Fig. 4

Comparing real versus simulated group responses from statistically aggregating individual responses. We used individual responses to simulate group confidences via CWMV (x-axis). These simulations predict responses from real, interacting groups (y-axis). In a, we used naive CWMV as in Eqs. 1 and 2. The dashed line represents predictions from naive CWMV. This is equivalent to our formal cognitive modeling with equality effect \(\beta = 1\) and group confidence effect \(\gamma = 1\). In b, we estimated the equality effect, \(\beta = 0.67\), and group confidence effect, \(\gamma = 0.53\), see Eqs. 3 and 4. This model predicts real group responses (solid line) but incorporates the fact that real groups treated individual votes more equal and displayed an underconfidence effect. In both subfigures, confidence ratings are inverted for incorrect responses. For example, the point (34%, 35%) in a corresponds to a trial with a simulated confidence of 66% and a reported confidence of 65% with both decisions being the same but incorrect; hence, both confidences were inverted