Aggregation of opinions in networks of individuals and collectives
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.
scientific article; zbMATH DE number 7458541
scientific article