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The limitations of the Arrovian consistency of domains with a fixed preference

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  • James Nguyen

    (University College London
    University of London
    London School of Economics and Political Science)

Abstract

In this paper I investigate the properties of social welfare functions defined on domains where the preferences of one agent remain fixed. Such a domain is a degenerate case of those investigated, and proved Arrow consistent, by Sakai and Shimoji (Soc Choice Welf 26(3):435–445, 2006). Thus, they admit functions from them to a social preference that satisfy Arrow’s conditions of Weak Pareto, Independence of Irrelevant Alternatives, and Non-dictatorship. However, I prove that according to any function that satisfies these conditions on such a domain, for any triple of alternatives, if the agent with the fixed preferences does not determine the social preference on any pair of them, then some other agent determines the social preference on the entire triple.

Suggested Citation

  • James Nguyen, 2019. "The limitations of the Arrovian consistency of domains with a fixed preference," Theory and Decision, Springer, vol. 87(2), pages 183-199, September.
    • Handle: RePEc:kap:theord:v:87:y:2019:i:2:d:10.1007_s11238-019-09702-x
    DOI: 10.1007/s11238-019-09702-x
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    References listed on IDEAS

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    1. Le Breton, Michel & Weymark, John A., 2011. "Chapter Seventeen - Arrovian Social Choice Theory on Economic Domains," 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 2, chapter 17, pages 191-299, Elsevier.
    2. Gaertner,Wulf, 2006. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521028745.
    3. Gaertner,Wulf, 2001. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521791021.
    4. Serge-Christophe Kolm, 1996. "Rational Just Social Choice," International Economic Association Series, in: Kenneth J. Arrow & Amartya Sen & Kotaro Suzumura (ed.), Social Choice Re-Examined, chapter 14, pages 167-196, Palgrave Macmillan.
    5. Marc Fleurbaey & Maurice Salles & John A. Weymark (ed.), 2011. "Social Ethics and Normative Economics," Studies in Choice and Welfare, Springer, number 978-3-642-17807-8, June.
    6. Sen, Amartya Kumar, 1970. "The Impossibility of a Paretian Liberal," Scholarly Articles 3612779, Harvard University Department of Economics.
    7. Sen, Amartya, 1970. "The Impossibility of a Paretian Liberal," Journal of Political Economy, University of Chicago Press, vol. 78(1), pages 152-157, Jan.-Feb..
    8. John Geanakoplos, 2005. "Three brief proofs of Arrow’s Impossibility Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(1), pages 211-215, July.
    9. Ning Yu, 2012. "A one-shot proof of Arrow’s impossibility theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 523-525, June.
    10. Toyotaka Sakai & Masaki Shimoji, 2006. "Dichotomous preferences and the possibility of Arrovian social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(3), pages 435-445, June.
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