Expected utility and risk

Abstract

The rule to maximize expected utility is intended for decisions where options involve risk. In those decisions the decision maker's attitude toward risk is important, and the rule ought to take it into account. Allais's and Ellsberg's paradoxes, however, suggest that the rule ignores attitudes toward risk. This suggestion is supported by recent psychological studies of decisions. These studies present a great variety of cases where apparently rational people violate the rule because of aversion or attraction to risk. Here I attempt to resolve the issue concerning expected utility and risk. I distinguish two versions of the rule to maximize expected utility. One adopts a broad interpretation of the consequences of an option and has great intuitive appeal. The other adopts a narrow interpretation of the consequences of an option and seems to have certain technical and practical advantages. I contend that the version of the rule that interprets consequences narrowly does indeed neglect attitudes toward risk. That version of the rule excludes the risk involved in an option from the consequences of the option and, contrary to what is usually claimed, cannot make up for this exclusion through adjustments in probability and utility assignments. I construct a new, general argument that establishes this in a rigorous way. On the other hand, I contend that the version of the rule that interprets consequences broadly takes account of attitudes toward risk by counting the risk involved in an option among the consequences of the option. I rebut some objections to this version of the rules, in particular, the objection that the rule lacks practical interest. Drawing upon the literature on 'mean-risk' decision rules, I show that this version of the rule can be used to solve some realistic decision problems.

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2009-01-28

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Paul Weirich
University of Missouri, Columbia

References found in this work

The Logic of Decision.Richard C. Jeffrey - 1965 - New York, NY, USA: University of Chicago Press.
Can Human Irrationality Be Experimentally Demonstrated?L. Jonathan Cohen - 1981 - Behavioral and Brain Sciences 4 (3):317-370.
The Logic of Decision.Brian Skyrms - 1965 - Journal of Symbolic Logic 50 (1):247-248.
Regret in Decision Making Under Uncertainty.David E. Bell - 1982 - Operations Research 30 (5):961–81.

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Citations of this work

Decision Theory.Johanna Thoma - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 57-106.
Counterfactual Desirability.Richard Bradley & H. Orri Stefansson - 2017 - British Journal for the Philosophy of Science 68 (2):485-533.
Decision Under Normative Uncertainty.Franz Dietrich & Brian Jabarian - forthcoming - Economics and Philosophy.

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