Majority Judgment: Difference between revisions

'''Majority Judgment''' is a single-winner [[voting system]] proposed by [[Michel Balinski]] and Rida Laraki.<ref>{{cite book|author= M. Balinski & R. Laraki|year=2010|title=Majority Judgment. |publisher=MIT Press|isbn=978-0-262-01513-4}}</ref><ref>{{Cite journal|last=de Swart|first=Harrie|date=2021-11-16|title=How to Choose a President, Mayor, Chair: Balinski and Laraki Unpacked|url=https://link.springer.com/10.1007/s00283-021-10124-3|journal=The Mathematical Intelligencer|language=en|doi=10.1007/s00283-021-10124-3|issn=0343-6993}}</ref> Voters freely grade[[Score voting|score]] each candidate in one of several named ranksqualities, for instance from "excellent" to "bad",. Each quality is associated with a numeric score and the candidate with the highest [[median]] gradescore is the winner. If more than one candidate has the same median grade, a tiebreaker is used which sees how "broad" that median grade is. Majority Judgment can be considered as a form of [[Bucklin voting]] which allows equal ranks.

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]], [[reversal symmetry]], and [[later-no-harm|later-no-help]]. Assuming that ratings are given independently of other candidates, it satisfies the [[independence of clones criterion]] and the [[independence of irrelevant alternatives|independence of irrelevant alternatives criterion]]<ref>Badinski and Laraki, ''Majority Judgment'', p. 217</ref> - although this latter criterion is incompatible with the majority criterion if voters shift their judgments in order to express their [[preferential voting|preferences]] between the available candidates.

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> [[consistencyConsistency criterion for voting systems|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]].

The median rating for Nashville and ChatanoogaChattanooga is "Good"; for Knoxville, "Fair"; and for Memphis, "Poor". Nashville and ChatanoogaChattanooga are tied, so "Good" ratings have to be removed from both, until their medians become different. After removing 16% "Good" ratings from the votes of each, the sorted ratings are now:

ChatanoogaChattanooga now has the same number of "Fair" ratings as "Good" and "Excellent" combined, so its median is rounded down to "Fair", while Nashville's median remains at "Good"<ref group="nb">After removal, ChatanoogaChattanooga has 42% of the initial electorate at "Fair", 27% "Good", and 15% "Excellent", while Nashville has 32% "Fair", 26% "Good", and 26% "Excellent"</ref> and so '''Nashville''', the capital in real life, wins.

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 ChatanoogaChattanooga win, the winner would still be Nashville.