Group decisions involve the combination of evidence accumulation by individual members and direct member-to-member interactions. We consider a simplified framework of two deciders, each undergoing a two alternative forced choice task, with the choices of early deciding members biasing members who have yet to choose. We model decision dynamics as a drift-diffusion process and present analysis of the associated Fokker-Planck equation for the group. We show that the probability of coordinated group decisions (both members make the same decision) is maximized by setting the decision threshold of one member to a lower value than its neighbors. This result is akin to a speed-accuracy tradeoff, where the penalty of lowering the decision threshold is choice inaccuracy while the benefit is that earlier decisions have a higher probability of influencing the other member. We numerically extend these results to large group decisions, where it is shown that by choosing the appropriate parameters, a small but vocal component of the population can have a large amount of influence on the total system.
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