This paper presents some graph-theoretic conditions for a democratic system controlled by a social network to converge to a regressive or progressive system over time. The democratic system is modeled as a finite state automaton, and a social network of agents is modeled as a directed graph. Agents are controllers making decisions to enable or disable events such that their objectives are to be met. Based on the individual decisions of agents, the final decision is made by the majority rule. Specifically, the conditions obtained imply two strategies for the groups of regressive or progressive agents to achieve their objectives: one is to prevent informed agents in other groups from influencing uninformed agents, and the other is to make at least one uninformed agent in every cycle follow the decisions of the group.
