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

Franz Dietrich and Christian List ()
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Christian List: LSE - London School of Economics and Political Science

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

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. We seek to fill this gap. This 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 judgmentaggregation variant of Arrow's classic impossibility theorem in social choice theory.

Date: 2018
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Published in Journal of Philosophy, 2018, 115 (5), pp.225-270. ⟨10.5840/jphil2018115516⟩

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Working Paper: From degrees of belief to binary beliefs: Lessons from judgment-aggregation theory (2018)
Working Paper: From degrees of belief to binary beliefs: Lessons from judgment-aggregation theory (2018)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:halshs-01744085

DOI: 10.5840/jphil2018115516

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