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In this short note we study what happens in a symmetric opinion model when wesend the total interacting population $N(t)$ to infinity as $t \to \infty$. Weassume that new population enters the system with opinions that are i.i.drandom vectors with finite mean and variance. We give sharp conditions on therate of population growth that is required for convergence to a globalconsensus in opinions. More particularly, we show that if the total populationincreases at a rate $N(t)\sim e^{t^\alpha}$, then $\alpha<1$ is necessary andsufficient condition for convergence to the mean of incoming opinions, and theconvergence is achieved at an algebraic rate.

A simple consensus model for an increasing population of agents with i.i.d incoming opinions