Infinite Populations, Choice and Determinacy

Studia Logica 106 (5):969-999 (2018)
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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 ), not as a replacement for Choice, but simply to eliminate applications of set theory violating the Hildenbrand criterion. A particularly appealing aspect of \ from the point of view of the research area in question is its game-theoretic character.

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Citations of this work

Social welfare relations and irregular sets.Ram Sewak Dubey & Giorgio Laguzzi - 2023 - Annals of Pure and Applied Logic 174 (9):103302.

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References found in this work

The iterative conception of set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.
The set-theoretic multiverse.Joel David Hamkins - 2012 - Review of Symbolic Logic 5 (3):416-449.
[Omnibus Review].Akihiro Kanamori - 1981 - Journal of Symbolic Logic 46 (4):864-866.

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