Social diffusion and global drift in adaptive social networks

TL;DR

This paper explores the mathematical modeling of social diffusion in networks, revealing how non-conservative social influence can cause unexpected global shifts in the network's average state, with implications for collective behavior and education.

Contribution

It introduces a novel mathematical model highlighting the non-trivial global drift caused by social diffusion, contrasting it with traditional infection models.

Findings

Social diffusion leads to global state drift in networks.

Mathematical model explains the mechanism of drift.

Implications for influencing collective behavior.

Abstract

Social contagion has been studied in various contexts. Many instances of social contagion can be modeled as an infection process where a specific state (adoption of product, fad, knowledge, behavior, etc.) spreads from individual to individual through links between them. In the meantime, other forms of social contagion may better be understood as a diffusion process where the state of an individual tends to assimilate with the social norm (i.e., local average state) within his/her neighborhood. Unlike infection scenarios where influence is nonlinear, unidirectional, fast, and potentially disruptive, social diffusion is linear, bidirectional, gradual, and converging. The distance between an individual's state and his/her neighbors' average state always decreases, and thus a homogeneous global state is guaranteed to be the network's stable equilibrium state in the long run. This does not sound as intriguing or exciting as infection dynamics, which might be why there are very few studies on mathematical models of social diffusion processes. Here, this study attempts to shed new light on an unrecognized characteristic of social diffusion, i.e., non-trivial drift it can cause to the network's global average state. Although somewhat counterintuitive, such global drift is indeed possible because, unlike physical diffusion processes, social diffusion processes are not conservational. In what follows, a mathematical model of social diffusion will be presented to explain the mechanism of this phenomenon, and some possible collective actions for influencing the direction of global drift will be proposed. The relevance of social diffusion to individual and collective improvement will be discussed briefly, with an emphasis on educational applications.