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On constrained dual recoverability theorems

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  • Suzumura, Kotaro
  • Xu, Yongsheng

Abstract

In a recent paper ["Paretian Welfare Judgements and Bergsonian Social Choice," Economic Journal, Vol. 109, 1999, pp. 204-220], Suzumura proposed a possible way of relating the two schools of "new" welfare economics. According to his proposal, the logical possibility of the Paretian "new" welfare economics can be reduced to the constrained dual choice-functional recoverability of the Pareto-compatible Bergson-Samuelson social welfare ordering by means of the Pareto-compatible and consistent sub-relations thereof. He also identified the necessary and sufficient condition for this crucial property to hold. However, he posed but left open the problem of the constrained dual choice-functional recoverability of the Pareto-compatible Bergson-Samuelson social welfare ordering by means of the Pareto-compatible and transitive sub-relations thereof. The first purpose of this paper is to settle this open question. The second purpose of this paper is to pose and settle related problems of the constrained dual relational recoverability of the Pareto-compatible Bergson-Samuelson social welfare ordering by means of the Pareto-compatible and either consistent or transitive sub-relations thereof.
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Suggested Citation

  • Suzumura, Kotaro & Xu, Yongsheng, 2003. "On constrained dual recoverability theorems," Mathematical Social Sciences, Elsevier, vol. 45(2), pages 143-154, April.
  • Handle: RePEc:eee:matsoc:v:45:y:2003:i:2:p:143-154
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    References listed on IDEAS

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    1. Banerjee, Asis & Pattanaik, Prasanta K., 1996. "A note on a property of maximal sets and choice in the absence of universal comparability," Economics Letters, Elsevier, vol. 51(2), pages 191-195, May.
    2. Mishan, E J, 1980. "The New Welfare Economics: An Alternative View," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(3), pages 691-705, October.
    3. T. de Scitovszky, 1941. "A Note on Welfare Propositions in Economics," Review of Economic Studies, Oxford University Press, vol. 9(1), pages 77-88.
    4. Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro, 2002. "Upper semicontinuous extensions of binary relations," Journal of Mathematical Economics, Elsevier, vol. 37(3), pages 231-246, May.
    5. Jaffray, Jean-Yves, 1975. "Semicontinuous extension of a partial order," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 395-406, December.
    6. Suzumura, Kotaro, 1999. "Paretian Welfare Judgements and Bergsonian Social Choice," Economic Journal, Royal Economic Society, vol. 109(455), pages 204-220, April.
    7. Madden, Paul, 1996. "Suppes-Sen dominance, generalised Lorenz dominance and the welfare economics of competitive equilibrium: Some examples," Journal of Public Economics, Elsevier, vol. 61(2), pages 247-262, August.
    8. Suzumura, Kataro, 1976. "Remarks on the Theory of Collective Choice," Economica, London School of Economics and Political Science, vol. 43(172), pages 381-390, November.
    9. W. M. Gorman, 1955. "The Intransitivity Of Certain Criteria Used In Welfare Economics," Oxford Economic Papers, Oxford University Press, vol. 0(1), pages 25-34.
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    Cited by:

    1. Athanasios Andrikopoulos, 2011. "Characterization of the existence of semicontinuous weak utilities for binary relations," Theory and Decision, Springer, vol. 70(1), pages 13-26, January.
    2. Athanasios Andrikopoulos, 2007. "A representation of consistent binary relations," Spanish Economic Review, Springer;Spanish Economic Association, vol. 9(4), pages 299-307, December.

    More about this item

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D60 - Microeconomics - - Welfare Economics - - - General
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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