Majority vote and monopolies in social networks

Abstract

Occasionaly, every society needs to reach a decision among its members. For this, it may use a voting mechanism, i.e., collect the votes of the group members and output a decision that best expresses the group's will. To make up their minds, individuals often discuss the issue with friends before taking their votes, thus mutually affecting each other's votes. Individuals are also, to some extent, influenced by the opinions of key figures in their culture, such as politicians, publicists, etc., commonly considered as the "elite" of the society. This work studies the "power of the elite": to what extent can the elite of a social network influence the rest of society to accept its opinion, and thus become a monopoly. We present an empirical study of local majority voting in social networks, where the elite forms a coalition against all other (common) nodes. The results, obtained on several social networks, indicate that an elite of size [MATH HERE] (where m is the number of connections) has disproportionate power, relative to its size, with respect to the rest of society: it wins the majority voting and remains stable over time.