Opinion Fluctuations and Disagreement in Social Networks

By Daron Acemoglu, Giacomo Como, Fabio Fagnani, Asuman E. Ozdaglar. Mathematics of Operations Research, 2010

452 citations recorded by the source corpus.

We study a tractable opinion dynamics model that generates long-run disagreements and persistent opinion fluctuations. Our model involves an inhomogeneous stochastic gossip process of continuous opinion dynamics in a society consisting of two types of agents: 1 regular agents who update their beliefs according to information that they receive from their social neighbors and 2 stubborn agents who never update their opinions and might represent leaders, political parties, or media sources attempting to influence the beliefs in the rest of the society. When the society contains stubborn agents with different opinions, the belief dynamics never lead to a consensus among the regular agents. Instead, beliefs in the society fail to converge almost surely, the belief profile keeps on fluctuating in an ergodic fashion, and it converges in law to a nondegenerate random vector. The structure of the graph describing the social network and the location of the stubborn agents within it shape the opinion dynamics. The expected belief vector is proved to evolve according to an ordinary differential equation coinciding with the Kolmogorov backward equation of a continuous-time Markov chain on the graph with absorbing states corresponding to the stubborn agents, and hence to converge to a harmonic vector, with every regular agent's value being the weighted average of its neighbors' values, and boundary conditions corresponding to the stubborn agents' beliefs. Expected cross products of the agents' beliefs allow for a similar characterization in terms of coupled Markov chains on the graph describing the social network. We prove that, in large-scale societies, which are highly fluid, meaning that the product of the mixing time of the Markov chain on the graph describing the social network and the relative size of the linkages to stubborn agents vanishes as the population size grows large, a condition of homogeneous influence emerges, whereby the stationary beliefs' marginal distributions of most of the regular agents have approximately equal first and second moments.

Subfields: Management Science and Operations Research, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2600f34bef2828b8fede669cc4326a1a733b5cfa

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In Management Science and Operations Research

In Statistical and Nonlinear Physics

Citations in the corpus

A lecture on the averaging process (2012, background): “, and this reaction may explain the comparative lack of mathematical literature on the model.”
Distributed Network Optimization With Heuristic Rational Agents (2012, background): “Consensus formation [15], [16] and opinion propagation [17] in social networks can also be understood in terms of distributed network optimization.”
Distributed Finite-Time Average Consensus in Digraphs in the Presence of Time Delays (2015, unknown): “, dynamics of opinion forming [8]).”
Binary Opinion Dynamics with Stubborn Agents (2013, methodology): “Acemoglu et al. consider an extension of the DeGroot model, where updates are asynchronous and certain individuals are spreading misinformation by not updating their own beliefs ([Acemoglu et al. 2011]). Under the assumption that no man is an island, that is, each and every individual will update he”
Social Networks and Housing Markets (2018, unknown): “, Akerlof and Shiller, 2010; Acemoglu et al., 2011, 2013; Angeletos and La’O, 2013; Shiller, 2015; Burnside, Eichenbaum and Rebelo, 2016). Our second contribution is to introduce a new methodology for analyzing the role of individuals’ housing market expectations in determining individual and aggreg”