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

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

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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 analysed 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.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Dietrich, Franz
List, Christian
Keywords: Degrees of belief, full beliefs, quantitative and qualitative belief, closure, lottery paradox, belief binarization, judgment aggregation, discursive dilemma, Arrow's theorem, formal epistemology
Subjects: General Issues > Decision Theory
Specific Sciences > Economics
Specific Sciences > Probability/Statistics
Depositing User: Christian List
Date Deposited: 10 May 2018 15:23
Last Modified: 10 May 2018 15:23
Item ID: 14659
Journal or Publication Title: The Journal of Philosophy
Publisher: The Journal of Philosophy, Inc
Official URL: https://doi.org/10.5840/jphil2018115516
DOI or Unique Handle: https://doi.org/10.5840/jphil2018115516
Subjects: General Issues > Decision Theory
Specific Sciences > Economics
Specific Sciences > Probability/Statistics
Date: May 2018
Page Range: pp. 225-270
Volume: 115
Number: 5
ISSN: 0022-362X
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/14659

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