Incorporating a monetary variable into the Schelling model addresses the issue of a decreasing entropy trace

Alexander V Mantzaris

doi:10.1038/s41598-020-74125-6

Abstract

The Schelling model of segregation has been shown to have a simulation trace which decreases the entropy of its states as the aggregate number of residential agents surrounded by a threshold of equally labeled agents increases. This introduces a paradox which goes against the second law of thermodynamics that states how entropy must increase. In the efforts to bring principles of physics into the modeling of sociological phenomena this must be addressed. A modification of the model is introduced where a monetary variable is provided to the residential agents (sampled from reported income data), and a dynamic which acts upon this variable when an agent changes its location on the grid. The entropy of the simulation over the iterations is estimated in terms of the aggregate residential homogeneity and the aggregate income homogeneity. The dynamic on the monetary variable shows that it can increase the entropy of the states over the simulation. The path of the traces with both variables in the results show that the shape of the region of entropy is followed supporting that the decrease of entropy due to the residential clustering has a parallel and independent effect increasing the entropy via the monetary variable.

Highlights

The Schelling model of segregation has been shown to have a simulation trace which decreases the entropy of its states as the aggregate number of residential agents surrounded by a threshold of labeled agents increases
The basic rule set for the agents is that there is a constraint upon each agent to have a minimum number of agents with the same label in their adjacent surroundings for them to remain in the sample grid cell, or else they move to a different cell in which the sufficient number of same labelled agents exist adjacently
The trace of the simulations with this models shows a decreasing entropy trace which goes against the maximum entropy principle if it is to find a correspondence with models in physics

Summary

Introduction

The Schelling model of segregation has been shown to have a simulation trace which decreases the entropy of its states as the aggregate number of residential agents surrounded by a threshold of labeled agents increases. It is interesting to note that the rule set is not complex since the local agent homogeneity criteria on the local environment has no explicit description for the macroscopic grid state, and yet it results in the whole grid state to be altered in a small number of iterations For this reason it can spark interest from researchers not working directly on the social issues of segregation (and related issues such as polarization) to apply their domain expertise to understand the dynamics of self-organization[4] to a greater depth just as the Conway Game of Life[5] has provided much insight[6]. Subfigure (b) displays the state of the grid after each resident has been given the opportunity to move to a new cell in which the homogeneity satisfaction can be achieved (one iteration forward in the simulation from the initialization) This altered the value of R to increase to the value of R = 133 and the increased clustering between homogeneous labels shows this. It is noteworthy that the Schelling model can be expected to produce these results with few iterations

Methods

Results

Conclusion