Opinion Dynamics with State-Dependent Susceptibility to Influence

A general discrete-time opinion dynamics model is studied in this paper. It is proposed that each individual has a susceptibility to being influenced by his/her neighbours, and that this susceptibility depends on the individuals current opinion value. This precept is captured by a state-dependent susceptibility function. Two different susceptibility functions are proposed to describe individuals who are stubborn conformists and stubborn extremists. Stubborn conformists are individuals who become more closed to influence when they have an opinion similar to the network average, while stubborn extremists are less susceptible when they hold opinions at either end of the opinion interval. Convergence results are established for networks where all individuals are stubborn conformists, or all individuals are stubborn extremists. Simulations are provided to illustrate the results. Key conclusions, consistent with sociology literature and exemplified by the simulations are that (i) stubborn conformists typify observed phenomenon whereby it takes a long time for people to agree on social norms, and an equally difficult time breaking them, and (ii) existence of stubborn extremists can pull individuals with an initial neutral opinion to the extremes.