Arrow's impossibility theorem: Two simple single-profile versions
AbstractIn 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.
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Bibliographic InfoPaper provided by Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales in its series Working Papers with number 2007-07.
Date of creation: 28 Feb 2007
Date of revision:
Publication status: Published in Harvard College Mathematics Review 2(2), December 2008: 46-57
Arrow's theorem; single-profile;
Find related papers by JEL classification:
- D60 - Microeconomics - - Welfare Economics - - - General
- D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
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- Pollak, Robert A, 1979. "Bergson-Samuelson Social Welfare Functions and the Theory of Social Choice," The Quarterly Journal of Economics, MIT Press, vol. 93(1), pages 73-90, February.
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"The News of the Death of Welfare Economics is Greatly Exaggerated,"
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- 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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