Does Public Knowledge Help Us Agree?: The Dynamics of Consensus from Models of Learning on Networks

Abstract

This paper intends to examine the role of public knowledge on the rate at which populations, modeled as agents interacting within a graphical network, are able to come to a consensus. Canonical situations in which interactive consensus is an important topic of study include marketing, technology adoption, and corporate teamwork. This paper’s results are motivated by applying network-based models to study the rate of consensus in relation to political mobilization for revolution. Within this study, public knowledge is modeled as information about agents’ beliefs or actions derived from all agents within the population, while private knowledge concerns only an agent’s neighbors on the network. Ultimately, this paper provides theoretical evidence, by employing standard methods of spectral graph theory, matrix analysis, and probability theory, that public knowledge increases the rate at which consensus on beliefs about a parameter or consensus on action is achieved. However, as a “cautionary tale,” if public knowledge increases the rate at which agents’ beliefs are updated, the rate at which consensus is achieved is slower for an important class of graphs.