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Equity Principles and Interpersonal Comparison of Well-being: Old and New Joint Characterizations of Generalized Leximin, Rank-dependent Utilitarian, and Leximin Rules

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  • Sakamoto, Norihito

Abstract

This paper characterizes new efficient and equitable social welfare orderings when individual well-beings are fully interpersonal comparable. Previous studies show that social welfare orderings satisfying the axioms of strong Pareto, anonymity, separability, and minimal equity are either weak utilitarian or leximin rules. By dropping the separability axiom, this study shows that there are various classes of distribution-sensitive social welfare orderings. In fact, simply imposing rank-separability instead of separability enables a class of social welfare orderings satisfying the axioms of strong Pareto, anonymity, and Pigou-Dalton transfer equity to be a generalized leximin rule (a general distribution-sensitive rule including leximin, rank-dependent utilitarianism, and their lexicographic compositions). This result is proved by a simple method that is intuitive and easy to understand without the need for advanced mathematical techniques, such as functional analysis and the hyperplane separation theorem, which are often used in typical social choice analyses. Following this new proof, the mechanism by which a class of reasonable social welfare orderings satisfying separability is limited to weak utilitarian and leximin rules can be easily understood and proved. This study also shows the impossibility theorem between the axioms of equity and continuity. Based on the results of previous studies and this paper, theoretical relationships between interpersonal comparability of individual well-being and equality axioms are clarified. That is, if the interpersonal comparability of well-being is a cardinal unit or ratio one, then Paretian and anonymous social welfare orderings are limited to Kolm-Pollack or Atkinson social welfare functions. If it is the ordinal level comparability, the desirable rule must be leximin. If it is the cardinal full comparability, the generalized leximin should be used.

Suggested Citation

  • Sakamoto, Norihito, 2020. "Equity Principles and Interpersonal Comparison of Well-being: Old and New Joint Characterizations of Generalized Leximin, Rank-dependent Utilitarian, and Leximin Rules," RCNE Discussion Paper Series 7, Research Center for Normative Economics, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hit:rcnedp:7
    Note: First Draft, August 2019. This version, April 2020.
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    More about this item

    Keywords

    Social Welfare Ordering; Joint Characterization; Generalized Leximin;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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