Dietrich, Franz and List, Christian (2013): Probabilistic opinion pooling generalized Part one: General agendas.

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Abstract
How can different individuals' probability assignments to some events be aggregated into a collective probability assignment? Classic results on this problem assume that the set of relevant events  the agenda  is a σalgebra and is thus closed under disjunction (union) and conjunction (intersection). We drop this demanding assumption and explore probabilistic opinion pooling on general agendas. One might be interested in the probability of rain and that of an interestrate increase, but not in the probability of rain or an interestrate increase. We characterize linear pooling and neutral pooling for general agendas, with classic results as special cases for agendas that are σalgebras. As an illustrative application, we also consider probabilistic preference aggregation. Finally, we unify our results with existing results on binary judgment aggregation and Arrovian preference aggregation. Our unified theorems show why the same kinds of axioms (independence and consensus preservation) have radically different implications for different aggregation problems: linearity for probability aggregation and dictatorship for binary judgment or preference aggregation.
Item Type:  MPRA Paper 

Original Title:  Probabilistic opinion pooling generalized Part one: General agendas 
Language:  English 
Keywords:  Probabilistic opinion pooling, judgment aggregation, subjective probability, probabilistic preferences, vague/fuzzy preferences, agenda characterizations, a unified perspective on aggregation 
Subjects:  D  Microeconomics > D7  Analysis of Collective DecisionMaking > D70  General D  Microeconomics > D7  Analysis of Collective DecisionMaking > D71  Social Choice ; Clubs ; Committees ; Associations D  Microeconomics > D8  Information, Knowledge, and Uncertainty D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D80  General 
Item ID:  57253 
Depositing User:  Franz Dietrich 
Date Deposited:  11 Jul 2014 14:56 
Last Modified:  26 Sep 2019 08:13 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/57253 