Template:Short description In decision theory, subjective expected utility (SEU) is a framework for modeling how individuals make choices under uncertainty. In particular, it posits that decision-makers have 1) a subjective probability distribution over uncertain states of the world; and 2) a utility function over consequences such that their choice behavior can be described as maximizing expected utility over consequences with respect to their subjective probability.<ref name = "kreps1988">Template:Cite book</ref> This way, the theory of subjective expected utility combines two subjective concepts: a personal utility function, and a personal probability distribution (usually based on Bayesian probability theory).<ref>Template:Cite book</ref>
SEU is a different approach from the one put forward by the one put forward by von Neumann and Morgenstern in that it does not take (objecive) probabilities (i.e., lotteries) as given. Instead, subjective probabilities are used, which are assumed to be consistent with choice behavior.<ref>Template:Cite journal</ref>
The main contribution to formalizing SEU was done by L. J. Savage in 1954 (see Savage's axioms),<ref>Savage, Leonard J. 1954. The Foundations of Statistics. New York, Wiley.</ref><ref>Karni, Edi. "Savage's subjective expected utility model." The New Palgrave Dictionary of Economics. Second Edition. Eds. Steven N. Durlauf and Lawrence E. Blume. Palgrave Macmillan, 2008. The New Palgrave Dictionary of Economics Online. Palgrave Macmillan. 23 August 2014 <http://www.dictionaryofeconomics.com/article?id=pde2008_S000479> {{#invoke:doi|main}}</ref> following previous work by Ramsey<ref name = "ramsey1931">Template:Cite book</ref> and von Neumann.<ref>Template:Cite book</ref>Template:R Savage proved that, if the decision-maker preferences over acts satisfy some reasonable axioms, then their choices can be explained as arising from a utility function <math>u(x_i)</math> combined with the subjective belief that there is a probability of each outcome <math>P(x_i).</math> The subjective expected utility is the resulting expected value of the utility:
- <math>\Epsilon[u(X)] = \sum_i \; u(x_i) \; P(x_i) .</math>
Experiments have shown that many individuals do not behave in a manner consistent with Savage's axioms of subjective expected utility, e.g. most prominently Allais (1953)<ref>Template:Cite journal</ref> and Ellsberg (1961).<ref>Template:Cite journal</ref>
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- Template:Cite journal http://psychclassics.yorku.ca/Peirce/small-diffs.htm
- Ramsey, Frank Plumpton; “Truth and Probability” (PDF), Chapter VII in The Foundations of Mathematics and other Logical Essays (1931).
- de Finetti, Bruno. "Probabilism: A Critical Essay on the Theory of Probability and on the Value of Science," (translation of 1931 article) in Erkenntnis, volume 31, September 1989.
- de Finetti, Bruno. 1937, “La Prévision: ses lois logiques, ses sources subjectives,” Annales de l'Institut Henri Poincaré,
- de Finetti, Bruno. "Foresight: its Logical Laws, Its Subjective Sources," (translation of the 1937 article in French) in H. E. Kyburg and H. E. Smokler (eds), Studies in Subjective Probability, New York: Wiley, 1964.
- de Finetti, Bruno. Theory of Probability, (translation by AFM Smith of 1970 book) 2 volumes, New York: Wiley, 1974–5.
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