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Impossibility theorems in the arrovian framework

In: Handbook of Social Choice and Welfare

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  • Campbell, Donald E.
  • Kelly, Jerry S.
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    Abstract

    Given a set of outcomes that affect the welfare of the members of a group, K.J. Arrow imposed the following five conditions on the ordering of the outcomes as a function of the preferences of the individual group members, and then proved that the conditions are logically inconsistent:- The social choice rule is defined for a large family of assignments of transitive orderings to individuals.- The social ordering itself is always transitive.- The social choice rule is not dictatorial. (An individual is a dictator if the social ordering ranks an outcome x strictly above another outcome y whenever that individual strictly prefers x to y.)- If everyone in the group strictly prefers outcome x to outcome y, then x should rank strictly above y in the social ordering.- The social ordering of any two outcomes depends only on the way that the individuals in the group order those same two outcomes.The chapter proves Arrow's theorem and investigates the possibility of uncovering a satisfactory social choice rule by relaxing the conditions while remaining within the Arrovian framework, which is identified by the following five characteristics:- The outcome set is unstructured.- The society is finite and fixed.- Only information about the ordering of the outcome set is used to convey information about individual welfare.- The output of the social choice process is an ordering of the outcome set.- Strategic play by individuals is not considered.

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    This chapter was published in:

  • K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2002. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 1, number 1.
    This item is provided by Elsevier in its series Handbook of Social Choice and Welfare with number 1-01.

    Handle: RePEc:eee:socchp:1-01

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    Cited by:
    1. Christian List & Ben Polak, 2010. "Introduction to judgment aggregation," LSE Research Online Documents on Economics 27900, London School of Economics and Political Science, LSE Library.
    2. Roberto Serrano & Allan M. Feldman, 2007. "Arrow’S Impossibility Theorem: Preference Diversity In A Single-Profile World," Working Papers wp2007_0710, CEMFI.
    3. Brandt, Felix & Harrenstein, Paul, 2011. "Set-rationalizable choice and self-stability," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1721-1731, July.
    4. Allan M. Feldman & Roberto Serrano, 2007. "Arrow's impossibility theorem: Two simple single-profile versions," Working Papers 2007-07, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    5. Donald Campbell & Jerry Kelly, 2007. "Pareto, anonymity, and independence: four alternatives," Social Choice and Welfare, Springer, vol. 29(1), pages 83-104, July.
    6. Kant, Shashi & Lee, Susan, 2004. "A social choice approach to sustainable forest management: an analysis of multiple forest values in Northwestern Ontario," Forest Policy and Economics, Elsevier, vol. 6(3-4), pages 215-227, June.
    7. Susumu Cato, 2013. "Social choice, the strong Pareto principle, and conditional decisiveness," Theory and Decision, Springer, vol. 75(4), pages 563-579, October.
    8. Michel Le Breton & John A. Weymark, 2002. "Arrovian Social Choice Theory on Economic Domains," Vanderbilt University Department of Economics Working Papers 0206, Vanderbilt University Department of Economics, revised Sep 2003.
    9. Christian List & Ben Polak, 2010. "Introduction to Judgment Aggregation," Levine's Working Paper Archive 661465000000000006, David K. Levine.
    10. Donald E. Campbell & Jerry S. Kelly, 2006. "Pareto, Anonymity, and Independence: Four Alternatives," Working Papers 39, Department of Economics, College of William and Mary.
    11. Donald E. Campbell & Jerry S. Kelly, 2006. "Social Welfare Functions that Satisfy Pareto, Anonymity, and Neutrality, but not IIA," Working Papers 38, Department of Economics, College of William and Mary.
    12. Allan M. Feldman & Roberto Serrano, 2006. "Darwinian Arrow's Impossibility Theorem: Two Simple Single-Profile Versions," Working Papers 2006-11, Brown University, Department of Economics.
    13. Allan M Feldman & Roberto Serrano, 2008. "Arrow's Impossibility Theorem: Preference Diversity in a Single-Profile World," Working Papers 2008-8, Brown University, Department of Economics.
    14. Donald E. Campbell & Jerry S. Kelly, 2007. "Uniformly Bounded Information and Social Choice," Working Papers 49, Department of Economics, College of William and Mary.
    15. Mariotti, Marco & Veneziani, Roberto, 2013. "On the impossibility of complete Non-Interference in Paretian social judgements," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1689-1699.
    16. Prof. Dr. Bernd Meyer & Gerd Ahlert & Roland Zieschank & Prof. Dr. Hans Diefenbacher, 2012. "Grundstrukturen eines nachhaltigen Wohlfahrtsmodells und Implikationen für die Politik," GWS Discussion Paper Series 12-6, GWS - Institute of Economic Structures Research.

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