The Principal Principle and subjective Bayesianism

This paper poses a problem for Lewis’ Principal Principle in a subjective Bayesian framework: we show that, where chances inform degrees of belief, subjective Bayesianism fails to validate normal informal standards of what is reasonable. This problem points to a tension between the Principal Principle and the claim that conditional degrees of belief are conditional probabilities. However, one version of objective Bayesianism has a straightforward resolution to this problem, because it avoids this latter claim. The problem, then, offers some support to this version of objective Bayesianism.

We show in Section 1 that standard subjective Bayesianism has a problem in accommodating David Lewis’ Principal Principle. In Section 2, we see that the problem does not beset a recent version of objective Bayesianism. In Section 3, we consider three possible ways in which a subjectivist might try to avoid the problem but we argue that none of these suggestions succeed. We conclude that the problem favours objective Bayesianism over subjective Bayesianism (Section 4). In Section 4 we also compare our results to some other lines of recent work.