The Matthew Effect: Its Definition, Measurement and Explanation

The objective of this paper is to provide readers with a comprehensive framework for a deeper understanding of the Matthew effect in society. This includes its mathematical definition, method of measurement, and theoretical framework for explanatory mechanisms. To the best of our knowledge, no existing literature addresses the Matthew effect from as thorough and coherent a theoretical standpoint as we do here. First, the definition of the Matthew effect extends beyond the simple comparison between “the haves” and “the have-nots.” It recognizes that society consists of multiple groups of people while remaining consistent with the commonly understood definition of the Matthew effect (i.e., the rich-get-richer and the poor-get-poorer effect). Second, the method for measuring the Matthew effect directly applies its definition to data. A theoretical model or real-world data set is characterized by the Matthew effect if the Lyapunov characteristic exponent associated with the model or data is positive. A positive Lyapunov characteristic exponent, therefore, defines the Matthew effect, and we explain how to estimate this measure and statistically test for the Matthew effect. Third, because this procedure is the same as when measuring the butterfly effect, insights from chaos theory impose constraints on the theoretical framework for the explanatory mechanisms behind the Matthew effect. Given that society is composed of numerous interacting individuals, we argue that agent-based modeling, particularly multilayer modeling, is the most appropriate framework for developing theoretical models that explain the Matthew effect as observed in real-world data. Multilayer modeling recognizes that individuals maintain different sets of connections in different arenas of life. In network terms, individuals belong to different layers, each with its own set of connections within the social network. Furthermore, these layers are interconnected, forming a potentially nonlinear network, which is crucial for generating the Matthew effect.