Conclusion
From the arguments presented in this paper I trust that we are in a position to see that Bayesian decision theory is inadequate both from the descriptive and normative standpoints. As a descriptive theory it is just false. As a normative theory we can say that there is a presumption in favour of the view that it is not irrational to value certainty as such (because this is in accord with ordinary intuition) and that no argument has been presented — and there seems little prospect of such an argument being presented — that would force us to abandon that presumption. That is, from the normative standpoint Bayesian decision theory is prima facie implausible. We have located the problem for Bayesianism in one of its rationality postulates, viz., the Sure-Thing Principle. Of course, this paper does not go very far in suggesting what is to supplant Bayesian decision theory as a theory of rational decision making. Nonetheless, I take the arguments in this paper to present a compelling reason for embarking on such a program.
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I have benefited from discussions with a number of people, but I would like particularly to single out Professor John Watkins who made several substantive points on an earlier version of this material. Most notably he made explicit a thought which I had seen only inchoately, viz., the importance of the difference between the two Bayesian Rationality Postulates discussed in this paper. I have found Professor Watkin's papers very enlightening and I see my own effort here as generally in support of his arguments for a conclusion which is very similar to my own. I am also indebted to the writings of Professor John Harsanyi: while his work is the focus of attack in this paper this is as much as anything indicative of the fact that his papers have done most to state the Bayesian position clearly and cogently. I wish to thank him and Professor Watkins for permission to quote from their unpublished papers.
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Sowden, L. The inadequacy of Bayesian decision theory. Philosophical Studies 45, 293–313 (1984). https://doi.org/10.1007/BF00355440
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DOI: https://doi.org/10.1007/BF00355440