Majority Judgment

Majority judgment is a single-winner voting system proposed by Michel Balinski and Rida Laraki. Voters freely grade each candidate in one of several named ranks, for instance from "excellent" to "bad", and the candidate with the highest median grade is the winner. If more than one candidate has the same median grade, a tiebreaker is used which sees the "closest to median" grade. Majority judgment can be considered as a form of Bucklin voting which allows equal ranks.

Voters are allowed rated ballots, on which they may assign a grade or judgment to each candidate. Balinski and Laraki suggest six grading levels, from "Excellent" to "Reject", as used in some French schools. Multiple candidates may be given the same grade if the voter wants to.

The median grade for each candidate is found, for instance by sorting their list of grades and finding the middle one. If the middle falls between two different grades, the lower of the two is used. The candidate with the highest median grade wins.

If several candidates share the highest median grade, all other candidates are eliminated. Then, one copy of that grade is removed from each remaining candidate's list of grades, and the new median is found, until there is an unambiguous winner. For instance, if candidate X's sorted ratings were ("Good", "Good", "Fair", "Poor"), while candidate Y had ("Excellent", "Fair", "Fair", "Fair"), the rounded medians would both be "Fair". After removing one "Fair" from each list, the new lists are, respectively, ("Good", "Good", "Poor") and ("Excellent", "Fair", "Fair"), so X would win with a recalculated median of "Good". To help communicate how this tiebreaker works, a plus sign or minus sign can be added to the median of each candidate, depending on whether the median would eventually rise or fall if the tiebreaker were applied to them.

Majority judgment voting satisfies the majority criterion for rated ballots, the mutual majority criterion, the monotonicity criterion, and later-no-help. By assuming that ratings are given independently of other candidates, it satisfies the independence of clones criterion and the independence of irrelevant alternatives criterion, but the latter criterion is incompatible with the majority criterion if voters shift their judgments in order to express their preferences between the available candidates.

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