Trust in society: A stochastic compartmental model

This paper studies a novel stochastic compartmental model for the dynamics of trust in society. The population is split into three compartments representing levels of trust in society: trusters, skeptics and cynics. The focus lies on assessing the long-term dynamics, under ‘bounded confidence’ (i.e., trusters and cynics do not communicate). We state and classify the stationary points of the system's mean behavior. We find that in the model an increase in life-expectancy, and a greater population may increase the proportion of individuals who lose their trust completely. In addition, the relationship between the rate at which cynics convince skeptics to join their cause and the expected number of cynics is not monotonic — it does not always help to be more convincing to ensure the survival of your group. We numerically illustrate the workings of our analysis. Because the study of stochastic compartmental models for social dynamics is not common, we in particular shed light on the limitations of deterministic compartmental models. In our experiments we make use of fluid and diffusion approximation techniques as well as Gillespie simulation.