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

La relation entre les degrés de croyance et les croyances binaires: un théorème d'impossibilité général

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

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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: subjective probabilities; construction of binary beliefs from subjective probabilities; binary beliefs (yes/no); impossibility theorem; croyances binaires (oui/non); probabilités subjectives; théorème d'impossibilité; construction de croyances binaires à partir des probabilités subjectives (search for similar items in EconPapers)
Date: 2019-01
New Economics Papers: this item is included in nep-upt
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01999527v1
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Published in 2019

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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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