Philippe Mongin, What the decision theorist could tell the Bayesian philosopher

Conférence plénière affiliée (EPSA) du 22 juillet - CLMPS 2011 / Affiliated plenary lecture (EPSA), Fri. 22 July - CLMPS 2011

Bayesianism is a pervasive doctrine in current epistemology, philosophy of science and statistics. There are three main Bayesian tenets, i.e., that (i) empirical claims are to be evaluated by their probability values, (ii) evidence for or against them is to be weighed through probabilistic conditioning, and (iii) decisions are to be made as prescribed by the expected utility rule or the equivalent conditions on preferences. Arguments for (i) and (ii) may be classified as pragmatic or non-pragmatic, depending on whether the justification strategy also involves (iii) or puts it aside. Furthermore, pragmatic arguments may rely more or less heavily on the apparatus of decision theory: some are pretheoretic, like the Dutch Book argument, while others take the advanced form of a representation theorem, as in Savage’s Foundations of Statistics. This lecture is concerned only with pragmatic arguments, and it will take the line, already present in today’s Bayesian philosophy, that they cannot win the day if they fall short of a proper representation theorem. However, the lecture will unconventionally emphasize that Savage’s classic does not yet deliver the appropriate result and that more sophisticated decision-theoretic work must be carried if one is to establish (i), (ii) and (iii) jointly. One major complication we will emphasize stems from event-dependence of utility values; it calls for a much richer framework of preferences than in Savage. An even more dramatic departure we will propose is to disconnect (i) and (ii) from (iii) by replacing expected utility by a more general, and arguably more appropriate, rule of decision under uncertainty. Despite the Pandora’s box of initially unnoticed problems, not all of which are resolved in the state of the art, we will strongly maintain that the detour by decision theory is unavoidable if one is to justify Bayesianism pragmatically.