, Volume 53, Issue 1, pp 9-25
Date: 25 Jun 2009

Expected utility theory from the frequentist perspective

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Abstract

We present an axiomatization of expected utility from the frequentist perspective. It starts with a preference relation on the set of infinite sequences with limit relative frequencies. We consider three axioms parallel to the ones for the von Neumann–Morgenstern (vN–M) expected utility theory. Limit relative frequencies correspond to probability values in lotteries in the vN–M theory. This correspondence is used to show that each of our axioms is equivalent to the corresponding vN–M axiom in the sense that the former is an exact translation of the latter. As a result, a representation theorem is established: The preference relation is represented by an average of utilities with weights given by the relative frequencies.

I am very grateful to Kalyan Chatterjee for his guidance and support. I am also indebted to Jeff Kline for his comments. I received many helpful comments from Mamoru Kaneko that significantly improved the paper.