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Majority judgment
Majority judgment (MJ) is a single-winner voting system proposed in 2010 by Michel Balinski and Rida Laraki. It is a kind of highest median rule, a cardinal voting system that elects the candidate with the highest median rating.
Voters grade as many of the candidates as they wish with regard to their suitability for office according to a series of grades. Balinski and Laraki suggest the options "Excellent, Very Good, Good, Acceptable, Poor, or Reject," but any scale can be used (e.g. the common letter grade scale). Voters can assign the same grade to multiple candidates.
As with all highest median voting rules, the candidate with the highest median grade is declared winner. If more than one candidate has the same median grade, majority judgment breaks the tie by removing (one-by-one) any grades equal to the shared median grade from each tied candidate's column. This procedure is repeated until only one of the tied candidates is found to have the highest median grade.
Like most other cardinal voting rules, majority judgment satisfies the monotonicity criterion, the later-no-help criterion, and independence of irrelevant alternatives.
Like any deterministic voting system (except dictatorship), MJ allows for tactical voting in cases of more than three candidates, as a consequence of Gibbard's theorem.
Majority judgment voting fails the Condorcet criterion, later-no-harm,consistency, the Condorcet loser criterion, the participation criterion, the majority criterion, and the mutual majority criterion.
Unlike score voting, majority judgment can have no-show paradoxes, situations where a candidate loses because they won "too many votes". In other words, adding votes that rank a candidate higher than their opponent can still cause this candidate to lose.
In their 2010 book, Balinski and Laraki demonstrate that the only join-consistent methods are point-summing methods, a slight generalization of score voting that includes positional voting. Specifically, their result shows the only methods satisfying the slightly stronger consistency criterion have:
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Majority judgment
Majority judgment (MJ) is a single-winner voting system proposed in 2010 by Michel Balinski and Rida Laraki. It is a kind of highest median rule, a cardinal voting system that elects the candidate with the highest median rating.
Voters grade as many of the candidates as they wish with regard to their suitability for office according to a series of grades. Balinski and Laraki suggest the options "Excellent, Very Good, Good, Acceptable, Poor, or Reject," but any scale can be used (e.g. the common letter grade scale). Voters can assign the same grade to multiple candidates.
As with all highest median voting rules, the candidate with the highest median grade is declared winner. If more than one candidate has the same median grade, majority judgment breaks the tie by removing (one-by-one) any grades equal to the shared median grade from each tied candidate's column. This procedure is repeated until only one of the tied candidates is found to have the highest median grade.
Like most other cardinal voting rules, majority judgment satisfies the monotonicity criterion, the later-no-help criterion, and independence of irrelevant alternatives.
Like any deterministic voting system (except dictatorship), MJ allows for tactical voting in cases of more than three candidates, as a consequence of Gibbard's theorem.
Majority judgment voting fails the Condorcet criterion, later-no-harm,consistency, the Condorcet loser criterion, the participation criterion, the majority criterion, and the mutual majority criterion.
Unlike score voting, majority judgment can have no-show paradoxes, situations where a candidate loses because they won "too many votes". In other words, adding votes that rank a candidate higher than their opponent can still cause this candidate to lose.
In their 2010 book, Balinski and Laraki demonstrate that the only join-consistent methods are point-summing methods, a slight generalization of score voting that includes positional voting. Specifically, their result shows the only methods satisfying the slightly stronger consistency criterion have: