The Birth of Social Choice Theory from the Spirit of Mathematical Logic: Arrow’s Theorem in the Framework of Model Theory

Studia Logica 106 (5):893-911 (2018)

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 Arrow’s use of von Neumann and Morgenstern’s concept of winning coalitions allows to exploit the algebraic structures involved in preference aggregation; this approach entails an alternative indirect ultrafilter proof for Arrow’s dictatorship result. This link also connects Arrow’s seminal result to key developments and concepts in the history of model theory, notably ultraproducts and preservation results.
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DOI 10.1007/s11225-018-9794-8
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References found in this work BETA

Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
Arrow's Theorem in Judgment Aggregation.Franz Dietrich & Christian List - 2007 - Social Choice and Welfare 29 (1):19-33.
A Generalised Model of Judgment Aggregation.Franz Dietrich - 2007 - Social Choice and Welfare 4 (28):529-565.
Introduction to Judgment Aggregation.Christian List & Ben Polak - 2010 - Journal of Economic Theory 145 (2):441-466.

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