Arrow's Theorem Through a Fixpoint Argument

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.
Comment: In Proceedings TARK 2019, arXiv:1907.08335