Abstract
Although many philosophers and statisticians believe that only an objectivistic theory of probability can have serious application in the sciences, there is a growing number of physicists and statisticians, if not philosophers, who advocate a subjective theory of probability. The increasing advocacy of subjective probability is surely due to the increasing awareness that the foundations of statistics are most properly constructed on the basis of a general theory of decision-making. In a given decision situation subjective elements seem to enter in three ways: (i) in the determination of a utility function (or its negative, a loss function) on the set of possible consequences, the actual consequence being determined by the true state of nature and the decision taken; (ii) in the determination of an a priori probability distribution on the states of nature; (iii) in the determination of other probability distributions in the decision situation.
Reprinted from The Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–55 5 (1956), 61–73.
I am indebted to Herman Rubin for a number of helpful suggestions.
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Notes
Article 8 in this volume.
The term `mixed decision’ is used here in the very restricted sense of referring to gambles involving just this special chance event independent of the state of nature; formally such gambles are the elements of D x D
An analogue of our AS is not included among Savage’s seven axioms unless his set F of acts (corresponding to our set D of decisions) is meant to be the set of all functions mapping S into C, which is of course a stronger assumption than A8. In any case it is essential to his formal developments to have such decisions at hand (see Savage, 1954, from p. 25 on).
This is certainly not always the case. The strong structure axiom in Davidson and Suppes (1956), which asserts that consequences are equally spared in utility, is not existential in character.
Article 8 in this volume.
In Suppes and Winet (1955; Article 8 in this volume) the inequalities of (3) are actually reversed, but trivial changes in the axioms given there yield (3) as a consequence.
Article 8 in this volume.
A central problem in confirmation theory is what a priori distribution to choose when there is no information whatsoever. Chernoff (1954) has shown that if certain reasonable postulates are accepted and if the number of states of nature is finite, then the distribution to choose is that one which makes each state equally probable.
This remark is controversial. In the opinion of many competent investigators an adequate confirmation theory would dispense with any need for subjective probability. I cannot here state my reasons for disagreeing with this view.
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© 1969 Springer Science+Business Media Dordrecht
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Suppes, P. (1969). The Role of Subjective Probability and Utility in Decision-Making. In: Studies in the Methodology and Foundations of Science. Synthese Library, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3173-7_6
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