How Do Cultural Classes Emerge from Assimilation and Distinction? An Extension of the Cucker-Smale Flocking Model

Abstract

When cultural tastes are not neutral but hierarchically matched to social status, people assimilate themselves to higher status by consuming cultural goods while distinguishing themselves from lower status by developing new tastes. Extending the Cucker-Smale model for mutual influence among agents, we examine when and how many cultural classes emerge from continuous distributions of tastes and what conditions those classes satisfy, through the assimilation-distinction mechanism. We simulate the models with different initial distributions of tastes (uniform, normal, and chi-square), given various ranges of 2 parameters: (a) the strength and (b) the range of distinction relative to assimilation. Tastes are flocking and cultural classes emerge when the range of assimilation is much larger than that of distinction. The number of classes increases with the strength of distinction, whereas the distance between classes equals the range of distinction. Some properties of emergent classes are mathematically proved. First, in a two-class system, the stronger distinction, the larger the upper class. Second, in a three-class system, the middle class is necessarily larger than the lower class and likely larger than the upper class. Third, a 3-class system cannot emerge if distinction is weaker than assimilation. These properties are universal and do not depend on the initial distribution of cultural tastes. This independence predicts homogeneous cultural classes emerging across different social conditions. Also, the cultural middle class as the largest group may explain why subjective class consciousness is often higher than objective position. Unless assimilating efforts can reach an infinite range, there emerges a cultural outcast at the lowest end of the cultural hierarchy.

Existence of piecewise weak solutions of a discrete Cucker–Smale's flocking model with a singular communication weight

“…The C-S model with weight ψ cs was introduced in 2007 by Cucker and Smale in [12] and was in some sense based on the paper by Viscek [36] from 1995 in which a model of flocking was introduced, such that each particle adjusted it's velocity with respect to the avarage velocity of it's neighbors. Since then existence, uniqueness, asymptotics and stability for alignment models similar to C-S (both in continuous and discrete cases) were extensively studied, both from physical and biological point of view [13] - [16], [30], [33] - [35] and from more theoretical point of view [1,2], [4] - [11], [17] - [25], [29,31]. A nice and thorough study of the C-S flocking model with a bounded communication weight can be found in [28], where the interplay between dicrete and continuous model is studied with measure valued solutions of the Vlasov type equation (1.3) or in [26], where the authors present a new, simple aproach to the problem of existence and asymptotics.…”

On the Cucker-Smale flocking with alternating leaders

“…In particular, an unexpected application was proposed by Perea, Gómez and Elosegui [27] who suggested to use the C-S flocking mechanism [11] in the formation of spacecrafts for the Darwin space mission. Recently, the C-S flocking mechanism was also applied to the modeling of emergent cultural classes in sociology and the stochastic volatility in financial markets [1], [15], [21].…”

Emergence of Multi-Cluster Configurations From Attractive and Repulsive Interactions

“…4 This emergence of cultural diversity as an outcome of local consenses has been recently simulated using several agent-based models to capture more nuanced collective motions of multi-agent systems. 4,24,35 Among them, our interest lies in the first-order Cucker-Smale-type model 33 introduced for the emergence of cultural classes in human society due to assimilations and distinctions between agents. Other agent-based models for cultural diversity specify the rules of interactions between agents using verbal statements rather than mathematical equations and do not admit analytic proofs as opposed to simulation results.…”

“…33 to study the emergence of cultural classes, when both assimilation and distinction between agents are present in the dynamics, and the formation of clustering was numerically observed. Although the original Cucker-Smale model and its variants (see Refs.…”