Arrow's impossibility theorem: Two simple single-profile versions
In this short paper we provide two simple new versions of Arrow's impossibility theorem, in a world with only one preference profile. Both versions are extremely transparent. The first version assumes a two-agent society; the second version, which is similar to a theorem of Pollak, assumes two or more agents. Both of our theorems rely on diversity of preferences axioms, and we explore alternative notions of diversity at length. Our first theorem also uses a neutrality assumption, commonly used in the literature; our second theorem uses a neutrality/monotonicity assumption, which is stronger and less commonly used. We provide examples to show the logical independence of the axioms, and to illustrate our points.
|Date of creation:||28 Feb 2007|
|Date of revision:|
|Publication status:||Published in Harvard College Mathematics Review 2(2), December 2008: 46-57|
|Contact details of provider:|| Postal: Veláquez 76, 28001 Madrid|
Web page: http://www.cienciassociales.imdea.org/
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- 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.
- 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.
- Marc Fleurbaey & Philippe Mongin, 2005. "The news of the death of welfare economics is greatly exaggerated," Post-Print hal-00246986, HAL.
- Marc Fleurbaey & Philippe Mongin, 2004. "The News of the Death of Welfare Economics is Greatly Exaggerated," Working Papers hal-00242931, HAL.
- 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.
- 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.
- 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.
- Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
- Rubinstein, Ariel, 1984. "The Single Profile Analogues to Multi Profile Theorems: Mathematical Logic's Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(3), pages 719-30, October.
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