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

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  • Cho, Wonki Jo

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.

Suggested Citation

  • Cho, Wonki Jo, 2022. "How to add apples and oranges: Aggregating performances of different nature," Games and Economic Behavior, Elsevier, vol. 131(C), pages 222-244.
    • Handle: RePEc:eee:gamebe:v:131:y:2022:i:c:p:222-244
    DOI: 10.1016/j.geb.2021.11.005
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    Cited by:

    1. Martínez, Ricardo & Moreno-Ternero, Juan D., 2022. "An axiomatic approach towards pandemic performance indicators," Economic Modelling, Elsevier, vol. 116(C).
    2. Cho, Wonki Jo & Moreno-Ternero, Juan D., 2024. "On reaching social consent," Journal of Mathematical Economics, Elsevier, vol. 110(C).

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    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D89 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Other

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