Anubav Vasudevan characterized van Fraassen’s “Infomin” solution to the Judy Benjamin Problem (i.e. the solution by way of minimizing the Kullback-Leibler divergence between the posterior and prior) as an implementation of a “brand of epistemic charity” taking “the form of an assumption on the part of Judy Benjamin that her informant’s evidential report leaves out no relevant information”. After an analysis of the example that led Vasudevan to this way of thinking about Infomin, as well as of a (...) new one that supports the rival position of Douven and Romeijn in favor of minimizing the inverse Kullback-Leibler divergence between the posterior and the prior, we come to a different and more enlightening characterization of Infomin’s implicit assumptions. (shrink)

The technique of minimizing information (infomin) has been commonly employed as a general method for both choosing and updating a subjective probability function. We argue that, in a wide class of cases, the use of infomin methods fails to cohere with our standard conception of rational degrees of belief. We introduce the notion of a deceptive updating method and argue that non-deceptiveness is a necessary condition for rational coherence. Infomin has been criticized on the grounds that there (...) are no higher order probabilities that ‘support’ it, but the appeal to higher order probabilities is a substantial assumption that some might reject. Our elementary arguments from deceptiveness do not rely on this assumption. While deceptiveness implies lack of higher order support, the converse does not, in general, hold, which indicates that deceptiveness is a more objectionable property. We offer a new proof of the claim that infomin updating of any strictly-positive prior with respect to conditional-probability constraints is deceptive. In the case of expected-value constraints, infomin updating of the uniform prior is deceptive for some random variables but not for others. We establish both a necessary condition and a sufficient condition (which extends the scope of the phenomenon beyond cases previously considered) for deceptiveness in this setting. Along the way, we clarify the relation which obtains between the strong notion of higher order support, in which the higher order probability is defined over the full space of first order probabilities, and the apparently weaker notion, in which it is defined over some smaller parameter space. We show that under certain natural assumptions, the two are equivalent. Finally, we offer an interpretation of Jaynes, according to which his own appeal to infomin methods avoids the incoherencies discussed in this paper. (shrink)

Probability kinematics is the theory of how subjective probabilities change with time, in response to certain constraints . Rules are classified by the imposed constraints for which the rules prescribe a procedure for updating one's opinion. The first is simple conditionalization , and the second Jeffrey conditionalization . It is demonstrated by a symmetry argument that these rules are the unique admissible rules for those constraints, and moreover, that any probability kinematic rule must be equivalent to a conditionalization preceded by (...) a determination of the values x i to be given to the members of such a partition. Next two rival rules which can go beyond such conditionalization are described. INFOMIN and MTP . Their properties are investigated and compared. (shrink)