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In this paper we study the impact of active participation -- or deliberatelyseeking out other agents with an aim to convince them -- on the dynamics ofconsensus formation. For this purpose, we propose an adaptive network model inwhich two processes shape opinion dynamics at interwoven time-scales: (i)agents adapt their opinions subject to influence from social network neighbourswho hold opinions within a tolerance interval $\delta$ and (ii) agents rewirenetwork connections with an aim to maximize their own influence on overallsystem opinion. We study this system in both an endogenous setting in which allagents are subject to influence and also attempt to maximize influence, and ina setting of exogenous control, in which external agents not subject toinfluence adaptively attempt to maximize their influence. In both settings wefind three regimes of stationary opinion configurations: (i) for low $\delta$ aregime of two evenly balanced radicalized opinion clusters at the extremes ofthe opinion space, (ii) for intermediate $\delta$ a 'winner-takes-most' regimeof two unevenly sized radicalized opinion clusters, and (iii) for large$\delta$ a regime in which very low spread compromise consensus states can bereached. Comparing to adaptive processes of random and deliberatelyspread-reducing rewiring, we demonstrate that in regime (iii) competitiveinfluence maximization can achieve near-minimal opinion spread withinnear-optimal times. Further, we also show that competitive influence maximizingrewiring can reduce the impact of small influential minorities on consensusstates.

How does active participation effect consensus: Adaptive network model of opinion dynamics and influence maximizing rewiring