Opinion formation models with heterogeneous persuasion and zealotry.

M. PEREZ LLANOS; A.SILVA; N. SAINTIER; J.P.PINASCO; M. PEREZ LLANOS; A.SILVA; N. SAINTIER; J.P.PINASCO

SIAM JOURNAL ON MATHEMATICAL ANALYSIS

SIAM PUBLICATIONS

Lugar: Philadelphia-USA; Año: 2018 vol. 50 p. 4812 - 4837

0036-1410

In this work an opinion formation model with heterogeneousagents is proposed. Each agent is supposed to have different power of persuasion, and besides itsown level of zealotry, that is, an individual willingness to being convinced by otheragent. In addition, our model includes zealots or stubborn agents, agents that never change opinions.We derive a Bolzmann-like equation for the distribution of agents on the space ofopinions, which is approximated by a transport equation with a nonlocal drift term. We study the long-time asymptotic behavior of solutions, characterizing the limit distribution of agents,which consists of the distribution of stubborn agents, plus a delta function at themean of their opinions, weighted by they power of persuasion. Moreover, explicit bounds on the rate of convergence are given, and thetime to convergence is shown to decrease when the number of stubborn agents increases. This is aremarkable fact observed in agent based simulations in different works.