The von Neumann-Morgenstern axioms were an attempt to characterize rational decision-making in the presence of risk. The von Neumann-Morgenstern utility theorem says that if someone is vNM-rational, i.e. their preferences obey the axioms, then there exists a function $u$ from the set of outcomes to the real numbers, such that they will have to maximize […]

I need some references (far away from Wikipedia) about the proof using Ultrafilters of Arrow’s Impossibility Theorem. Online resources are preferred.

A question emerging from reading Schummer, J., & Vohra, R. V. (2002). Strategy-proof Location on a Network. Journal of Economic Theory, 104(2), 405–428. The setting is as follows: A finite set of agents $N$ indexed by $i=1,…,n$. A network represented by a graph $G$ on which the decision maker must decide the location of a […]

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