Rationality and indeterminate probabilities

Synthese 187 (1):33-48 (2012)
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Abstract

We argue that indeterminate probabilities are not only rationally permissible for a Bayesian agent, but they may even be rationally required . Our first argument begins by assuming a version of interpretivism: your mental state is the set of probability and utility functions that rationalize your behavioral dispositions as well as possible. This set may consist of multiple probability functions. Then according to interpretivism, this makes it the case that your credal state is indeterminate. Our second argument begins with our describing a world that plausibly has indeterminate chances. Rationality requires a certain alignment of your credences with corresponding hypotheses about the chances. Thus, if you hypothesize the chances to be indeterminate, your will inherit their indeterminacy in your corresponding credences. Our third argument is motivated by a dilemma. Epistemic rationality requires you to stay open-minded about contingent matters about which your evidence has not definitively legislated. Practical rationality requires you to be able to act decisively at least sometimes. These requirements can conflict with each other-for thanks to your open-mindedness, some of your options may have undefined expected utility, and if you are choosing among them, decision theory has no advice to give you. Such an option is playing Nover and Hájek’s Pasadena Game , and indeed any option for which there is a positive probability of playing the Pasadena Game. You can serve both masters, epistemic rationality and practical rationality, with an indeterminate credence to the prospect of playing the Pasadena game. You serve epistemic rationality by making your upper probability positive-it ensures that you are open-minded. You serve practical rationality by making your lower probability 0-it provides guidance to your decision-making. No sharp credence could do both.

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Author Profiles

Alan Hajek
Australian National University
Michael Smithson
Australian National University

Citations of this work

Interpretations of probability.Alan Hájek - 2007 - Stanford Encyclopedia of Philosophy.
Imprecise Probabilities.Seamus Bradley - 2019 - Stanford Encyclopedia of Philosophy.
Imprecise evidence without imprecise credences.Jennifer Rose Carr - 2020 - Philosophical Studies 177 (9):2735-2758.
Chance and the Continuum Hypothesis.Daniel Hoek - 2021 - Philosophy and Phenomenological Research 103 (3):639-60.

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The Logic of Decision.Richard C. Jeffrey - 1965 - New York, NY, USA: University of Chicago Press.
Vagueness.Timothy Williamson - 1996 - New York: Routledge.
Humean Supervenience Debugged.David Lewis - 1994 - Mind 103 (412):473--490.

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