Multi-opinion Markovian agent networks: Parametrization, second order moment and social power

This paper extends the theory of Markovian multi-agent opinion networks, previously studied in the binary opinion case, to the situation of multiple opinions. The first step is the definition of a suitable canonical representation of a multi-state Markov chain, to describe the behavior of any non-interacting agent in terms of its prejudice. Based on this parametrization, the time evolution of both first- and second-order moments of the opinion shares when the agents are connected in a social network is completely characterized, both in transient and at steady-state. The steady-state analysis allows one to introduce an appropriate notion of marginal social power, measuring the sensitivity of the average network opinion to the agents’ prejudices.