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.(c) 2023 Elsevier Ltd. All rights reserved.