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The birth of social choice theory from the spirit of mathematical logic: Arrow's theorem in the framework of model theory

Author

Listed:
  • Daniel Eckert

    (University of Graz)

  • Frederik Herzberg

    (Bielefeld University)

Abstract

Arrow's axiomatic foundation of social choice theory can be understood as an application of Tarski's methodology of the deductive sciences which is closely related to the latter's foundational contribution to model theory. In this note we show in a model-theoretic framework how his use of von Neumann and Morgenstern's concept of winning coalitions allows to exploit the algebraic structures involved in preference aggregation and provides an alternative indirect ultrafilter proof for Arrow's dictatorship result. This link also connects Arrows seminal result to key developments and concepts in the history of model theory, notably ultraproducts and model-preservation results.

Suggested Citation

  • Daniel Eckert & Frederik Herzberg, 2016. "The birth of social choice theory from the spirit of mathematical logic: Arrow's theorem in the framework of model theory," Graz Economics Papers 2016-04, University of Graz, Department of Economics.
    • Handle: RePEc:grz:wpaper:2016-04
    as

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    File URL: http://www100.uni-graz.at/vwlwww/forschung/RePEc/wpaper/2016-04.pdf
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    References listed on IDEAS

    as
    1. Donald J. Brown, 1975. "Collective Rationality," Cowles Foundation Discussion Papers 393, Cowles Foundation for Research in Economics, Yale University.
    2. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2002. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 1, number 1.
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    More about this item

    Keywords

    Arrow's theorem; model theory; winning coalitions; ultrafilter; ultraproducts; Boolean algebra; homomorphism;
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