Aggregation of opinions in networks of individuals and collectives
type: Item
instance of: scholarly article
title: Aggregation of opinions in networks of individuals and collectives
zbMATH Open document ID: 1486.91061
author: Hervé Crès
author: Mich Tvede
published in: Journal of Economic Theory
publication date: 2022-01-18T00:00:00Z
review text: In this paper, the authors present a theoretical study of opinion formation in a bipartite network of boards and directors of firms. Their analysis focusses on stability of opinions and uses the concept of network connectedness to explain consensus in such networks of firms' boards and directors. The paper consists of 6 sections and an appendix presenting proofs of all results. The introduction (Section 1) begins with a presentation of the motivation of the study which comes from all decisions taken in 2014 in general assembly meetings of the 40 largest French corporations (CAC 40). Then, the section presents a detailed overview of the paper and the related literature. Section 2 is devoted to the model. In Section 3, the authors introduce and discuss the Pareto principle for opinion aggregation in boards and directors, and prove two related lemmas. The main results of the paper are presented in Section 4 devoted to stability of opinions and in Section 5 concerning convergence of opinions. Opinions are stable provided the opinions of everybody are not contradicted by the opinions of everybody else. In Section 4 the authors prove that for connected graphs, with every director and every board being connected directly or indirectly, opinions are stable if and only if they are identical and unambiguous. Section 5 presents several results on convergence of opinions. It is proven that repeated revision of opinions leads to elimination of ambiguity independently of initial opinions and a shared belief. It is also shown that for all beliefs in the relative interior of the convex hull of opinions there are revision functions such that repeated revision of opinions leads to the belief being established as the shared belief. Finally, the authors prove that revision functions respecting the weak Pareto principle can be approximated by revision functions respecting the Pareto principle. Section 6 presents a short discussion of the results and some extensions.
reviewed by: Agnieszka Rusinowska
Mathematics Subject Classification ID: 91D30
zbMATH DE Number: 7458541
zbMATH Keywords: boards
zbMATH Keywords: directors
zbMATH Keywords: networks
zbMATH Keywords: Pareto principle
MaRDI profile type: Publication
full work available at URL: j.jet.2021.105305
OpenAlex ID: W3177451597
cites work: Opinion dynamics and learning in social networks
cites work: Knightian decision theory. I.
cites work: Testing Models of Social Learning on Networks: Evidence From Two Experiments
cites work: Aggregation of multiple prior opinions
cites work: Q5588318
cites work: Reaching a Consensus
cites work: Persuasion Bias, Social Influence, and Unidimensional Opinions
cites work: Risk, ambiguity and the Savage axioms
cites work: Representation and aggregation of preferences under uncertainty
cites work: Combining probability distributions: A critique and an annotated bibliography
cites work: Q3630149
cites work: Maxmin expected utility with non-unique prior
cites work: Rationality of belief or: why Savage's axioms are neither necessary nor sufficient for rationality
cites work: The Impossibility of Bayesian Group Decision Making with Separate Aggregation of Beliefs and Values
cites work: Q3526040
cites work: A Theory of Non-Bayesian Social Learning
cites work: Consistent Bayesian aggregation
cites work: The doctrinal paradox, the discursive dilemma, and logical aggregation theory
cites work: Q4477880
cites work: Q5599348
cites work: Q5826088
cites work: Integral Representation Without Additivity
cites work: Subjective Probability and Expected Utility without Additivity
cites work: The Opinion Pool
DOI: 10.1016/J.JET.2021.105305
description: scientific article; zbMATH DE number 7458541