Effect of social influence on a two-party election: A Markovian multiagent model

In digital social networks, the filtering algorithms employed by the platform management to sieve the contents shared among the users can alter the social influence intensity. In this paper, a Markov multi-agent model of opinion dynamics is used to analyze possible opinion manipulation under apparently neutral interventions on the influence intensity. We consider a two-party election whose voters, modeled as heterogeneous agents, are connected in a social network with arbitrary topology. The equations describing the variance of the vote share, both in transient and steady state, are derived. The key is the solution of the second-order marginalization problem under the form of a numerically tractable characterization of pairwise joint probabilities of the voters' opinions. In particular, these probabilities are computed by means of a Lyapunov-like matrix differential equation driven by first-order moments. This result is used to answer some important questions, like the possible nonmonotonic effect of the influence intensity on the vote volatility and the interplay of topology and individuals' stubborness to determine the electoral balance between two parties.