Trust in society: A stochastic compartmental model

TL;DR

This paper introduces a stochastic compartmental model for societal trust dynamics, analyzing long-term behavior and highlighting limitations of deterministic models through simulations and mathematical techniques.

Contribution

It presents a novel stochastic model for trust in society, classifies its stationary points, and compares stochastic and deterministic approaches.

Findings

Increased life expectancy and population can lead to more individuals losing trust.

The relationship between convincing skeptics and trust levels is non-monotonic.

Stochastic models reveal limitations of deterministic approaches in social trust dynamics.

Abstract

This paper studies a novel stochastic compartmental model that describes the dynamics of trust in society. The population is split into three compartments representing levels of trust in society: trusters, skeptics and doubters. The focus lies on assessing the long-term dynamics, under `bounded confidence' i.e., trusters and doubters do not communicate). We state and classify the stationary points of the system's mean behavior. We find that 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 doubters convince skeptics to join their cause and the expected number of doubters 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.