Arrow's Theorem Through a Fixpoint Argument

Frank M. V. Feys
(Delft University of Technology)
Helle Hvid Hansen
(Delft University of Technology)

We present a proof of Arrow's theorem from social choice theory that uses a fixpoint argument. Specifically, we use Banach's result on the existence of a fixpoint of a contractive map defined on a complete metric space. Conceptually, our approach shows that dictatorships can be seen as fixpoints of a certain process.

In Lawrence S. Moss: Proceedings Seventeenth Conference on Theoretical Aspects of Rationality and Knowledge (TARK 2019), Toulouse, France, 17-19 July 2019, Electronic Proceedings in Theoretical Computer Science 297, pp. 175–188.
Published: 19th July 2019.

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