Jeffrey Helzner

Ambiguity aversion: the explanatory power of indeterminate probabilities

Daniel Ellsberg presented in Ellsberg (The Quarterly Journal of Economics 75:643–669, 1961) various examples questioning the thesis that decision making under uncertainty can be reduced to decision making under risk. These examples constitute one of the main challenges to the received view on the foundations of decision theory offered by Leonard Savage in Savage (1972). Craig Fox and Amos Tversky have, nevertheless, offered an indirect defense of Savage. They provided in Fox and Tversky (1995) an explanation of Ellsberg’s two-color problem in terms of a psychological effect: ambiguity aversion. The ‘comparative ignorance’ hypothesis articulates how this effect works and explains why it is important to an understanding of the typical pattern of responses associated with Ellsberg’s two-color problem. In the first part of this article we challenge Fox and Tversky’s explanation. We present first an experiment that extends Ellsberg’s two-color problem where certain predictions of the comparative ignorance hypothesis are not confirmed. In addition the hypothesis seems unable to explain how the subjects resolve trade-offs between security and expected pay-off when vagueness is present. Ellsberg offered an explanation of the typical behavior elicited by his examples in terms of these trade-offs and in section three we offer a model of Ellsberg’s trade-offs. The model takes seriously the role of imprecise probabilities in explaining Ellsberg’s phenomenon. The so-called three-color problem was also considered in Fox and Tversky (1995). We argue that Fox and Tversky’s analysis of this case breaks a symmetry with their analysis of the two-color problem. We propose a unified treatment of both problems and we present a experiment that confirms our hypothesis.

Rationalizing two-tiered choice functions through conditional choice

Set-valued choice functions provide a framework that is general enough to encompass a wide variety of theories that are significant to the study of rationality but, at the same time, offer enough structure to articulate consistency conditions that can be used to characterize some of the theories within this encompassed variety. Nonetheless, two-tiered choice functions, such as those advocated by Isaac Levi, are not easily characterized within the framework of set-valued choice functions. The present work proposes conditional choice functions as the proper carriers of synchronic rationality. The resulting framework generalizes the familiar one mentioned above without emptying it and, moreover, provides a natural setting for two-tiered choice rules.

Epistemology and economics

On April 14th and 15th of 2010 the Synthese Conference on Epistemology and Economics was held at Columbia University in the City of New York. The conference included eleven talks: five invited, five contributed, and one by the winner of the Synthese Distinguished Paper Award. It is not easy to pull off a conference of this sort, especially in a place like New York where the cost of doing business is significant, but all of the reports that I have received suggest that the conference was a great success. I would like to thank the following people for their hard work: the Synthese Editors-in-Chief at the time of the conference, Johan van Benthem, Vincent Hendricks, and John Symons; my fellow members of the Local Organizing Committee, John Collins, Haim Gaifman, and Philip Kitcher; Ties Nijssen and Ingrid van Laarhoven at Springer; Stacey Quartaro, Department Administrator for the Department of Philosophy at Columbia, and Achille Varzi, Chair of the Department of Philosophy at Columbia. The papers in this volume represent some of the work that was presented at the conference. Before turning attention to the specific papers in this volume, it seems appropriate to make some general comments on the conference theme since it might not be clear what sorts of philosophically interesting relations exist between epistemology and economics. After all, epistemology is often identified with attempts to analyze terms like knows and believes, while much of classical economics (e.g., consumer theory, the theory of the firm) can be understood as being about rational agents and the various equilibria that could result from their interactions. The following is a brief survey of just some of the philosophically interesting relations between epistemology and economics:

Combining probability and logic: Papers from Progic 2011

The Progic conferences are intended to promote interactions between probability and logic. The fifth installment of the series was held at Columbia University in New York on September 10th and 11th of 2011. The meeting was made possible by generous financial support from Columbia’s Faculty of Arts and Sciences and Department of Philosophy. Progic 2011 would not have been a success without the efforts of Stacey Quartaro – the Department Administrator for Columbia’s Department of Philosophy – and her staff. While several of the earlier Progic meetings included a special focus, Progic 2011 honored Columbia’s own Haim Gaifman for his many contributions to the intersection of probability and logic. The meeting consisted of 11 talks – including invited talks by Haim Gaifman (Columbia), Rohit Parikh (CUNY), Jeff Paris (Manchester), and Dana Scott (Carnegie Mellon) – as well as a memorial session to honor Horacio Arlo-Costa (Carnegie Mellon) who was invited to speak at the conference but passed away on July 14, 2011. The papers in this volume represent a selection of the work that was presented at Progic 2011.

More foundations of the decision sciences: introduction

This second part of the special issue on the foundations of the decision sciences continues with the treatment of some topics that were discussed in the first part and includes papers on four additional areas of research. The first part of this special issue—which was published as Volume 172, Number 1 of Synthese in 2010—features various papers that focus on models of choice under uncertainty. In this second part we are pleased to present two additional papers that elaborate on this topic. The first of these is by Itzhak Gilboa, Andrew Postlewaite, and David Schmeidler. Their paper is a criticism of the classical Bayesian approach that the authors think is neither necessary nor sufficient for the rationality of belief. Therefore this paper has a rather general scope focusing on the normative limitations of Savage’s approach. The second of these two papers on choice under uncertainty is by Alan Hajek and Michael Smithson. Their paper presents a novel argument for models that allow for doxastic indeterminacy via the use of sets of probabilities. There is some overlap between these two papers because Gilboa et al. think that one of the reasons for the alleged inadequacy of the Bayesian approach is the fact that in many cases there is not sufficient information for a rational agent to form a Bayesian prior. Therefore they also recommend the use of sets of probabilities and discuss in certain detail (in an Appendix) Ellsberg’s paradox.