Minimax Condorcet method: Difference between revisions
Rewrote the defeat-dropper note to clarify how they fail DMTBR.
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{{Wikipedia|Minimax Condorcet method}}
In [[voting system]]s, the '''Minimax Condorcet method''' (often referred to as "'''the Minimax method'''" and 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–Kramer method''',<ref name="Caplin">{{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> and the '''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>
Minimax selects as the winner the candidate whose greatest pairwise defeat is smaller than the greatest pairwise defeat of any other candidate: or, put another way, "the only candidate whose support never drops below [N] percent" in any pairwise contest.<ref>The introduction to this article was initially copied from https://en.wikipedia.org/w/index.php?title=Minimax_Condorcet_method&oldid=1156877070</ref>
== Variants ==
'''Minmax''' or Minimax method, also referred to as the '''Simpson-Kramer method''',<ref name="Caplin
'''Minmax(winning votes)''' elects the candidate whose greatest pairwise loss to another candidate is the least, when the strength of a pairwise loss is measured as the number of voters who voted for the winning side.
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MMPO has been criticized for its counter-intuitive behavior on some elections.<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2016-September/000523.html|title=Re: MMPO objections (hopefully better posted)|website=Election-methods mailing list archives|date=2016-09-21|last=Benham|first=C.}}</ref> Given this election (called the "bad-example" on EM):
* 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.
== Notes ==
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This contrasts with [[Schulze]], which alternates between eliminating all candidates not in the [[Schwartz set]] and dropping defeats.
All [[:Category:Defeat-dropping Condorcet methods|defeat-dropping Condorcet methods]] become equivalent to Minimax
Since the defeat-droppers are equivalent to
▲Since the defeat-droppers are equivalent to either Minmax or Smith//Minmax when three or fewer candidates run, they all fail dominant mutual third burial resistance.
== References ==
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