This paper seeks to defend the following conclusions: The program advanced by Carnap and other necessarians for probability logic has little to recommend it except for one important point. Credal probability judgments ought to be adapted to changes in evidence or states of full belief in a principled manner in conformity with the inquirer’s confirmational commitments—except when the inquirer has good reason to modify his or her confirmational commitment. Probability logic ought to spell out the constraints on rationally coherent confirmational (...) commitments. In the case where credal judgments are numerically determinate confirmational commitments correspond to Carnap’s credibility functions mathematically represented by so—called confirmation functions. Serious investigation of the conditions under which confirmational commitments should be changed ought to be a prime target for critical reflection. The necessarians were mistaken in thinking that confirmational commitments are immune to legitimate modification altogether. But their personalist or subjectivist critics went too far in suggesting that we might dispense with confirmational commitments. There is room for serious reflection on conditions under which changes in confirmational commitments may be brought under critical control. Undertaking such reflection need not become embroiled in the anti inductivism that has characterized the work of Popper, Carnap and Jeffrey and narrowed the focus of students of logical and methodological issues pertaining to inquiry. (shrink)

Experimental results on the Ellsberg paradox typically reveal behavior that is commonly interpreted as ambiguity aversion. The experiments reported in the current paper find the objective probabilities for drawing a red ball that make subjects indifferent between various risky and uncertain Ellsberg bets. They allow us to examine the predictive power of alternative principles of choice under uncertainty, including the objective maximin and Hurwicz criteria, the sure-thing principle, and the principle of insufficient reason. Contrary to our expectations, the principle of (...) insufficient reason performed substantially better than rival theories in our experiment, with ambiguity aversion appearing only as a secondary phenomenon. (shrink)

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. (shrink)

We suggest to define objective probabilities by similarity-weighted empirical frequencies, where more similar cases get a higher weight in the computation of frequencies. This formula is justified intuitively and axiomatically, but raises the question, which similarity function should be used? We propose to estimate the similarity function from the data, and thus obtain objective probabilities. We compare this definition to others, and attempt to delineate the scope of situations in which objective probabilities can be used.

Daniel Ellsberg presented in Ellsberg 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. Craig Fox and Amos Tversky have, nevertheless, offered an indirect defense of Savage. They provided in Fox and Tversky 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. 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. (shrink)