Discrete Event Dynamic Modeling and Analysis of the Democratic Progress in a Society Controlled by Networked Agents

Abstract

This article proposes a formal framework based on discrete event systems in order to analyze the democratic progress and regression in a society controlled by networked agents. For this purpose, we construct a simple model using a finite state automaton that describes the dynamic behavior of progress and regression in a democracy. We represent a network of agents as a directed graph where each agent has its own objective. Each agent may be a citizen or a group of people sharing a common objective, and it makes decisions on enabling or disabling events upon the observation of states of a system. Agents may have different decisions on the same event, and the final decision follows the majority rule. Upon this framework, we derive the necessary and sufficient conditions for a democratic system controlled by networked agents to be progressive or regressive, where a progressive one implies that it reaches a more equal state at which a larger number of agents meet their objectives. Finally, we obtain some convergence results for special graph topologies.