Arrow’s Theorem Through a Fixpoint Argument
Frank Feys (TU Delft - Technology, Policy and Management)
Helle Hansen (TU Delft - Technology, Policy and Management)
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Abstract
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.
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