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Bayesianism, Fundamentally

"Comparative Probability, Comparative Confirmation, and the `Conjunction Fallacy'"
Branden Fitelson
Department of Philosophy
University of California at Berkeley

The “conjunction fallacy” has been a key topic in discussions and debates on the quality of human reasoning performance and its limitations, yet the attempt of providing a satisfactory account of the phenomenon has proven challenging. Here, we propose a new analysis, suggesting that the fallacious probability judgments experimentally observed are typically guided by sound assessments of confirmation (or evidential support) relations. The proposed analysis is shown robust (i.e., not depending on various alternative ways of measuring degree of confirmation), consistent with available data, and prompting further empirical investigations. The present approach emphasizes the relevance of the notion of confirmation in the assessments of the relationships between the normative and descriptive study of inductive reasoning. All requisite historical, philosophical, and psychological background will be provided during the talk. [Note: this is joint work with psychologists Vincenzo Crupi and Katya Tentori at the University of Trento.]

"Objective Bayes: Old and New Questions, Some Answers"
Jayanta K. Ghosh
Department of Statistics
Purdue University

I will discuss the different contexts in which objective priors are used and in what sense there is no conflict with normative subjective Bayesian analysis. Most the talk will however be devoted to two algorithmic constructions , one due to Bernardo and the other implicit in a paper of D. Basu and further developed by us. I will discuss in detail various criticisms of such priors (for example lack of invariance)and answer some of them

"Ignorance and Indifference"
John D. Norton
Department of History & Philosophy of Science and Center for Philosophy of Science
University of Pittsburgh

Two instruments can be used to delineate epistemic states of ignorance: the principle of indifference and invariance conditions. Even when both are given in their most secure formulation, they are troubled by paradoxes of similar origin. The central claim of my talk is that these paradoxes do not reveal a deficiency in the two instruments. Rather they arise because of an added assumption that the ignorance states must also be probability distributions. Without than assumption, both instruments consistently pick out a unique ignorance state, that proves to be incompatible with both the additivity of and also the Bayesian dynamics of the probability calculus.

::: "A price too great for unbounded utilities?"
Teddy Seidenfeld (speaker), Mark J. Schervish and Joseph B. Kadane
Departments of Statistics and Philosophy
Carnegie Mellon University

We extend de Finetti's (1974) theory of coherence to apply also to unbounded random variables. We show that for random variables with mandated infinite prevision, such as for the St. Petersburg gamble, coherence precludes indifference between equivalent random quantities. That is, we demonstrate when the prevision of the difference between two such equivalent random variables must be positive. This result conflicts with the usual approach to theories of Subjective Expected Utility, where preference is defined over lotteries. In addition, we explore similar results for unbounded variables when their previsions, though finite, exceed their expected values, as is permitted within de Finetti's theory. In such cases, the decision maker's coherent preferences over random quantities is not even a function of probability and utility. One upshot of these findings is to explain further the differences between Savage's theory (1954), which requires bounded utility for non-simple acts, and de Finetti's theory, which does not. And it raises a question whether there is a theory that fits between these two.