Probabilistic opinion pooling generalized Part one: General agendas

Franz Dietrich and Christian List

MPRA Paper from University Library of Munich, Germany

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 σ-algebra 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 interest-rate increase, but not in the probability of rain or an interest-rate increase. We characterize linear pooling and neutral pooling for general agendas, with classic results as special cases for agendas that are σ-algebras. 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.

Keywords: Probabilistic opinion pooling; judgment aggregation; subjective probability; probabilistic preferences; vague/fuzzy preferences; agenda characterizations; a unified perspective on aggregation (search for similar items in EconPapers)
JEL-codes: D70 D71 D8 D80 (search for similar items in EconPapers)
Date: 2013-05, Revised 2014-07
New Economics Papers: this item is included in nep-cdm, nep-mic and nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Related works:
Journal Article: Probabilistic opinion pooling generalized. Part one: general agendas (2017)
Working Paper: Probabilistic opinion pooling generalized. Part one: general agendas (2017)
Working Paper: Probabilistic opinion pooling generalized. Part one: General agendas (2017)
Working Paper: Probabilistic opinion pooling generalized. Part one: General agendas (2017)
Working Paper: Probabilistic opinion pooling generalized. Part one: General agendas (2017)
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