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

Franz Dietrich and Christian List

MPRA Paper from University Library of Munich, Germany

Abstract: What is the relationship between degrees of belief and (all-or-nothing) beliefs? Can the latter be expressed as a function of the former, without running into paradoxes? We reassess this “belief-binarization” problem from the perspective of judgmentaggregation theory. Although some similarities between belief binarization and judgment aggregation have been noted before, the literature contains no general study of the implications of aggregation-theoretic impossibility and possibility results for belief binarization. We seek to fill this gap. At the centre of this paper is an impossibility theorem showing that, except in simple cases, there exists no belief-binarization rule satisfying four baseline desiderata (“universal domain”, “belief consistency and completeness”, “propositionwise independence”, “certainty preservation”). We show that this result is a corollary of the judgment-aggregation variant of Arrow’s impossibility theorem and explore several escape routes from it.

Keywords: subjective probability; yes/no belif; impossibility theorem on binarization; analytic philosophy; judgment aggregation (search for similar items in EconPapers)
JEL-codes: C0 C02 D0 D01 D7 D70 D8 D80 D81 D89 (search for similar items in EconPapers)
Date: 2014-08
New Economics Papers: this item is included in nep-hpe and nep-mic
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https://mpra.ub.uni-muenchen.de/80844/1/MPRA_paper_80844.pdf revised version (application/pdf)

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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:58257

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