2016/03/02 by Francesca Colaiori, Claudio Castellano · 18 citations
Mathematics · Physics and Astronomy · #Class (philosophy) #Critical mass (sociodynamics) #Fraction (chemistry) #Mathematical Biology Tumor Growth #Opinion Dynamics and Social Influence #Pairwise comparison #Persistence (discontinuity) #Phase diagram #Population #Theoretical and Computational Physics #cond-mat.stat-mech #physics.soc-ph
paper · pdf · doi:10.1088/1742-5468/2016/03/033401
published in Journal of Statistical Mechanics Theory and Experiment 2016(3), 033401 (Institute of Physics) · This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Statistical Mechanics: Theory and Experiment. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/1742-5468/2016/03/033401
openalex publication_date 2016/03/02 · arxiv created 2016/03/08 · arxiv updated 2016/03/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider a general class of three-state models where individuals hold one of two opposite opinions, or are neutral, and exchange opinions in generic pairwise interactions. We show that when opinions spread in a population where a fraction of individuals (zealots) unshakably maintain their view, one of four qualitatively distinct kinds of collective dynamics arises, depending on the specific rules governing the social interactions. Unsurprisingly, when their density is high, zealots drive the whole population to consensus on their opinion. For low densities a rich phase diagram emerges: a finite population of dissenters can survive and be the only stationary state or may need a critical initial mass of dissenters to be sustained; the critical mass may vanish or not as the density is reduced; the transition to the high density regime can be smooth or abrupt, and shows interesting hysteretic effects. For each choice of the interaction rules we calculate the critical density of zealots above which diverse opinions cannot survive.