Dietrich, Franz and List, Christian (2014): From degrees of belief to binary beliefs: Lessons from judgmentaggregation theory.
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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 socalled “beliefbinarization rule” – without running into difficulties such as the lottery paradox? We show that this problem can be usefully analyzed from the perspective of judgmentaggregation 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 beliefbinarization problem. Our theorem shows that, except in limiting cases, there exists no beliefbinarization 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.
Item Type:  MPRA Paper 

Original Title:  From degrees of belief to binary beliefs: Lessons from judgmentaggregation theory 
Language:  English 
Keywords:  subjective probability, yes/no belif, impossibility theorem on binarization, analytic philosophy, judgment aggregation 
Subjects:  C  Mathematical and Quantitative Methods > C0  General C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods D  Microeconomics > D0  General D  Microeconomics > D0  General > D01  Microeconomic Behavior: Underlying Principles D  Microeconomics > D7  Analysis of Collective DecisionMaking D  Microeconomics > D7  Analysis of Collective DecisionMaking > D70  General D  Microeconomics > D8  Information, Knowledge, and Uncertainty D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D80  General D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D89  Other 
Item ID:  80844 
Depositing User:  Franz Dietrich 
Date Deposited:  19 Aug 2017 14:07 
Last Modified:  27 Sep 2019 00:03 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/80844 
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From degrees of belief to beliefs: Lessons from judgmentaggregation theory. (deposited 05 Sep 2014 07:32)
 From degrees of belief to binary beliefs: Lessons from judgmentaggregation theory. (deposited 19 Aug 2017 14:07) [Currently Displayed]