Abstract: Recent work in the Everett interpretation has suggested that the problem of probability can be solved by understanding probability in terms of rationality. However, there are two problems relating to probability in Everett --- one practical, the other epistemic --- and the rationality-based program directly addresses only the practical problem. One might therefore worry that the problem of probability is only `half solved' by this approach. This paper aims to dispel that worry: a solution to the epistemic problem follows from the rationality-based solution to the practical problem.
Forthcoming in Studies in History and Philosophy of Modern Physics, March 2007.
With David Wallace.
Link to e-print
Abstract: According to Bayesian epistemology, the epistemically rational agent updates her beliefs by conditionalisation: that is, her posterior subjective probability after taking account of evidence X, p', is to be set equal to her prior conditional probability p(.|X). Bayesians can be challenged to provide a justification for their claim that conditionalisation is recommended by rationality --- whence the normative force of the injunction to conditionalise?
There are several existing justifications for conditionalisation, but none directly addresses the idea that conditionalisation 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 conditionalisation 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, conditionalisation is the unique updating rule that maximizes expected epistemic utility.
In Mind 115(459):607-632, July 2006.
Abstract: Difficulties over probability have often been considered fatal to the Everett interpretation of quantum mechanics. Here I argue that the Everettian can have everything she needs from `probability' without recourse to indeterminism, ignorance, primitive identity over time or subjective uncertainty: all she needs is a particular *rationality principle*.
The decision-theoretic approach recently developed by Deutsch and Wallace claims to provide just such a principle. But, according to Wallace, decision theory is itself applicable only if the correct attitude to a future Everettian measurement outcome is subjective uncertainty. I argue that subjective uncertainty is not to be had, but I offer an alternative interpretation that enables the Everettian to live without uncertainty: we can justify Everettian decision theory on the basis that an Everettian should *care about* all her future branches. The probabilities appearing in the decision-theoretic representation theorem can then be interpreted as the degrees to which the rational agent cares about each future branch. This reinterpretation, however, reduces the intuitive plausibility of one of the Deutsch-Wallace axioms (Measurement Neutrality).
In Studies in History and Philosophy of Modern Physics 35(3), September 2004, pp.423-456.