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Probabilistic opinion pooling generalised. Part one: general agendas

Dietrich, Franz and List, Christian (2017) Probabilistic opinion pooling generalised. Part one: general agendas. Social Choice and Welfare.

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Abstract

How can several 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. We show that 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.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Dietrich, Franz
List, Christian
Keywords: Probabilistic opinion pooling, judgment aggregation, subjective probability, probabilistic preferences, vague/fuzzy preferences, agenda characterizations, a unified perspective on aggregation, Arrow's theorem
Subjects: General Issues > Decision Theory
Specific Sciences > Economics
Specific Sciences > Probability/Statistics
Depositing User: Christian List
Date Deposited: 11 Apr 2017 13:12
Last Modified: 11 Apr 2017 13:12
Item ID: 12982
Journal or Publication Title: Social Choice and Welfare
Official URL: http://link.springer.com/article/10.1007/s00355-01...
DOI or Unique Handle: https://doi.org/10.1007/s00355-017-1034-z
Subjects: General Issues > Decision Theory
Specific Sciences > Economics
Specific Sciences > Probability/Statistics
Date: 2017
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/12982

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