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Probabilistic opinion pooling generalized. Part one: general agendas

Dietrich, Franz and List, Christian (2017) Probabilistic opinion pooling generalized. Part one: general agendas. Social Choice and Welfare, 48 (4). pp. 747-786. ISSN 0176-1714

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Identification Number: 10.1007/s00355-017-1034-z

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.

Item Type: Article
Official URL: https://link.springer.com/journal/355
Additional Information: © 2017 The Authors © CC BY 4.0
Divisions: Government
Philosophy, Logic and Scientific Method
CPNSS
Subjects: B Philosophy. Psychology. Religion > B Philosophy (General)
H Social Sciences > HB Economic Theory
Sets: Departments > Government
Departments > Philosophy, Logic and Scientific Method
Research centres and groups > Centre for Philosophy of Natural and Social Science (CPNSS)
Date Deposited: 11 Apr 2017 15:45
Last Modified: 20 Jun 2020 02:27
Projects: ANR-12-INEG-0006-01, MRF-2012-100
Funders: Ludwig Lachmann Fellowship at the LSE, French Agence Nationale de la Recherche, Leverhulme Major Research Fellowship, Harsanyi Fellowship at the Australian National University, Canberra
URI: http://eprints.lse.ac.uk/id/eprint/73508

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