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An extension of Majority Judgment to non-uniform qualitative scales

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  • García-Lapresta, José Luis
  • Marques Pereira, Ricardo Alberto

Abstract

We consider the context of social choice in which individual evaluations of the alternatives are expressed over an ordered qualitative scale. We propose to extend the framework of Majority Judgment to the case of non-uniform ordered qualitative scales, described by an ordinal proximity measure. The central construct in our model is a weak order defined over multisets of ordinal proximity degrees. On the basis of this weak order, each alternative profile is represented by an ordinal mean which balances the multisets of ordinal proximity degrees associated with the upper and lower ordinal evaluations. The procedure for ranking the alternative profiles consists primarily in comparing means, plus a tie-breaking scheme in which the weak order plays once more an important role.

Suggested Citation

  • García-Lapresta, José Luis & Marques Pereira, Ricardo Alberto, 2022. "An extension of Majority Judgment to non-uniform qualitative scales," European Journal of Operational Research, Elsevier, vol. 301(2), pages 667-674.
    • Handle: RePEc:eee:ejores:v:301:y:2022:i:2:p:667-674
    DOI: 10.1016/j.ejor.2021.11.002
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    References listed on IDEAS

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    1. Ngoie, Ruffin-Benoît M. & Savadogo, Zoïnabo & Ulungu, Berthold E.-L., 2014. "Median and average as tools for measuring, electing and ranking: new prospects," MPRA Paper 64731, University Library of Munich, Germany, revised 01 Sep 2014.
    2. Michel Balinski & Rida Laraki, 2020. "Majority judgment vs. majority rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 429-461, March.
    3. García-Lapresta, José Luis & González del Pozo, Raquel, 2019. "An ordinal multi-criteria decision-making procedure under imprecise linguistic assessments," European Journal of Operational Research, Elsevier, vol. 279(1), pages 159-167.
    4. Adrien Fabre, 2021. "Tie-breaking the highest median: alternatives to the majority judgment," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(1), pages 101-124, January.
    5. Michel Balinski & Rida Laraki, 2011. "Election by Majority Judgment: Experimental Evidence," Studies in Public Choice, in: Bernard Dolez & Bernard Grofman & Annie Laurent (ed.), In Situ and Laboratory Experiments on Electoral Law Reform, chapter 0, pages 13-54, Springer.
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    9. Michel Balinski & Rida Laraki, 2020. "Majority judgment vs. majority rule," Post-Print hal-03070420, HAL.
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