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Arrovian aggregation in economic environments: How much should we know about indifference surfaces?

Author

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  • Marc Fleurbaey

    () (CERSES - UMR 8137 - Centre de recherche sens, ethique, société - UPD5 - Université Paris Descartes - Paris 5 - CNRS - Centre National de la Recherche Scientifique)

  • Kotaro Suzumura
  • Koichi Tadenuma

Abstract

Arrow's celebrated theorem of social choice shows that the aggregation of individual preferences into a social ordering cannot make the ranking of any pair of alternatives depend only on individual preferences over that pair, unless the fundamental weak Pareto and non-dictatorship principles are violated. In the standard model of division of commodities, we investigate how much information about indifference hypersurfaces is needed to construct social ordering functions satisfying the weak Pareto principle and anonymity. We show that local information such as marginal rates of substitution or the shapes "within the Edgeworth box" is not enough, and knowledge of substantially non-local information is necessary.

Suggested Citation

  • Marc Fleurbaey & Kotaro Suzumura & Koichi Tadenuma, 2005. "Arrovian aggregation in economic environments: How much should we know about indifference surfaces?," Post-Print hal-00246987, HAL.
  • Handle: RePEc:hal:journl:hal-00246987
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00246987
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    References listed on IDEAS

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    1. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58, pages 328-328.
    2. Kevin W. S. Roberts, 1980. "Interpersonal Comparability and Social Choice Theory," Review of Economic Studies, Oxford University Press, vol. 47(2), pages 421-439.
    3. Tadenuma, Koichi, 2002. "Efficiency First or Equity First? Two Principles and Rationality of Social Choice," Journal of Economic Theory, Elsevier, vol. 104(2), pages 462-472, June.
    4. M. Fleurbaey & F. Maniquet, 2000. "Fair Social Orderings With Unequal Production Skills," THEMA Working Papers 2000-17, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
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    6. Dirk Van de gaer & Marc Fleurbaey & Walter Bossert, 1999. "Responsibility, talent, and compensation: A second-best analysis," Review of Economic Design, Springer;Society for Economic Design, vol. 4(1), pages 35-55.
    7. Suzumura, Kotaro, 1981. "On pareto-efficiency and the no-envy concept of equity," Journal of Economic Theory, Elsevier, vol. 25(3), pages 367-379, December.
    8. M. Fleurbaey & F. Maniquet, 2008. "Fair social orderings," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(1), pages 25-45, January.
    9. Ehud Kalai & Eitan Muller & Mark Satterthwaite, 1979. "Social welfare functions when preferences are convex, strictly monotonic, and continuous," Public Choice, Springer, vol. 34(1), pages 87-97, March.
    10. Elisha A. Pazner & David Schmeidler, 1978. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," The Quarterly Journal of Economics, Oxford University Press, vol. 92(4), pages 671-687.
    11. Claude D'Aspremont & Louis Gevers, 1977. "Equity and the Informational Basis of Collective Choice," Review of Economic Studies, Oxford University Press, vol. 44(2), pages 199-209.
    12. Bordes, Georges & Breton, Michel Le, 1989. "Arrovian theorems with private alternatives domains and selfish individuals," Journal of Economic Theory, Elsevier, vol. 47(2), pages 257-281, April.
    13. Suzumura, Kotaro, 1981. "On the Possibility of "Fair" Collective Choice Rule," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(2), pages 351-364, June.
    14. Marc Fleurbaey & Maurice Salles & John Weymark, 2008. "Justice, Political Liberalism and Utilitarianism," Post-Print hal-00246415, HAL.
    15. Hammond, Peter J, 1976. "Equity, Arrow's Conditions, and Rawls' Difference Principle," Econometrica, Econometric Society, vol. 44(4), pages 793-804, July.
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    Cited by:

    1. VALLETTA, Giacomo, 2012. "Health, fairness and taxation," CORE Discussion Papers 2012016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Marc Fleurbaey, 2003. "Social Welfare, Priority to the Worst-Off And the Dimensions of Individual Well-Being," IDEP Working Papers 0312, Institut d'economie publique (IDEP), Marseille, France.
    3. BOSSERT, Walter & WEYMARK, J.A., 2006. "Social Choice: Recent Developments," Cahiers de recherche 01-2006, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    4. Jean-François Laslier, 2004. "Strategic Approval Voting in a large electorate," Working Papers hal-00242909, HAL.
    5. Susumu Cato, 2016. "Weak independence and the Pareto principle," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 295-314, August.
    6. SPRUMONT, Yves, 2009. "Relative Egalitarianism and Related Criteria," Cahiers de recherche 2009-02, Universite de Montreal, Departement de sciences economiques.
    7. Daniel J. Benjamin & Ori Heffetz & Miles S. Kimball & Nichole Szembrot, 2013. "Aggregating Local Preferences to Guide Marginal Policy Adjustments," American Economic Review, American Economic Association, vol. 103(3), pages 605-610, May.
    8. Christopher Chambers & Takashi Hayashi, 2012. "Money-metric utilitarianism," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 809-831, October.
    9. Campbell, Donald E. & Kelly, Jerry S., 2009. "Uniformly bounded information and social choice," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 415-421, July.
    10. Donald E. Campbell & Jerry S. Kelly, 2007. "Uniformly Bounded Information and Social Choice," Working Papers 49, Department of Economics, College of William and Mary.
    11. Valletta Giacomo, 2012. "Health, Fairness and Taxation," Research Memorandum 017, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    12. Marc Fleurbaey & Koichi Tadenuma, 2007. "Do Irrelevant Commodities Matter?," Econometrica, Econometric Society, vol. 75(4), pages 1143-1174, July.
    13. Marc Fleurbaey & Guillaume Gaulier, 2009. "International Comparisons of Living Standards by Equivalent Incomes," Scandinavian Journal of Economics, Wiley Blackwell, vol. 111(3), pages 597-624, September.
    14. Susumu Cato, 2014. "Independence of irrelevant alternatives revisited," Theory and Decision, Springer, vol. 76(4), pages 511-527, April.
    15. Fleurbaey, Marc, 2006. "Is commodity taxation unfair?," Journal of Public Economics, Elsevier, vol. 90(10-11), pages 1765-1787, November.
    16. M. Fleurbaey & F. Maniquet, 2008. "Fair social orderings," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(1), pages 25-45, January.
    17. Mohamed Mabrouk, 2005. "Intergenerational anonymity as an alternative to the discounted- sum criterion in the calculus of optimal growth II: Pareto optimality and some economic interpretations," GE, Growth, Math methods 0511007, EconWPA.
    18. repec:spr:sochwe:v:50:y:2018:i:2:d:10.1007_s00355-017-1085-1 is not listed on IDEAS
    19. Mohamed Mabrouk, 2005. "Intergenerational anonymity as an alternative to the discounted- sum criterion in the calculus of optimal growth I: Consensual optimality," GE, Growth, Math methods 0510013, EconWPA.
    20. Dan Qin, 2014. "Refining the Information Function Method: Instrument and Application," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 8(2), pages 84-101, October.
    21. Mabrouk, Mohamed, 2006. "Allais-anonymity as an alternative to the discounted-sum criterion in the calculus of optimal growth I: Consensual optimality," MPRA Paper 10512, University Library of Munich, Germany.
    22. Sakai, Toyotaka, 2009. "Walrasian social orderings in exchange economies," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 16-22, January.
    23. Giacomo Valletta, 2014. "Health, fairness and taxation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(1), pages 101-140, June.
    24. Dan Qin, 2015. "On $$\mathcal {S}$$ S -independence and Hansson’s external independence," Theory and Decision, Springer, vol. 79(2), pages 359-371, September.

    More about this item

    Keywords

    social choice; independence of irrelevant alternatives;

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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