Threshold model with anticonformity under random sequential updating

We study an asymmetric version of the threshold model of binary decision making with anticonformity under an asynchronous update mode that mimics continuous time. We analyze this model on a complete graph using three different approaches: the mean-field approximation, Monte Carlo simulation, and the Markov chain approach. The latter approach yields analytical results for arbitrarily small systems, in contrast to the mean-field approach, which is strictly correct only for an infinite system. We show that, for sufficiently large systems, all three approaches produce the same results, as expected. We consider two cases: (1) homogeneous, in which all agents have the same tolerance threshold, and (2) heterogeneous, in which thresholds are given by a beta distribution parametrized by two positive shape parameters ?? and /3. The heterogeneous case can be treated as a generalized model that reduces to a homogeneous model in special cases. We show that particularly interesting behaviors, including social hysteresis and critical mass reported in innovation diffusion, arise only for values of ?? and /3 that yield the shape of the distribution observed in reality.

Automated summary

This study investigates an asymmetric version of the threshold model of binary decision-making with anticonformity under an asynchronous update mode that mimics continuous time. The model is analyzed on a complete graph using three different approaches: mean-field approximation, Monte Carlo simulation, and the Markov chain approach. The results from all three approaches are found to be the same for sufficiently large systems. Two cases are considered: homogeneous, where all agents have the same tolerance threshold, and heterogeneous, where thresholds are given by a beta distribution parametrized by two positive shape parameters. Particularly interesting behaviors, such as social hysteresis and critical mass, are observed only for parameter values that match the shape of the distribution observed in reality.