Majority Judgment: Difference between revisions
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== Satisfied and failed criteria ==
Majority Judgment voting satisfies the [[Majority criterion for rated ballots|majority criterion for rated ballots]], and also a weak form of the [[mutual majority criterion]] (a majority giving only and all of their preferred candidates perfect grades will win), the [[monotonicity criterion
It fails the [[Condorcet criterion]],<ref group="nb">Strategically in the [[strong Nash equilibrium]], MJ passes the Condorcet criterion.</ref> [[later-no-harm]],<ref group="nb">MJ provides a weaker guarantee similar to LNH: rating another candidate at or below your preferred winner's median rating (as opposed to your own rating for the winner) cannot harm the winner.</ref> [[Consistency criterion|consistency]], the [[Condorcet method|Condorcet loser criterion]],<ref group="nb">Nevertheless, it passes a slightly weakened version, the majority condorcet loser criterion, in which all defeats are by an absolute majority (for instance, if there aren't equal rankings).</ref> and the [[participation criterion]].<ref group="nb">It can only fail the participation criterion when, among other conditions, the new ballot rates both of the candidates in question on the same side of the winning median, and the prior distribution of ratings is more sharply-peaked or irregular for one of the candidates.</ref> It also fails the ranked or preferential [[majority criterion]], which is incompatible with the passed criterion [[independence of irrelevant alternatives]], and [[reversal symmetry]].
==Example application==
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The median rating for Nashville and
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If voters from Knoxville and Chattanooga were to rate Nashville as "Poor" and/or both sets of voters were to rate Chattanooga as "Excellent", in an attempt to make their preferred candidate
==Variants==
Variants of majority judgment have been described. Fabre considers three: the typical judgment, usual judgment, and central judgment.<ref name="Fabre20">{{Cite journal |first=Adrien |last=Fabre |title=Tie-breaking the Highest Median: Alternatives to the Majority Judgment |journal=[[Social Choice and Welfare]] |year=2020 |volume=56 |pages=101–124 |url=https://github.com/bixiou/highest_median/raw/master/Tie-breaking%20Highest%20Median%20-%20Fabre%202019.pdf |doi=10.1007/s00355-020-01269-9|issn=0176-1714}}</ref>. He argues that all of these are less sensitive to noise than the majority judgment, with the usual judgment being the most robust, though the calculation that determines the winner is more complex.
==See also==
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