Theoretical Economics
Journal of the Econometric Society
Edited by: Federico Echenique • ISSN (e): 1555-7561 • ISSN (print): 1933-6837
Edited by: Federico Echenique • ISSN (e): 1555-7561 • ISSN (print): 1933-6837
Theoretical Economics: Jan, 2018, Volume 13, Issue 1
https://doi.org/10.3982/TE2446
p. 1-18
Ranking by Rating consists in evaluating the performances of items using exogenous rating functions, and ranking these 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. When performances belong to a finite set, ranking by rating is characterized by separability and a property of 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₊^{m}, a separable, symmetric, monotonic, continuous, and invariant method must rank items according to a weighted geometric mean of their performances along the m dimensions.