Communication Reliably Improves Individual But Not Group Accuracy

Prior research offers mixed evidence on whether and when communication improves belief accuracy for numeric estimates. Experiments on one-to-one advice suggest that communication between peers usually benefits accuracy, while group experiments indicate that communication networks produce highly variable outcomes. Notably, it is possible for a group's average estimate to become less accurate even as its individual group members -- on average -- become more accurate. However, the conditions under which communication improves group and/or individual outcomes remain poorly characterised. We analyse an empirically supported model of opinion formation to derive these conditions, formally explicating the relationship between group-level effects and individual outcomes. We reanalyze previously published experimental data, finding that empirical dynamics are consistent with theoretical expectations. We show that 3 measures completely describe asymptotic opinion dynamics: the initial crowd bias; the degree of influence centralisation; and the correlation between influence and initial biases. We find analytic expressions for the change in crowd and individual accuracy as a function of the product of these three measures, which we describe as the truth alignment. We show how truth alignment can be decomposed into calibration (influence/accuracy correlation), and herding (influence/averageness correlation), and how these measures relate to changes in accuracy. Overall, we find that individuals can and usually do improve even when groups get worse.