Majority judgment

[6] Specifically, their result shows the only methods satisfying the slightly stronger consistency criterion have:

[7] This result is closely related to and relies on the Von Neumann–Morgenstern utility theorem and Harsanyi's utilitarian theorem, two critical results in social choice theory and decision theory used to characterize the conditions for rational choice.

Despite this result, Balinski and Laraki claim that participation failures would be rare in practice for majority judgment.

[8] However, some writers have disputed the significance of these results, as they do not apply in cases of imperfect information or collusion between voters.

[citation needed] In "left-right" environments, majority judgment tends to favor the most homogeneous camp, instead of picking the middle-of-the-road, Condorcet winner candidate.

In so doing, the majority judgment elects the best compromise for voters on the left side of the political axis (as they are slightly more numerous than those on the right) instead of choosing a more consensual candidate such as the center-left or the center.

These methods, introduced more recently, maintain many desirable properties of majority judgment while avoiding the pitfalls of its tie-breaking procedure.

Since there is a tie between Nashville, Chattanooga, and Knoxville, "Fair" ratings are removed from all three, until their medians become different.

The somewhat-related median voting rule method was first explicitly proposed to assign budgets by Francis Galton in 1907.

[12] Hybrid mean/median systems based on the trimmed mean have long been used to assign scores in contests such as Olympic figure skating, where they are intended to limit the impact of biased or strategic judges.

The first highest median rule to be developed was Bucklin voting, a system used by Progressive Era reformers in the United States.

Although this regional poll was not intended to be representative of the national result, it agreed with other local or national experiments in showing that François Bayrou, rather than the eventual runoff winner, Nicolas Sarkozy, or two other candidates (Ségolène Royal or Jean-Marie Le Pen) would have won under most alternative rules, including majority judgment.

They also note: Everyone with some knowledge of French politics who was shown the results with the names of Sarkozy, Royal, Bayrou and Le Pen hidden invariably identified them: the grades contain meaningful information.