* 1: '''B=C'''>A

* x: '''B'''>A=C

MMPO elects C even if x is made arbitrarily large (say, 3.95 billion voters). This is a [[Plurality criterion|Plurality]] failure.

All [[:Category:Defeat-dropping Condorcet methods|defeat-dropping Condorcet methods]] become equivalent to Minimax whenwith there are 3three or fewer candidates with no pairwise ties between them. Because of this, defeat-droppersdropping methods that pass [[ISDA]] are equivalent to [[Smith//Minimax]] when the abovecycle conditionsinvolves holdonly for3 the Smith setcandidates. Example:

Since the defeat-droppers are equivalent to either Minmax or Smith//MinmaxMinimax when three or fewer candidates run, they all fail [[dominant mutual third burial resistance]]. This follows from the equivalence and the three-candidate Minimax DMTBR failure example given above.