Heterophobic interactions hinder consensus formation in sparse random networks

Heterophobic interactions, which drive individuals to be repelled from others with opposite opinions, play a role as important as homophilic ones in shaping many dynamical processes on social networks, such as opinion formation, social balance, or epidemic spreading. In this paper, we use belief propagation and Monte Carlo simulations on treelike signed graphs to predict that a sufficient propensity to heterophobia can impede a consensus that would otherwise emerge via a phase transition. As the strength of heterophobic interactions and the rationality of individuals with respect to social stress decrease, this transition changes from continuous to discontinuous, with a strong dependence on the initial conditions. The size of the parameter region where consensus can be reached from any initial condition decays as a power-law function of the number of discussed topics.