Philosophy of Probability pp 109-127 | Cite as

# Probability and Utility

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## Abstract

“The subject of [our] investigation is sometimes the instruments, sometimes the use of them.”^{1}

## Keywords

Simple Theory Indifference Curve General Utility Partial Belief Objective Rule
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## Notes

- 1.Aristotle,
*Nichomachean Ethics*, 1112b.Google Scholar - 2.The general theory was developed by G. Debreu in
*Theory of Value: An Axiomatic Analysis of Economic Equilibrium*(Cowles Foundation Monograph, 17) Yale University Press, New Haven, 1959.Google Scholar - 2a.For a more recent and slightly more comprehensive development see Kenneth J. Arrow and F. J. Hahn,
*General Competitive Analysis*, Holden-Day, Inc. San Francisco, and Oliver and Boyd, Edinburgh, 1971.Google Scholar - 3.See, for example, the theory of R. C. Jeffrey in
*The Logic of Decision*, University of Chicago Press, Chicago and London, 1983 (second edition).Google Scholar - 4.This is the Weber — Fechner law. See, for example, E. G. Boring,
*History of Experimental Psychology*, New York, 1950 (second edition) for an account.Google Scholar - 5.The view of Hans-Werner Sinn is not far from this. See “Psychophysical laws in risk theory,”
*Journal of Economic Psychology*, 6, (2) (June, 1985) 185–206.Google Scholar - 6.
*Capital*, International Publishers, New York, 1967, I.1.3, (page 47).Google Scholar - 7.As is attested to by the burgeoning recent literature on common knowledge. See, for example, Brian Skyrms,
*The Dynamics of Rational Deliberation*, Harvard University Press, Cambridge, Massachusetts and London, England, 1990.Google Scholar - 8.The principle is asserted with certain variations in many works in classical decision theory, such as L. J. Savage,
*The Foundations of Statistics*, New York, John Wiley and Sons, 1954, as well as in the work of Jeffrey cited above. The variations are unimportant for the present discussion.Google Scholar - 9.The history of commodity utility is recounted in George Stigler, “The Development of Utility Theory,”
*Journal of Political Economy*, 58, (1950) 307–396CrossRefGoogle Scholar - 9a.Kenneth Arrow, “Alternative Approaches to the Theory of Choice in Risk-Taking Situations,” Econometrica, 19 (1951) 405–438. The best account of the history of propositional utility is still that of L. J. Savage in
*The Foundations of Statistics*, ch. 5.Google Scholar - 10.In books 2 and 3 of
*De Anima*. Google Scholar - 11.With the evident exception of cases like that of the frog and its fly.Google Scholar
- 12.
*Capital*, I.1.1, 35.Google Scholar - 13.John von Neumann and Oskar Morgenstern,
*The Theory of Games and Economic Behavior*, Princeton, Princeton University Press, 1953 (third edition). The theory of utility is given in section 3 of chapter 1.Google Scholar - 14.“Concepts like “specific utility of gambling” cannot be formulated free of contradiction on this level.” 28.Google Scholar
- 15.
*Nichomachean Ethics*, 1142b. Aristotle does not however agree that such a man deliberates well; for him good deliberation tends to achieve good ends. He would say that one who brings evil upon himself may have calculated well, but that he could not have deliberated well.Google Scholar - 16.Maurice Allais, “Le comportement de l’homme rationnel devant le risque: Critique des postulats et axiomes de l’école américaine,”
*Econometrica*, 21 (1953) 503–546.CrossRefGoogle Scholar - 16a.Daniel Ellsberg, “Risk, Ambiguity, and the Savage Axioms,”
*Quarterly Journal of Economics*, 75 (1961) 643–669. More recent work on the question (as well as Ellsberg’s article) is found in the valuable collection,*Decision, Probability, and Utility*, ed. Peter Gardenfors and Neils-Eric Sahlin, Cambridge, Cambridge University Press, 1988.CrossRefGoogle Scholar - 17.In the worked-out theory, Q is strict preference (transitive and asymmetric) and events neither of which is preferred to the other are indifferent.Google Scholar
- 18.This is not to ignore the many complexities and difficulties in the way of this expression. There is nevertheless substantial work on the question. Let me cite just two sources: John Barwise and John Perry,
*Situations and Attitudes*, MIT Press, Cambridge, Mass., 1983Google Scholar - 18a.Donald Davidson,
*Essays on Actions and Events*, Oxford, Clarendon Press, 1980, essays 6–10.Google Scholar - 19.See R. Duncan Luce,
*Individual Choice Behavior*, John Wiley and Sons, New York, 1959. The approach sketched here is a ramification and reformulation of Luce’s account. The leading idea is that preference is fundamentally stochastic or probabilistic.Google Scholar - 20.A general and simple theory of probability as an operator of this sort (as a quantifier) is developed in J. M. Vickers, Chance and Structure: An Essay in the Logical Foundations of Probability, Clarendon Press, Oxford, 1988, chapters 4 and 5.Google Scholar
- 21.See Donald Davidson, “The Logical Form of Action Sentences,” in
*Actions and Events*. Google Scholar

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© Springer Science+Business Media Dordrecht 1993