A stochastic opinion dynamics model with multiple contents

We introduce a new model of opinion dynamics in which agents interact with each other about several distinct opinions/contents. In most of the literature about opinion dynamics, agents perform convex combinations of other agents´ opinions. In our framework, a competition between opinions takes place: agents do not exchange all their opinions with each other, they only communicate about the opinions they like the most. Our model uses scores to take this competition into account: each agent maintains a list of scores for each opinion held. Opinions are selected according to their scores (the higher its score, the more likely an opinion is to be expressed) and then transmitted to neighbors. Once an agent receives an opinion it gives more credit to it, i.e. a higher score to this opinion. Under this new framework, we derive a convergence result which holds under mild assumptions on the way information is transmitted by agents and leads to consensus in a particular case. We also provide some numerical results illustrating the formation of consensus under different topologies (complete and ring graphs) and different initial conditions (random and biased towards a specific content).