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Arrow’s Impossibility Theorem: Preference Diversity in a Single-Profile World

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  • Allan M. Feldman
  • Roberto Serrano

Abstract

In this paper we provide a simple new version of Arrow’s impossibility theorem, in a world with only one preference profile. This theorem relies on a new assumption of preference diversity, and we explore alternative notions of preference diversity at length.

Suggested Citation

  • Allan M. Feldman & Roberto Serrano, 2007. "Arrow’s Impossibility Theorem: Preference Diversity in a Single-Profile World," Working Papers wp2007_0710, CEMFI.
  • Handle: RePEc:cmf:wpaper:wp2007_0710
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    References listed on IDEAS

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    1. Robert P. Parks, 1976. "An Impossibility Theorem for Fixed Preferences: A Dictatorial Bergson-Samuelson Welfare Function," Review of Economic Studies, Oxford University Press, vol. 43(3), pages 447-450.
    2. Kevin W. S. Roberts, 1980. "Social Choice Theory: The Single-profile and Multi-profile Approaches," Review of Economic Studies, Oxford University Press, vol. 47(2), pages 441-450.
    3. Bossert, Walter & Suzumura, Kotaro, 2008. "A characterization of consistent collective choice rules," Journal of Economic Theory, Elsevier, vol. 138(1), pages 311-320, January.
    4. Marc Fleurbaey & Philippe Mongin, 2005. "The news of the death of welfare economics is greatly exaggerated," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 381-418, December.
    5. 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.
    6. Reny, Philip J., 2001. "Arrow's theorem and the Gibbard-Satterthwaite theorem: a unified approach," Economics Letters, Elsevier, vol. 70(1), pages 99-105, January.
    7. Blau, Julian H & Deb, Rajat, 1977. "Social Decision Functions and the Veto," Econometrica, Econometric Society, vol. 45(4), pages 871-879, May.
    8. Abram Burk, 1938. "A Reformulation of Certain Aspects of Welfare Economics," The Quarterly Journal of Economics, Oxford University Press, vol. 52(2), pages 310-334.
    9. Robert A. Pollak, 1979. "Bergson-Samuelson Social Welfare Functions and the Theory of Social Choice," The Quarterly Journal of Economics, Oxford University Press, vol. 93(1), pages 73-90.
    10. Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
    11. Samuelson, Paul A, 1977. "Reaffirming the Existence of "Reasonable" Bergson-Samuelson Social Welfare Functions," Economica, London School of Economics and Political Science, vol. 44(173), pages 81-88, February.
    12. Kemp, Murray C & Ng, Yew-Kwang, 1976. "On the Existence of Social Welfare Functions, Social Orderings and Social Decision Functions," Economica, London School of Economics and Political Science, vol. 43(169), pages 59-66, February.
    13. Campbell, Donald E. & Kelly, Jerry S., 2002. "Impossibility theorems in the arrovian framework," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 1, pages 35-94 Elsevier.
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    Cited by:

    1. Yusuke Kamishiro & Roberto Serrano, 2011. "Equilibrium Blocking in Large Quasilinear Economies," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 552-567, August.
    2. Roberto Serrano, 2009. "On Watson's Non-Forcing Contracts and Renegotiation," Economics Bulletin, AccessEcon, vol. 29(3), pages 2350-2360.
    3. Jamal Nazrul Islam & Haradhan Kumar Mohajan & Pahlaj Moolio, 2009. "Preference of Social Choice in Mathematical Economics," Indus Journal of Management & Social Science (IJMSS), Department of Business Administration, vol. 3(1), pages 18-38, June.
    4. Rafael Repullo & Javier Suarez, 2008. "The Procyclical Effects of Basel II," Working Papers wp2008_0809, CEMFI.
    5. Max Bruche, 2009. "Bankruptcy Codes, Liquidation Timing, and Debt Valuation," Working Papers wp2009_0902, CEMFI.
    6. Joan Llull, 2008. "The Impact of Immigration on Productivity," Working Papers wp2008_0802, CEMFI.
    7. David Martinez-Miera & Rafael Repullo, 2010. "Does Competition Reduce the Risk of Bank Failure?," Review of Financial Studies, Society for Financial Studies, vol. 23(10), pages 3638-3664, October.
    8. Manuel Arellano & Lars Peter Hansen & Enrique Sentana, 2009. "Underidentification? (Resumen)," Working Papers wp2009_0905, CEMFI.
    9. Serrano, Roberto & Vohra, Rajiv, 2010. "Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 775-785, September.

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