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The Aggregation of Individual Distributive Preferences through the Distributive Liberal Social Contract : Normative Analysis

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  • Jean Mercier-Ythier
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    Abstract

    We consider abstract social systems of private property, made of n individuals endowed with non-paternalistic interdependent preferences, who interact through exchanges on competitive markets and Pareto-efficient lumpsum transfers. The transfers follow from a distributive liberal social contract defined as a redistribution of initial endowments such that the resulting market equilibrium allocation is both Pareto-efficient relative to individual interdependent preferences, and unanimously weakly preferred to the initial market equilibrium. We notably elicit two global properties of Pareto-efficient redistribution in smooth differentiable social systems of the type above. The first one is the separability of allocation and distribution: Pareto-efficient redistribution leaves unaltered the role of market prices in the coordination of market exchanges, as expressed, notably, by the existence and efficiency properties of competitive equilibrium. The second one is the global structure of the set of Pareto-efficient allocations: its relative interior is a simply connected smooth manifold of dimension n-1, homeomorphic to the relative interior of the unit-simplex of Rn. Both properties obtain under three suitable conditions on the partial preordering of Pareto associated with individual interdependent preferences, which essentially state that: the social utility functions built from weighted sums of individual interdependent utilities, by means of arbitrary positive weights, exhibit a property of differentiable nonsatiation and some suitably defined property of inequality aversion; and individuals have diverging views on redistribution, in some suitable sense, at (inclusive) distributive optima. The set of market equilibrium allocations associated with the transfers of the inclusive distributive liberal social contracts then consists of the maxima, in the set of attainable allocations unanimously weakly preferred to the initial market equilibrium, of the weighted sums of individual interdependent utilities derived from arbitrary vectors of positive weights of R++ n. Its relative interior is a simply connected smooth manifold of dimension n-1 whenever the initial market equilibrium is not Paretoefficient relative to individual interdependent preferences. It is shown, finally, that the liberal social contract’s inclusive solutions for redistribution, so characterized, maximize a family of social welfare functionals that verify Arrow’s non-dictatorship axiom and Sen’s liberty axiom for the social systems to which it applies.

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    Paper provided by Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg in its series Working Papers of BETA with number 2010-01.

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    Date of creation: 2010
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    Handle: RePEc:ulp:sbbeta:2010-01

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    Keywords: Walrasian equilibrium; Pareto-efficiency; liberal social contract; social preferences; social choice; allocation; distribution.;

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    1. Sen, Amartya, 1970. "The Impossibility of a Paretian Liberal," Journal of Political Economy, University of Chicago Press, vol. 78(1), pages 152-57, Jan.-Feb..
    2. Sen, Amartya Kumar, 1970. "The Impossibility of a Paretian Liberal," Scholarly Articles 3612779, Harvard University Department of Economics.
    3. Jean Mercier Ythier, 2004. "A limit theorem on the dual core of a distributive social system," Social Choice and Welfare, Springer, vol. 22(1), pages 147-174, 02.
    4. Kolm, Serge-Christophe, 2006. "Reciprocity: Its Scope, Rationales, and Consequences," Handbook on the Economics of Giving, Reciprocity and Altruism, Elsevier.
    5. Levy-Garboua, Louis & Meidinger, Claude & Rapoport, Benoit, 2006. "The Formation of Social Preferences: Some Lessons from Psychology and Biology," Handbook on the Economics of Giving, Reciprocity and Altruism, Elsevier.
    6. Rader, Trout, 1980. "The second theorem of welfare economics when utilities are interdependent," Journal of Economic Theory, Elsevier, vol. 23(3), pages 420-424, December.
    7. Mercier Ythier, Jean, 2006. "The Economic Theory of Gift-Giving: Perfect Substitutability of Transfers and Redistribution of Wealth," Handbook on the Economics of Giving, Reciprocity and Altruism, Elsevier.
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