Models for understanding and quantifying feedback in societal systems

Abstract

When it comes to long-term fairness in decision-making settings, many studies have focused on closed systems with a specific appointed decision-maker and certain engagement rules in place. However, if the objective is to achieve equity in a broader societal system, studying the system in isolation is insufficient. In a societal system, neither a singular decision maker nor defined agent behavior rules exist. Additionally, analysis of societal systems can be complicated by the presence of feedback, in which historical and current inequities influence future inequity. In this paper, we present a model to quantify feedback in social systems so that the long-term effects of a policy or decision process may be investigated, even when the feedback mechanisms are not individually characterized. We explore the dynamics of real social systems and find that many examples of feedback are qualitatively similar in their temporal characteristics. Using a key idea in linear systems theory, namely proportional-integral-derivative (PID) feedback, we propose a model to quantify three types of feedback. We illustrate how different components of the PID capture analogous aspects of societal dynamics such as the persistence of current inequity, the cumulative effects of long-term inequity, and the response to the speed at which society is changing. Our model does not attempt to describe underlying systems or capture individual actions. It is a system-based approach to study inequity in feedback loops, and as a result unlocks a direction to study social systems that would otherwise be almost impossible to model and can only be observed. Our framework helps elucidate the ability of fair policies to produce and sustain equity in the long-term.