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Ranking Rankings: An Axiomatic Analysis

Author

Listed:
  • Eric Rémila

    (UJM EPE - Université Jean Monnet (EPSCPE))

  • Philippe Solal

    (UJM EPE - Université Jean Monnet (EPSCPE))

  • Zoi Terzopoulou

    (UJM EPE - Université Jean Monnet (EPSCPE))

Abstract

Various occasions require that an individual ranks others in her environment based on how these others rank her; consider a company that seeks an employee who values her back, and a student that works better with a professor who also appreciates her strengths. We introduce a formal framework for the ranking of rankings. A set of objects are weakly ranked by a set of items, and a given object (e.g., the company or the student) must obtain a weak ranking of the items (e.g., all employees or all professors) that depends on their provided rankings of the objects. To conduct an axiomatic analysis of this setting, we propose several normative properties that apply to solutions for the ranking of rankings. Our axioms are inspired by analogous properties in the fields of decision and social choice theory, such as anonymity, monotonicity, and independence. By considering combinations of different axioms, we characterise natural families of solutions, as well as unique solutions therein: lexicographic solutions, and a scoring one.

Suggested Citation

  • Eric Rémila & Philippe Solal & Zoi Terzopoulou, 2025. "Ranking Rankings: An Axiomatic Analysis," Post-Print hal-05395399, HAL.
    • Handle: RePEc:hal:journl:hal-05395399
    DOI: 10.1007/s11238-025-10027-1
    Note: View the original document on HAL open archive server: https://hal.science/hal-05395399v1
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    References listed on IDEAS

    as
    1. Kelly, Jerry S, 1977. "Strategy-Proofness and Social Choice Functions without Singlevaluedness," Econometrica, Econometric Society, vol. 45(2), pages 439-446, March.
    2. William Thomson, 2001. "On the axiomatic method and its recent applications to game theory and resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(2), pages 327-386.
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