### DIMACS Graduate Student Combinatorics Seminar Series

Title: The Voter Model with Confidence Levels

Speaker: **Stephen Hartke**, Rutgers University

Date: Monday, October 6, 2003, 1:10 pm

Location: Hill Center, Room 525, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

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.