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Concept
Majority judgment
Summary
Majority judgment (MJ) is a single-winner voting system proposed in 2010 by Michel Balinski and Rida Laraki. It uses a highest median rule, i.e., a cardinal voting system that elects the candidate with the highest median rating.
Unlike other voting methods, MJ guarantees that the winner between three or more candidates will be the candidate who had received an absolute majority of the highest grades given by all the voters.
Voters grade as many of the candidates' as they wish with regard to their suitability for office as either Excellent (ideal), Very Good, Good, Acceptable, Poor, or Reject. Multiple candidates may be given the same grade by a voter. Any candidate not explicitly graded by a voter is counted as having been rejected by the voter. Therefore, each candidate receives the same total number of grades, but a different distribution of them.
The candidate with the highest median grade is the winner. This median-grade can be found as follows: Place all the grades, high to low, top to bottom, in side-by-side columns, the name of each candidate at the top of each of these columns. The median-grade for each candidate is the grade located halfway down each column, i.e. in the middle if there is an odd number of voters, the lower middle if the number is even. If more than one candidate has the same highest median-grade, the MJ winner is discovered by removing (one-by-one) any grades equal in value to the shared median grade from each tied candidate's column. This is repeated until only one of the previously tied candidates is currently found to have the highest median grade. Equivalently, the candidates can be ranked according to a simple mathematical formula described on the page: highest median voting rules.
As it is a highest median rule, MJ produces more informative results than the existing alternatives. It is true that if only one of two candidates is to be elected, and the winner has only a few votes more than the near winner, MJ and all the alternative voting methods would discover the same winner.
Official source
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