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Arrow´S Impossibility Theorem Is Not So Impossible And Condorcet´S Paradox Is Not So Paradoxical: The Adequate Definition Of A Social Choice Problem

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  • Daniel Castellanos

Abstract

In this article, we do two things: first, we present an alternative and simplified proof of the known fact that cardinal individual utility functions are necessary, but not sufficient, and that interpersonal comparability is sufficient, but not necessary, for the construction of a social welfare function. This means that Arrow´s impossibility theorem is simply a consequence of forcing the individual utility functions to be ordinal. And second, based on this proof, this article establishes two necessary conditions for the adequate definition of a social choice problem. It is shown that, if these two conditions are satisfied, a number of desirable properties for a social choice are satisfied, including transitivity. This means that Condorcet´s paradox is simply the result of a social choice problem that is not well defined.

Suggested Citation

  • Daniel Castellanos, 2005. "Arrow´S Impossibility Theorem Is Not So Impossible And Condorcet´S Paradox Is Not So Paradoxical: The Adequate Definition Of A Social Choice Problem," Documentos CEDE 2025, Universidad de los Andes, Facultad de Economía, CEDE.
    • Handle: RePEc:col:000089:002025
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    File URL: https://repositorio.uniandes.edu.co/bitstream/handle/1992/7972/dcede2005-63.pdf
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    References listed on IDEAS

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    1. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    2. Mueller,Dennis C., 2003. "Public Choice III," Cambridge Books, Cambridge University Press, number 9780521894753, September.
    3. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58(4), pages 328-328.
    4. A. J. Auerbach & M. Feldstein (ed.), 1987. "Handbook of Public Economics," Handbook of Public Economics, Elsevier, edition 1, volume 2, number 2.
    5. Ken Binmore, 1998. "Game Theory and the Social Contract - Vol. 2: Just Playing," MIT Press Books, The MIT Press, edition 1, volume 2, number 0262024446, April.
    6. Ken Binmore, 1994. "Game Theory and the Social Contract, Volume 1: Playing Fair," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262023636, April.
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    More about this item

    Keywords

    Condition of independence of irrevelant alternatives; social choice; social welfare function; cardinality and interpersonal comparability; Arrow s impossibility theorem; Condorcet s paradox;
    All these keywords.

    JEL classification:

    • I30 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General
    • D60 - Microeconomics - - Welfare Economics - - - General
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

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