Many organisms regularly make decisions regarding foraging, home-site selection, mating, and danger avoidance in groups ranging from two to hundreds up to millions of individuals. These decisions involve the accumulation of noisy and dynamic information by individuals that is exchanged between neighbors. We will present a statistical inference model describing how rational agents represent and share estimates of belief uncertainty. Our canonical Bayesian updating model describes temporal evidence accumulation to belief thresholds that generate decisions. For foraging decisions, The efficiency of different individual and social strategies is quantified by solving corresponding passage time problems for patch departure. Asymmetries in information transfer grossly exaggerate errors in patch quality estimates, triggering poorly timed departures. In a generic binary decision task performed by a large clique, the speed and accuracy of the majority group decision can be estimated using asymptotics for order statistics. We find that groups comprised of individuals with a distribution of decision thresholds make more efficient decisions than a group of individuals all with the same decision criteria.