Application of The Majority Criterion: Controversy
The majority criterion was initially defined with respect to voting systems based only on preference order. It is ambiguous how to apply it to systems with absolute rating categories such as Approval, Range, and Majority Judgment.
For approval voting, the difficulty is that the criterion refers to an exclusive preference, and it is unstated whether this preference is actually indicated on the ballot or not. The common simple statement of the criterion, as given in the introduction to this article, does not resolve this, for the word "prefer" can refer to a mental state or to an action; a complete statement of the criterion would either refer to actual marks on the ballot showing the required preference, or it could refer to the mental state of the voters. Since an approval voting ballot, for example, allows a voter to conceal the necessary exclusive preference without voting insincerely, the method cannot determine a majority preference based on what is not shown on the ballot. Thus, if "prefer" means an action, approval voting passes this criterion; if it means a mental state, approval voting does not pass.
For Majority Judgment, the difficulty is different. There are presumed to be enough rating categories to express any salient mental preference. If the word "prefer" is interpreted in a relative sense, as rating the preferred candidate above any other candidate, the method does not pass, even with only two candidates; If the word "prefer" is interpreted in an absolute sense, as rating the preferred candidate with the highest available rating then it does if there are moreover no ties.
Although the criterion's exact definition with respect to Range voting is unclear, the result is not: unstrategic Range voting does not pass this criterion under any definition.
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