DIMACS TR: 2003-45

The Voter Model with Confidence Levels

Author: Stephen Hartke

The voter model on a finite connected graph $G$ is a stochastic process where each vertex has an opinion, 0 or 1. As time progresses, each voter's opinion is influenced by its neighbors. We introduce a modification of the voter model that changes how quickly a voter will change its opinion based on its confidence in its opinion. We show that the voter model with confidence levels always results in a uniform opinion, and we determine the probability of each outcome (uniform 1 or 0) based on the initial opinions and the structure of the graph.

Keywords: voter model, interacting particle system

Mathematics Subject Classification: Primary 60K35, Secondary 82C20, 82C22

Paper available at ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-45.ps.gz

DIMACS Home Page