Decision Accuracy and the Role of Spatial Interaction in Opinion Dynamics

The opinions and actions of individuals within interacting groups are frequently determined by both social and personal information. When sociality (or the pressure to conform) is strong and individual preferences are weak, groups will remain cohesive until a consensus decision is reached. When group decisions are subject to a bias, representing for example private information known by some members of the population or imperfect information known by all, then the accuracy achieved for a fixed level of bias will increase with population size. In this work we determine how the scaling between accuracy and group size can be related to the microscopic properties of the decision-making process. By simulating a spatial model of opinion dynamics we show that the relationship between the instantaneous fraction of leaders in the population (L), system size (N), and accuracy depends on the frequency of individual opinion switches and the level of population viscosity. When social mixing is slow, and individual opinion changes are frequent, accuracy is determined by the absolute number of informed individuals. As mixing rates increase, or the rate of opinion updates decrease, a transition occurs to a regime where accuracy is determined by the value of L√N. We investigate the transition between different scaling regimes analytically by examining a well-mixed limit.