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We study the effects of inhomogeneous influence of individuals on collectivephenomena. We focus analytically on a typical model of the majority rule,applied to the completely connected agents. Two types of individuals $A$ and$B$ with different influence activity are introduced. The individuals $A$ and$B$ are distributed randomly with concentrations $\nu$ and $1-\nu$ at thebeginning and fixed further on. Our main result is that the location of theorder-disorder transition is affected due to the introduction of theinhomogeneous influence. This result highlights the importance of inhomogeneousinfluence between different types of individuals during the process of opinionupdating.

Effects of inhomogeneous influence of individuals on an order-disorder transition in opinion dynamics