How Does Active Participation Affect Consensus: Adaptive Network Model of Opinion Dynamics and Influence Maximizing Rewiring

Markus Brede

doi:10.1155/2019/1486909

Abstract

In this paper we study the impact of active participation, or deliberately seeking out other agents with an aim of convincing them, on the dynamics of consensus formation. For this purpose, we propose an adaptive network model in which two processes shape opinion dynamics at interwoven time-scales as follows: (i) agents adapt their opinions subject to influence from social network neighbours who hold opinions within a tolerance interval δ and (ii) agents rewire network connections with an aim of maximizing their own influence on overall system opinion. We study this system both in an endogenous setting, in which all agents are subject to influence and also attempt to maximize influence, and in a setting of exogenous control, in which external agents not subject to influence adaptively attempt to maximize their influence. In both settings we find three regimes of stationary opinion configurations: (i) for low δ a regime of two evenly balanced radicalized opinion clusters at the extremes of the opinion space, (ii) for intermediate δ a ’winner-takes-most’ regime of two unevenly sized radicalized opinion clusters, and (iii) for large δ a regime in which very low spread compromise consensus states can be reached. Comparing to adaptive processes of random and deliberately spread-reducing rewiring, we demonstrate that in regime (iii) competitive influence maximization can achieve near-minimal opinion spread within near-optimal times. Further, we also show that competitive influence maximizing rewiring can reduce the impact of small influential minorities on consensus states.

Highlights

Insights about the dynamics of opinion formation are relevant for our understanding of a number of social and economic processes, ranging from studies of radicalization [1, 2], political campaigns [3, 4], the spread of technology [5], or the development of industries [6] to applications in financial markets [7], and they might shed light on how democracies arrive at political decisions
In this paper we have investigated an adaptive network model of opinion formation that combines a dynamics of opinion change with competitive network rewiring of agents attempting to increase their respective influence on the rest of the population
The model is based on incremental adaptations of opinion states subject to network neighbours whose opinions differ less than a given bounded tolerance level 훿 and external effects modelled as white noise of strength Δ

Summary

Introduction

Insights about the dynamics of opinion formation are relevant for our understanding of a number of social and economic processes, ranging from studies of radicalization [1, 2], political campaigns [3, 4], the spread of technology [5], or the development of industries [6] to applications in financial markets [7], and they might shed light on how democracies arrive at political decisions. We will consider a simultaneous dynamics of opinion change and network change in which individual agents competitively attempt to rewire connections to enhance their influence on the overall consensus state. For this purpose, we will assume that each agent can change who she/he influences (i.e., adjust her/his out-connections), but note that we do not allow for self-connections. (iii) The iteration of steps (i) and (ii) are repeated until a quasistationary state has been reached Note that both parameters 푚 and 훼 essentially define the time scale of network change relative to the consensus dynamics, which is slow for small 푚 (or large 훼) and increases in relative speed when 푚 increases (or 훼 decreases). T󸀠 =0 which can capture the effect of multiple relaxation times for a monotonically decaying function

Results

Competitive Rewiring

Summary and Conclusions