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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Special Issue: Logics for Social Behaviour.
Edited by Alessandra Palmigiano and Marcus Pivato
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Eckert, D., Herzberg, F.S. The Birth of Social Choice Theory from the Spirit of Mathematical Logic: Arrow’s Theorem in the Framework of Model Theory. Stud Logica 106, 893–911 (2018). https://doi.org/10.1007/s11225-018-9794-8
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DOI: https://doi.org/10.1007/s11225-018-9794-8