Indecision and accuracy under social information across groups sizes

Observing the decisions and actions of others provides social information that can inform decisions such as whether to follow. We consider a model where agents simultaneously gather stochastic private information, each deciding once sufficiently confident. Observed decisions and indecision provide social information that triggers discrete waves of collective response: a first decision causes others to update and potentially follow, whose decisions in turn provide further social information, generating successive waves. We explore this model across a range of group sizes and report three main findings. First, social information leads to faster and more accurate decisions than individual decision-making, but agent-level accuracy is maximised at a finite optimal group size. This contrasts with the accuracy of the majority choice, which increases monotonically with the number of agents. Second, waves frequently fail to resolve collective indecision, particularly for smaller groups and when the first decision is incorrect, leaving a subgroup of agents unconvinced. Third, these remaining undecided agents are systematically biased and make less accurate subsequent decisions, with this inaccuracy growing with group size.