Ranking by rating

Each item in a given collection is characterized by a set of possible performances. A (ranking) method is a function that assigns an ordering of the items to every performance profile. Ranking by Rating consists in evaluating each item’s performance by using an exogenous rating function, and ranking items according to their performance ratings. Any such method is separable: the ordering of two items does not depend on the performances of the remaining items. Consistency requires that if a change in an item’s performance improves its relative ranking against some other item at a given profile, the same change never decreases its relative ranking against any item at any profile. When performances belong to a finite set, ranking by rating is characterized by Separability and Consistency; this characterization generalizes to the infinite case under a continuity axiom. Consistency follows from Separability and Symmetry, or from Monotonicity alone. When performances are vectors in R+ , a separable, symmetric, monotonic, continuous, and invariant method must rank items according to a weighted geometric mean of their performances along the m dimensions. JEL Classification: D71, D89.