The relation between degrees of belief and binary beliefs: A general impossibility theorem

Franz Dietrich and Christian List ()
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Christian List: London School of Economics, http://personal.lse.ac.uk/list/

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne

Abstract: Agents are often assumed to have degrees of belief (“credences”) and also binary beliefs (“beliefs simpliciter”). How are these related to each other? A much-discussed answer asserts that it is rational to believe a proposition if and only if one has a high enough degree of belief in it. But this answer runs into the “lottery paradox”: the set of believed propositions may violate the key rationality conditions of consistency and deductive closure. In earlier work, we showed that this problem generalizes: there exists no local function from degrees of belief to binary beliefs that satisfies some minimal conditions of rationality and non-triviality. “Locality” means that the binary belief in each proposition depends only on the degree of belief in that proposition, not on the degrees of belief in others. One might think that the impossibility can be avoided by dropping the assumption that binary beliefs are a function of degrees of belief. We prove that, even if we drop the “functionality” restriction, there still exists no local relation between degrees of belief and binary beliefs that satisfies some minimal conditions. Thus functionality is not the source of the impossibility; its source is the condition of locality. If there is any non-trivial relation between degrees of belief and binary beliefs at all, it must be a “holistic” one. We explore several concrete forms this “holistic” relation could take.

Keywords: binary beliefs (yes/no); subjective probabilities; construction of binary beliefs from subjective probabilities; impossibility theorem (search for similar items in EconPapers)
JEL-codes: D81 (search for similar items in EconPapers)
Pages: 28 pages
Date: 2019-01
New Economics Papers: this item is included in nep-hpe, nep-mic and nep-upt
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ftp://mse.univ-paris1.fr/pub/mse/CES2019/19001.pdf (application/pdf)

Related works:
Working Paper: The Relation between Degrees of Belief and Binary Beliefs: A General Impossibility Theorem (2021)
Working Paper: The Relation between Degrees of Belief and Binary Beliefs: A General Impossibility Theorem (2021)
Working Paper: The Relation between Degrees of Belief and Binary Beliefs: A General Impossibility Theorem (2021)
Working Paper: The relation between degrees of belief and binary beliefs: A general impossibility theorem (2019)
Working Paper: The relation between degrees of belief and binary beliefs: A general impossibility theorem (2019)
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Persistent link: https://EconPapers.repec.org/RePEc:mse:cesdoc:19001

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