Bayesian Rationality and Decision Making : A Critical Review

Bayesianism is the predominant philosophy of science in North-America, the most important school of statistics world-wide, and the general version of the rationalchoice approach in the social sciences. Although often rejected as a theory of actual behavior, it is still the benchmark case of perfect rationality. The paper reviews the development of Bayesianism in philosophy, statistics and decision making and questions its status as an account of perfect rationality. Bayesians, who otherwise are squarely in the empiricist camp, invoke a priori reasoning when they recommend Bayesian methods—a recommendation that is not justified by their own standards. 1. From the Problem of Induction to Subjective Bayesianism Induction is the process of inferring, from past observations, either predictions or generalizations that then can be used to deduce predictions. David Hume had famously argued that induction is an irrational but unbreakable habit—irrational because, in fact, any beliefs about the future are as reasonable or unreasonable as any other, no matter what experiences one has made in the past. This view, often called Humean irrationalism, conflicts with the empiricist view that, by and large, science proceeds in a rational and inductive way, thus giving rise to the problem(s) of induction: Is science, or learning in general, inductive? Is it rational? Many attempts have been made to refute Hume. One of the earliest is due to Thomas Bayes and was embraced by Pierre Simon Laplace. According to Bayes, rational learning proceeds by assigning probabilities, usually called prior probabilites, to hypotheses. Using Bayes’ theorem, these prior probabilities are then updated in the light of experience. In Laplace’s account, the precise meaning of the prior probabilities was unclear. To determine these probabilities, Laplace used what is often called the principle of insufficient reason. There is not much of a principle, though; it all ∗ For useful hints and discussions, I am grateful to Stefanie Mehret and to participants of the 2002 workshop “Reduction of Complexity—Necessity, Trade-offs, Methods” of the SFB 475 “Reduction of Complexity for Multivariate Data Structures” at the University of Dortmund, where a preliminary version of this paper was presented. 1 The subsequent remarks on the history of the problem of induction are based on Gillies 1988; Hacking 1990; Humphreys 1990 and Musgrave 1993, 151–166.