The Hunt Opinion Model—An Agent Based Approach to Recurring Fashion Cycles

Abstract

We study a simple agent-based model of the recurring fashion cycles in the society that consists of two interacting communities: “snobs” and “followers” (or “opinion hunters”, hence the name of the model). Followers conform to all other individuals, whereas snobs conform only to their own group and anticonform to the other. The model allows to examine the role of the social structure, i.e. the influence of the number of inter-links between the two communities, as well as the role of the stability of links. The latter is accomplished by considering two versions of the same model—quenched (parameterized by fraction L of fixed inter-links) and annealed (parameterized by probability p that a given inter-link exists). Using Monte Carlo simulations and analytical treatment (the latter only for the annealed model), we show that there is a critical fraction of inter-links, above which recurring cycles occur. For p ≤ 0.5 we derive a relation between parameters L and p that allows to compare both models and show that the critical value of inter-connections, p*, is the same for both versions of the model (annealed and quenched) but the period of a fashion cycle is shorter for the quenched model. Near the critical point, the cycles are irregular and a change of fashion is difficult to predict. For the annealed model we also provide a deeper theoretical analysis. We conjecture on topological grounds that the so-called saddle node heteroclinic bifurcation appears at p*. For p ≥ 0.5 we show analytically the existence of the second critical value of p, for which the system undergoes Hopf’s bifurcation.

Conformity, Anticonformity and Polarization of Opinions: Insights from a Mathematical Model of Opinion Dynamics

“…Otherwise nothing happens. It should be noted that a similar model, but with a broken symmetry between the cliques, was used in both the quenched and the annealed version to explain recurring fashion cycles [77]. Let us denote the state of the i-th agent at the discrete time τ by S i (τ).…”

Collective narratives catalyse cooperation

“…Beliefs might, therefore, be viewed as selfish elements. The effect on the population as a whole is inconsequential; thus, superficially, the rise and fall of beliefs might be likened to fashion dynamics [49].…”

Cultural evolution of conformity and anticonformity

“…In terms of the Ising (32) model of ferromagnetism, conformist bias produces ferromagnetic interactions, and anticonformist bias produces antiferromagnetic interactions (31,33). In agent-based models with conformist and anticonformist spinsons, stable "stationary concentrations" of up and down spins are possible (31,34), or periodic cycles may arise (35).…”