Subjective probability and expected utility without additivity

Abstract

Bayesian statistical techniques are applicablewhen the information anduncertainty with respect to the parameters or hypotheses in question can be expressed by a probability distribution. This prior probability is also the focus of most of the criticism against the Bayesian school. My starting point is to join the critics in attacking a certain aspect of the prior probability: The probability attached to an uncertain event does not reflect the heuristic amount of information that led to the assignment of that probability. For example, when the information on the occurrence of two events is symmetric they are assigned equal prior probabilities. If the events are complementary the probabilities will be 1/2, independently of whether the symmetric information is meager or abundant.