Fig. 1: Research design.
a–c We evaluated the efficiency of juries with N jurors by comparing the verdict accuracy with the deliberation time (a) using the majority-vote model with noise on a complete graph (b). The verdict accuracy 〈Accuracy〉 was defined as whether the jury verdicts σjury was the same as the verdicts hypothetically made by the full community members σComm. We then quantified the beneficial effect of N jurors on the verdict accuracy Δ〈Accuracy〉N by calculating how better the verdict accuracy in the N-juror system 〈Accuracy〉N was compared to 〈Accuracy〉2, the accuracy of the most basic collective decision-making system. The deliberation time T was summarised by its median value 〈T〉 because T showed a skewed distribution (c). Finally, we estimated the jury efficiency by calculating the ratio of Δ〈Accuracy〉 to 〈T〉. In the majority-vote model (b), the jurors change their opinions to the majority opinion at a time point with a probability 1–q or to the minor one with a probability q. If the opinion in the jury is equally divided, the jurors change their opinions randomly. The q is a noise parameter, which is also stated as social temperature (Vilela and Stanley, 2018) and anti-conformity index (Nowak and Sznajd-Weron, 2019). The FMajor represents the proportion of the major opinion in the entire community. d. The graph shows an association between the number of jurors N and the critical noise qc in the majority-vote model on complete graphs (Chen et al., 2015). In the range of q was set to [0.05, 0.2] so that q is less than qc even when the number of the jurors is relatively small (e.g., N ~ 10).
