How to add apples and oranges: Aggregating performances of different nature

Abstract

We study a model where evaluation consists of multiple components of different nature and (cardinal) performances in all components are aggregated into a summary index between 0 and 1. We propose what we call the normalizer-based aggregation rules and characterize them by individual separability, monotonicity, anonymity, and component independence. Each member in this family is distinguished by three parameters: (i) a profile of weights that determines the relative importance of each component; (ii) a profile of “individual normalizers” that converts an agent's performance in each component into a raw score (for that component) in the normalized scale of [0,1]; and (iii) a profile of “group normalizers” that adjusts a raw score for each component relative to all agents' performances. Given these parameters, the overall evaluation, or score, of an agent is obtained as a weighted average of his adjusted scores for all components produced by individual and group normalizers.