One well-known objection to the principle of maximum entropy is the so-called Judy Benjamin problem, first introduced by van Fraassen. The problem turns on the apparently puzzling fact that, on the basis of information relating an event’s conditional probability, the maximum entropy distribution will almost always assign to the event conditionalized on a probability strictly less than that assigned to it by the uniform distribution. In this article, I present an analysis of the Judy Benjamin problem that can help to (...) make sense of this seemingly odd feature of maximum entropy inference. My analysis is based on the claim that, in applying the principle of maximum entropy, Judy Benjamin is not acting out of a concern to maximize uncertainty in the face of new evidence, but is rather exercising a certain brand of epistemic charity towards her informant. This epistemic charity takes the form of an assumption on the part of Judy Benjamin that her informant’s evidential report leaves out no relevant information. Such a reconceptualization of the motives underlying Judy Benjamin’s appeal to the principle of maximum entropy can help to further our understanding of the true epistemological grounds of this principle and correct a common misapprehension regarding its relationship to the principle of insufficient reason. 1Introduction2The Principle of Maximum Entropy3An Apologia for Judy Benjamin4Conclusion: Entropy and Insufficient Reason. (shrink)

ABSTRACT For changing opinion, represented by an assignment of probabilities to propositions, the criterion proposed is motivated by the requirement that the assignment should have, and maintain, the possibility of matching in some appropriate sense statistical proportions in a population. This ‘tracking’ criterion implies limitations on policies for updating in response to a wide range of types of new input. Satisfying the criterion is shown equivalent to the principle that the prior must be a convex combination of the possible posteriors. (...) Furthermore, this is equivalent to the requirement that prior expected values must fall inside the range spanned by possible posterior expected values. The tracking criterion is liberal; it allows for, but does not require, a policy such as Bayesian conditionalization, and can be offered as a general constraint on policies for managing opinion over time. Examples are given of non-Bayesian policies, both ones that satisfy and ones that violate the criterion. _1_ Introduction _2_ Alternative Updating Policies _3_ Modelling the Situation for Normal Updating _4_ Tracking: A Criterion for Updating Policies _5_ Tracking: Precise Formulation and Relation to Convexity _6_ The Spanning Criterion _7_ Non-Bayesian Policies that Satisfy the Spanning and Tracking Criteria _8_ Policies that Violate the Spanning and Tracking Criteria Appendix Appendix. (shrink)

The principle of maximum entropy is a general method to assign values to probability distributions on the basis of partial information. This principle, introduced by Jaynes in 1957, forms an extension of the classical principle of insufficient reason. It has been further generalized, both in mathematical formulation and in intended scope, into the principle of maximum relative entropy or of minimum information. It has been claimed that these principles are singled out as unique methods of statistical inference that agree with (...) certain compelling consistency requirements. This paper reviews these consistency arguments and the surrounding controversy. It is shown that the uniqueness proofs are flawed, or rest on unreasonably strong assumptions. A more general class of inference rules, maximizing the so-called Re[acute ]nyi entropies, is exhibited which also fulfill the reasonable part of the consistency assumptions. (shrink)

This paper develops a compositional, type-driven constraint semantic theory for a fragment of the language of subjective uncertainty. In the particular application explored here, the interpretation function of constraint semantics yields not propositions but constraints on credal states as the semantic values of declarative sentences. Constraints are richer than propositions in that constraints can straightforwardly represent assessments of the probability that the world is one way rather than another. The richness of constraints helps us model communicative acts in essentially the (...) same way that we model agents’ credences. Moreover, supplementing familiar truth-conditional theories of epistemic modals with constraint semantics helps capture contrasts between strong necessity and possibility modals, on the one hand, and weak necessity modals, on the other. (shrink)

The current debate about peer disagreement has so far mainly focused on the question of whether peer disagreements provide genuine counterevidence to which we should respond by revising our credences. By contrast, comparatively little attention has been devoted to the question by which process, if any, such revision should be brought about. The standard assumption is that we update our credences by conditionalizing on the evidence that peer disagreements provide. In this paper, we argue that non-dogmatist views have good reasons (...) to reject conditionalization. Instead, peer disagreements should be understood to call for a revision of our prior conditional probabilities: rather than merely adding to our original evidence, they pose a challenge to the thought that we have properly assessed the probative force of our original evidence. (shrink)

A paper on how to adapt your probabilisitc beliefs when learning a conditional.

Sometimes we receive evidence in a form that standard conditioning (or Jeffrey conditioning) cannot accommodate. The principle of maximum entropy (MAXENT) provides a unique solution for the posterior probability distribution based on the intuition that the information gain consistent with assumptions and evidence should be minimal. Opponents of objective methods to determine these probabilities prominently cite van Fraassen’s Judy Benjamin case to undermine the generality of maxent. This article shows that an intuitive approach to Judy Benjamin’s case supports maxent. This (...) is surprising because based on independence assumptions the anticipated result is that it would support the opponents. It also demonstrates that opponents improperly apply independence assumptions to the problem. (shrink)

The strategy of updating credences by minimizing the relative entropy has been questioned by many authors, most strongly by means of the Judy Benjamin puzzle. I present a new analysis of Judy Benjamin–like forms of new information and defend the thesis that in general the rational posterior is indeterminate, meaning that a family of posterior credence functions rather than a single one is the rational response when that type of information becomes available. The proposed thesis extends naturally to all cases (...) in which new information is traditionally handled by minimizing the relative entropy. (shrink)

In this article, we address a major outstanding question of probabilistic Bayesian epistemology: how should a rational Bayesian agent update their beliefs upon learning an indicative conditional? A number of authors have recently contended that this question is fundamentally underdetermined by Bayesian norms, and hence that there is no single update procedure that rational agents are obliged to follow upon learning an indicative conditional. Here we resist this trend and argue that a core set of widely accepted Bayesian norms is (...) sufficient to identify a normatively privileged updating procedure for this kind of learning. Along the way, we justify a privileged formalization of the notion of ‘epistemic conservativity’, offer a new analysis of the Judy Benjamin problem, and emphasize the distinction between interpreting the content of new evidence and updating one’s beliefs on the basis of that content. (shrink)

According to the Bayesian paradigm in the psychology of reasoning, the norms by which everyday human cognition is best evaluated are probabilistic rather than logical in character. Recently, the Bayesian paradigm has been applied to the domain of argumentation, where the fundamental norms are traditionally assumed to be logical. Here, we present a major generalisation of extant Bayesian approaches to argumentation that utilizes a new class of Bayesian learning methods that are better suited to modelling dynamic and conditional inferences than (...) standard Bayesian conditionalization, is able to characterise the special value of logically valid argument schemes in uncertain reasoning contexts, greatly extends the range of inferences and argumentative phenomena that can be adequately described in a Bayesian framework, and undermines some influential theoretical motivations for dual function models of human cognition. We conclude that the probabilistic norms given by the Bayesian approach to rationality are not necessarily at odds with the norms given by classical logic. Rather, the Bayesian theory of argumentation can be seen as justifying and enriching the argumentative norms of classical logic. (shrink)

Adams famously suggested that the acceptability of any indicative conditional whose antecedent and consequent are both factive sentences amounts to the subjective conditional probability of the consequent given the antecedent. The received view has it that this thesis offers an adequate partial explication of Ramsey’s test, which characterizes graded acceptability for conditionals in terms of hypothetical updates on the antecedent. Some results in van Fraassen may raise hope that this explicatory approach to Ramsey’s test is extendible to left-nested conditionals, that (...) is, conditionals whose antecedent is itself conditional in form. We argue that this interpretation of van Fraassen’s results is to be rejected. Specifically, we provide an argument from material inadequacy against a generalization of Adams’ thesis for left-nested conditionals. (shrink)