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From degrees of belief to binary beliefs: lessons from judgment-aggregation theory

Dietrich, Franz and List, Christian ORCID: 0000-0003-1627-800X (2018) From degrees of belief to binary beliefs: lessons from judgment-aggregation theory. The Journal of Philosophy, 115 (5). 225 - 270. ISSN 0022-362X

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Identification Number: 10.5840/jphil2018115516


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.

Item Type: Article
Official URL:
Additional Information: © 2018 The Journal of Philosophy, Inc.
Divisions: Government
Philosophy, Logic and Scientific Method
Subjects: B Philosophy. Psychology. Religion > B Philosophy (General)
Date Deposited: 20 Apr 2018 10:49
Last Modified: 23 Jun 2024 23:12

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