Active speed role in opinion formation of interacting moving agents

We propose a general non-linear analytical framework to study the evolution of the opinion state of a population of moving individuals. This novel scheme allows us to study a broad range of social phenomena, like, for example, the influence of agent interaction dynamics in the opinion formation or the inclusion of different individual's idiosyncrasies. We consider societies composed by agents who adopt one of the n possible opinions or internal states. The opinion state may only be modified while the agent keeps contact with another one. In general, this framework could be solved numerically, and, for some special perturbative cases, it is possible to find analytical steady states. In order to check our scheme for different social conventions, we implement computational simulations of an ensemble of self-propelled agents, finding a good agreement between theory and simulation results. We found, for slow society kinetics in all the cases studied, that there exist a shift of the opinion populations towards the moderate opinion states. This suggest that active speed can be understood as a parameter measuring the social temperature of the community.