  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.
