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Infinite Populations, Choice and Determinacy

Abstract

This paper criticizes non-constructive uses of set theory in formal economics. The main focus is on results on preference aggregation and Arrow’s theorem for infinite electorates, but the present analysis would apply as well, e.g., to analogous results in intergenerational social choice. To separate justified and unjustified uses of infinite populations in social choice, I suggest a principle which may be called the Hildenbrand criterion and argue that results based on unrestricted axiom of choice do not meet this criterion. The technically novel part of this paper is a proposal to use a set-theoretic principle known as the axiom of determinacy (\(\mathsf {AD}\)), not as a replacement for Choice, but simply to eliminate applications of set theory violating the Hildenbrand criterion. A particularly appealing aspect of \(\mathsf {AD}\) from the point of view of the research area in question is its game-theoretic character.

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Correspondence to Tadeusz Litak.

Additional information

Special Issue: Logics for Social Behaviour

Edited by Alessandra Palmigiano and Marcus Pivato

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Cite this article

Litak, T. Infinite Populations, Choice and Determinacy. Stud Logica 106, 969–999 (2018). https://doi.org/10.1007/s11225-017-9730-3

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Keywords

  • Axiom of choice
  • Axiom of determinacy
  • Multiverse
  • intergenerational social choice
  • Preference aggregation
  • Arrow’s impossibility theorem
  • Social welfare analysis