A critique of Jaynes' maximum entropy principle

AbstractFriedman and Shimony exhibited an anomaly in Jaynes' maximum entropy prescription: that if a certain unknown parameter is assumed to be characterized a priori by a normalizable probability measure, then the prior and posterior probabilities computed by means of the prescription are consistent with probability theory only if this measure assigns probability 1 to a single value of the parameter and probability 0 to the entire range of other values. We strengthen this result by deriving the same conclusion using only the assumption that the probability measure is σ-finite. We also show that when the hypothesis and evidence to which the prescription is applied are expressed in certain rather simple languages, then the maximum entropy prescription yields probability evaluation in agreement with one of Carnap's λ-continuum of inductive methods, namely λ = ∞. We conclude that the maximum entropy prescription is correct only under special circumstances, which are essentially those in which it is appropriate to use λ = ∞