This chapter gives two distinct justifications of the Principal Principle (PP) for Humean objective chances (HOCs). The first justification is “consequentialist” in nature: it shows that in practical decision-making, an agent who has to make bets on repeated chancy events of type A, and who knows the chance of A but has no better information (the scenario of PP), will do better setting her credence equal to the chance of A than she can do with any other, significantly different, betting strategy. The second justification shows that an epistemic agent meeting the conditions for application of PP is irrational—logically incoherent, in fact—if she sets her credence to a level substantially different from the chance. This argument is an adaptation of one originally offered by Colin Howson and Peter Urbach (1993) to justify the PP for von Mises–style hypothetical frequentism. It is shown that the argument works better in support of HOC than it did in support of frequentism.
Everettian Probabilities, The Deutsch-Wallace Theorem and the Principal Principle
