Is it always rational to satisfy savage’s axioms

This note argues that, under some circumstances, it is more rational not to behave in accordance with a Bayesian prior than to do so. The starting point is that in the absence of information, choosing a prior is arbitrary. If the prior is to have meaningful implications, it is more rational to admit that one does not have sufficient information to generate a prior than to pretend that one does. This suggests a view of rationality that requires a compromise between internal coherence and justification, similarly to compromises that appear in moral dilemmas. Finally, it is argued that Savage’s axioms are more compelling when applied to a naturally given state space than to an analytically constructed one; in the latter case, it may be more rational to violate the axioms than to be Bayesian. CAN PROBABILITIES REFLECT IGNORANCE? Will the US president six years hence be a Democrat? The Bayesian approach requires that we be able to quantify this uncertainty by a single number; we should be able to state that our subjective belief for this event is, say, 62.4 % or 53.7%. Many people feel that they do not have sufficient information to come up with such an accurate probability estimate. Moreover, some people feel that it is more rational not to assign a probabilistic estimate for such an event than to assign one. Choosing one probability number in the interval [0,1] would be akin to pretending that we know something that we don’t. We wish to thank Eddie Dekel, Dov Samet and Peter Wakker for discussions and comments