The impact of competing zealots on opinion dynamics

An individual's opinion on an issue is greatly impacted by others in his or her social network. Most people are open-minded and ready to change their opinion when presented evidence; however, some are zealots or inflexibles, that is, individuals who refuse to change their opinion while staunchly advocating an opinion in hopes of convincing others. Zealotry is present in opinions of significant personal investment, such as political, religious or corporate affiliation; it tends to be less commonplace in opinions involving rumors or fashion trends. In this paper, we examine the effect that zealots have in a population whose opinion dynamics obey the naming game model. We present numerical and analytical results about the number and nature of steady state solutions, demonstrating the existence of a bifurcation in the space of zealot fractions. Our analysis indicates conditions under which a minority zealot opinion ultimately prevails, and conditions under which neither opinion attains a majority. We also present numerical and simulation analysis of finite populations and on networks with partial connectivity.