Social pressure in opinion dynamics

Motivated by privacy and security concerns in online social networks, we study the role of social pressure in opinion dynamics. These are dynamics, introduced in economics and sociology literature, that model the formation of opinions in a social network. We enrich one of the most classical opinion dynamics, by introducing the pressure, increasing with time, to reach an agreement. We prove that for clique social networks, the dynamics always converges to consensus (no matter the level of noise) if the social pressure is high enough. Moreover, we provide (tight) bounds on the speed of convergence; these bounds are polynomial in the number of nodes in the network provided that the pressure grows sufficiently fast. We finally look beyond cliques: we characterize the graphs for which consensus is guaranteed, and make some considerations on the computational complexity of checking whether a graph satisfies such a condition.