Opinion Formation Dynamics with Contrarians and Zealots

Abstract

Mean-field type ODE models for opinion dynamics often assume that the entire population is comprised of congregators, who are agreeable. On the other hand, a contrarian opinion dynamics ODE model assumes the population has two personality types: congregators, and contrarians, who are disagreeable. In this paper we broadly study how contrarians influence the ability of the population to form a fixed and stable opinion. In particular, we re-examine the dynamics associated with the model introduced by Tanabe and Masuda [12] by looking at how the parameters effect the formation of stable periodic solutions (whose existence implies there is no fixed consensus opinion). Afterwards, we refine and analyze the model under two new hypotheses: (a) the contrarians bow to peer pressure and change their personality type to congregators if a large enough proportion of the entire population agrees on an opinion, and (b) there are zealots associated with one of the opinions. We conclude with a brief discussion on possible extensions of this work.

Language competition on lattices

“…The existence problem is settled by finding solutions to the nonlinear ODE (11). Recalling 𝑅 = 𝜖 0 + 4𝜖 1 , under the assumption that neither language is more prestigious, 𝐴 = 1, there exists the exact compacton solution,…”

Dynamics of two languages competing on a network: a case study

“…This is in contrast to the conclusion of those models in which it is assumed there are only congregators, as here a majority opinion is always obtained. The TM model was later refined by Eekhoff [10], and the new model allowed for the effects of peer pressure, and incorporated the influence of zealots. From a qualitative perspective the mean-field models used for opinion dynamics and language death have many similarities.…”