Open AccessRanking by rating
Author(s) -
Sprumont Yves
Publication year - 2018
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te2446
Subject(s) - ranking (information retrieval) , monotonic function , axiom , consistency (knowledge bases) , mathematics , separable space , rank (graph theory) , invariant (physics) , set (abstract data type) , discrete mathematics , computer science , combinatorics , artificial intelligence , mathematical analysis , geometry , mathematical physics , programming language
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.