  Competitive information diffusion on large-scale social networks reveals
fundamental characteristics of rumor contagions and has profound influence on
public opinion formation. There has been growing interest in exploring
dynamical mechanisms of the competing evolutions recently. Nevertheless, the
impacts of population homophily, which determines powerful collective human
behaviors, remains unclear. In this paper, we incorporate homophily effects
into a modified competitive ignorant-spreader-ignorant (SIS) rumor diffusion
model with generalized population preference. Using microscopic Markov chain
approach, we first derive the phase diagram of competing diffusion results and
examine how competitive information spreads and evolves on social networks. We
then explore the detailed effects of homophily, which is modeled by a rewiring
mechanism. Results show that homophily promotes the formation of divided "echo
chambers" and protects the disadvantaged information from extinction, which
further changes or even reverses the evolutionary advantage, i.e., the
difference of final proportions of the competitive information. We highlight
the conclusion that the reversals may happen only when the initially
disadvantaged information has stronger transmission ability, owning diffusion
advantage over the other one. Our framework provides profound insight into
competing dynamics with population homophily, which may pave ways for further
controlling misinformation and guiding public belief systems. Moreover, the
reversing condition sheds light on designing effective competing strategies in
many real scenarios.
