Majority rule based opinion dynamics with biased and stubborn agents

Document Type

Conference Article

Publication Title

SIGMETRICS/ Performance 2016 - Proceedings of the SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Science

Abstract

In this paper, we investigate the impact of majority-rule based random interactions among agents in a large social network on the diffusion of opinions in the network. Opin-ion of each agent is assumed to be a binary variable taking values in the set {0, 1}. Interactions among agents are mod- eled using the majority rule, where each agent updates its opinion at random instants by adopting the 'majority' opin- ion among a group of randomly sampled agents. We investi-gate two scenarios that respectively incorporate 'bias' of the agents towards a specific opinion and stubbornness of some of the agents in the majority rule dynamics. For the first scenario, where all the agents are assumed to be 'biased' to- wards one of the opinions, it is shown that the agents reach a consensus on the preferred opinion (with high probabil-ity) only if the initial fraction of agents having the preferred opinion is above a certain threshold. Furthermore, the mean time taken to reach the consensus is shown to be logarithmic in the network size. In the second scenario, where the pres-ence of 'stubborn' agents, who never update their opinions, is assumed, we characterize the equilibrium distribution of opinions of the non-stubborn agents using mean field tech- niques. The mean field limit is shown to have multiple stable equilibrium points which leads to a phenomenon known as metastability.

First Page

385

Last Page

386

DOI

10.1145/2896377.2901488

Publication Date

6-14-2016

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