Journal of Philosophy 115 (5):225-270 (2018)

Authors
Franz Dietrich
Centre National de la Recherche Scientifique
Christian List
Ludwig Maximilians Universität, München
Abstract
What is the relationship between degrees of belief and binary beliefs? Can the latter be expressed as a function of the former—a so-called “belief-binarization rule”—without running into difficulties such as the lottery paradox? We show that this problem can be usefully analyzed from the perspective of judgment-aggregation theory. Although some formal similarities between belief binarization and judgment aggregation have been noted before, the connection between the two problems has not yet been studied in full generality. In this paper, we seek to fill this gap. The paper is organized around a baseline impossibility theorem, which we use to map out the space of possible solutions to the belief-binarization problem. Our theorem shows that, except in limiting cases, there exists no belief-binarization rule satisfying four initially plausible desiderata. Surprisingly, this result is a direct corollary of the judgment-aggregation variant of Arrow’s classic impossibility theorem in social choice theory.
Keywords beliefs  subjective probability  lottery paradox  judgment aggregation  formal epistemology
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ISBN(s) 0022-362X
DOI 10.5840/jphil2018115516
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References found in this work BETA

Probability and the Logic of Rational Belief.Henry E. Kyburg Jr - 1961 - Middletown, CT, USA: Wesleyan University Press.
Probability and the Logic of Rational Belief.Henry Ely Kyburg - 1961 - Middletown, CT, USA: Middletown, Conn., Wesleyan University Press.
The Stability Theory of Belief.Hannes Leitgeb - 2014 - Philosophical Review 123 (2):131-171.
Accuracy, Coherence and Evidence.Branden Fitelson & Kenny Easwaran - 2015 - Oxford Studies in Epistemology 5:61-96.

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Citations of this work BETA

The Relation Between Degrees of Belief and Binary Beliefs: A General Impossibility Theorem.Franz Dietrich & Christian List - 2021 - In Lotteries, Knowledge, and Rational Belief. Essays on the Lottery Paradox. Cambridge University Press. pp. 223-54.
Categorical Versus Graded Beliefs.Franz Dietrich - 2022 - Frontiers in Psychology 18.
Scientific Expertise and Risk Aggregation.Thomas Boyer-Kassem - 2019 - Philosophy of Science 86 (1):124-144.

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Similar books and articles

Arrow's Theorem in Judgment Aggregation.Franz Dietrich & Christian List - 2007 - Social Choice and Welfare 29 (1):19-33.
Natural Deduction for Modal Logic of Judgment Aggregation.Tin Perkov - 2016 - Journal of Logic, Language and Information 25 (3-4):335-354.
The Aggregation of Propositional Attitudes: Towards a General Theory.Franz Dietrich & List & Christian - 2010 - In Tamar Szabó Gendler & John Hawthorne (eds.), Oxford Studies in Epistemology Volume 3. Oxford University Press. pp. 215-234.
Factoring Out the Impossibility of Logical Aggregation.Philippe Mongin - 2008 - Journal of Economic Theory 141:p. 100-113.
Introduction to Judgment Aggregation.Christian List & Ben Polak - 2010 - Journal of Economic Theory 145 (2):441-466.

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