2013/03/29 by Feng Shi, Peter J. Mucha, Rick Durrett +1 · 21 citations
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Complex Network Analysis Techniques #Discrete mathematics #Epistemology #Function (biology) #Graph #Limit (mathematics) #Mathematical analysis #Mathematics #Opinion Dynamics and Social Influence #Order (exchange) #Phase transition #Physics #Probability and statistics #Quantum many-body systems #Quantum mechanics #Simple (philosophy) #Statistical physics #Statistics #Voter model #cond-mat.dis-nn #cs.SI #math.PR #nlin.AO #physics.soc-ph
paper · pdf · doi:10.1103/physreve.88.062818
published in Physical Review E 88(6), 062818 (American Physical Society) · 15 pages, 6 figures
arxiv created 2013/03/29 · openalex publication_date 2013/12/30 · arxiv updated 2015/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider an idealized model in which individuals' changing opinions and their social network coevolve, with disagreements between neighbors in the network resolved either through one imitating the opinion of the other or by reassignment of the discordant edge. Specifically, an interaction between x and one of its neighbors y leads to x imitating y with probability (1-α) and otherwise (i.e., with probability α) x cutting its tie to y in order to instead connect to a randomly chosen individual. Building on previous work about the two-opinion case, we study the multiple-opinion situation, finding that the model has infinitely many phase transitions (in the large graph limit with infinitely many initial opinions). Moreover, the formulas describing the end states of these processes are remarkably simple when expressed as a function of β=α/(1-α).