Adaptive voter model on simplicial complexes
Abstract
Collective decision making processes lie at the heart of many social, political, and economic challenges. The classical voter model is a wellestablished conceptual model to study such processes. In this work, we define a form of adaptive (or coevolutionary) voter model posed on a simplicial complex, i.e., on a certain class of hypernetworks or hypergraphs. We use the persuasion rule along edges of the classical voter model and the recently studied rewiring rule of edges towards likeminded nodes, and introduce a peerpressure rule applied to three nodes connected via a 2simplex. This simplicial adaptive voter model is studied via numerical simulation. We show that adding the effect of peer pressure to an adaptive voter model leaves its fragmentation transition, i.e., the transition upon varying the rewiring rate from a single majority state into a fragmented state of two different opinion subgraphs, intact. Yet, above and below the fragmentation transition, we observe that the peer pressure has substantial quantitative effects. It accelerates the transition to a singleopinion state below the transition and also speeds up the system dynamics towards fragmentation above the transition. Furthermore, we quantify that there is a multiscale hierarchy in the model leading to the depletion of 2simplices, before the depletion of active edges. This leads to the conjecture that many other dynamic network models on simplicial complexes may show a similar behavior with respect to the sequential evolution of simplices of different dimensions.
 Publication:

Physical Review E
 Pub Date:
 February 2020
 DOI:
 10.1103/PhysRevE.101.022305
 arXiv:
 arXiv:1909.05812
 Bibcode:
 2020PhRvE.101b2305H
 Keywords:

 Nonlinear Sciences  Adaptation and SelfOrganizing Systems;
 Mathematics  Dynamical Systems;
 Mathematics  General Topology;
 Quantitative Biology  Populations and Evolution
 EPrint:
 10 pages, 6 figures