Justifying Conditionalization: Conditionalization Maximizes Expected Epistemic Utility

Abstract

According to Bayesian epistemology, the epistemically rational agent updates her beliefs by conditionalization: that is, her posterior subjective probability after taking account of evidence X, pnew, is to be set equal to her prior conditional probability p old (·/X). Bayesians can be challenged to provide a justification for their claim that conditionalization is recommended by rationality -whence the normative force of the injunction to conditionalize?There are several existing justifications for conditionalization, but none directly addresses the idea that conditionalization will be epistemically rational if and only if it can reasonably be expected to lead to epistemically good outcomes. We apply the approach of cognitive decision theory to provide a justification for conditionalization using precisely that idea. We assign epistemic utility functions to epistemically rational agents; an agent's epistemic utility is to depend both upon the actual state of the world and on the agent's credence distribution over possible states. We prove that, under independently motivated conditions, conditionalization is the unique updating rule that maximizes expected epistemic utility.

Epistemic Decision Theory

“…Such an EDT can be based on a naive application of the framework of Savage 1972; this is the theory discussed in e.g. Oddie 1997, Greaves and Wallace 2006, Leitgeb and Pettigrew 2010a.…”

Epistemic values and the value of learning

“…Instead of looking only to cognitive utility that attaches to the act of acceptance of a hypothesis, we should consider also epistemic utlities-utilities that attach to a state of belief. This is an approach that has been advocated by, among others, Oddie (1997), Joyce (1998), and Greaves and Wallace (2006). See Fallis (2007) for a superb overview.…”

On the Everettian Epistemic Problem

“…What sort of utility function would do better justice to the spirit of epistemic rationality, then? The central idea behind our third argument for conditionalization (Greaves & Wallace, 2006) is that if we had a utility function that captured the epistemic value of being in a given belief state, then epistemic rationality would consist in maximizing the (subjective) expectation value of that utility function. It turns out that, on such an approach, conditionalization can be justified on the basis that, of all possible updating policies, conditionalization is the one that yields the highest value of expected epistemic utility.…”