Journal Article Unbounded Utility Functions in Expected Utility Theory Get access Peter C. Fishburn Peter C. Fishburn Pennsylvania State University Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Economics, Volume 90, Issue 1, February 1976, Pages 163–168, https://doi.org/10.2307/1886093 Published: 01 February 1976

[A choice function, which maps each set of alternatives in a domain of feasible sets into a non-empty subset of itself (called the choice set), is said to be representable by a weak order if some weak order on the alternatives has maximum elements within each feasible set, all of which are in the choice set of that feasible set. A Partial Congruence Axiom ("every non-empty finite collection of feasible sets has an alternative which is in the choice set of every feasible set in the collection which contains that alternative") is shown to be necessary and sufficient for weak order representability when all choice sets are finite. A stronger form of partial congruence is proved to be necessary and sufficient for weak order representability when the number of feasible sets is countable, regardless of the cardinalities of the choice sets. The general case of arbitrary cardinalities for the domain and the choice sets is presently unsettled.]

Abstract The article presents comments of the author on the article "Theory Versus Practice in Risk Analysis: An Empirical Study," by Willis R. Greer. In his Greer, claimed to show a conflict between utility theory and actual decisions made by representatives of twenty-seven Fortune 500 firms. Although the article provided an interesting analysis of firms' decisions, it seems misleading in two important respects. First, the hypothesis tested by Greer is quite different than the hypothesis that he suggested he was testing. Second in contrast to his claim of a substantial conflict between the decision processes used by actual decision makers and existing utility theory, the data give fairly good support to the counterclaim that the decision makers in his study tend to be expected utility maximizers. The latter point already has been discussed by scholar C.G. Hoskins and Greer and scholar Ted D. Skekel. More is said about this later in this comment. The interpretative problems with Greer's original article appear to arise from the author's conception of "existing utility theory." This conception is tied to a mean-standard deviation trade off model.