Abstract
Take a person who has preferences between uncertain prospects. Then between the prospects, there is a preference relation:
the person prefers _ to _ or is indifferent between them,
where the blanks are to be filled in with prospects. Expected utility theory lays down a number of axioms for this relation. Let us call the preferences coherent if they conform to these axioms. The theory shows that, provided the preferences are coherent, then probabilities and a utility function can be defined for them, having the following two properties. First, the utility of a prospect is the expectation of the utilities of its possible outcomes, evaluated according to the probabilities. And second, for any prospects X and Y, the utility of X is at least as great as the utility of Y if and only if the person prefers X to Y or is indifferent between them. If a utility function has the first property I call it expectational. If it has the second I say it represents the preference relation. In effect, utility is defined as that which the person maximizes the expectation of, and the axioms ensure that she maximizes the expectation of something.
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Broome, J. (1992). Bernoulli, Harsanyi, and the Principle of Temporal Good. In: Selten, R. (eds) Rational Interaction. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09664-2_21
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DOI: https://doi.org/10.1007/978-3-662-09664-2_21
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