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Old and new joint characterizations of leximin and variants of rank-weighted utilitarianism

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  • Norihito Sakamoto

Abstract

This paper proposes a new class of efficient and equitable social welfare orderings, a generalized leximin rule that includes rank-weighted utilitarianism, leximin, and their lexicographic compositions. While the famous Deschamps and Gevers’ joint characterization theorem shows that a Paretian, anonymous, separable social welfare ordering must be either weak utilitarianism, leximin, or leximax under the assumption of cardinal full comparability, this study provides a new joint characterization theorem in which imposing rank-separability, instead of separability, enables acceptable social welfare ordering to be the generalized leximin rule. This result is proven by an intuitive and easy-to-understand method, which also helps show the mechanism by which a class of Paretian, anonymous, and separable social welfare orderings is limited to weak utilitarianism and leximin.

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  • Norihito Sakamoto, 2024. "Old and new joint characterizations of leximin and variants of rank-weighted utilitarianism," PLOS ONE, Public Library of Science, vol. 19(1), pages 1-10, January.
    • Handle: RePEc:plo:pone00:0296351
    DOI: 10.1371/journal.pone.0296351
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    References listed on IDEAS

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    1. Tungodden, Bertil, 2000. "Egalitarianism: Is Leximin the Only Option?," Economics and Philosophy, Cambridge University Press, vol. 16(2), pages 229-245, October.
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    4. Sen, Amartya K, 1977. "On Weights and Measures: Informational Constraints in Social Welfare Analysis," Econometrica, Econometric Society, vol. 45(7), pages 1539-1572, October.
    5. Kevin W. S. Roberts, 1980. "Possibility Theorems with Interpersonally Comparable Welfare Levels," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(2), pages 409-420.
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