Highest median voting rules

Highest median voting rules are cardinal voting rules, where the winning candidate is a candidate with the highest median rating. As these employ ratings, each voter rates the different candidates on a numerical or verbal scale.

The various highest median rules differ in their treatment of ties, i.e., the method of ranking the candidates with the same median rating.

Proponents of highest median rules argue that they provide the most faithful reflection of the voters' opinion. They cite theorems showing that minimizes the share of voters with an incentive to vote strategically. They note that as with other cardinal voting rules, highest medians are not subject to Arrow's impossibility theorem, and so can satisfy both independence of irrelevant alternatives and Pareto efficiency.

However, critics note that highest median rules violate participation and fail the majority criterion. Highest median methods can sometimes fail to elect a candidate who is almost-unanimously preferred over all other candidates.