A numerical study on efficient jury size

For judicial democracy, many societies adopt jury trials, where verdicts are made by a unanimous vote of, conventionally, 12 lay citizens. Here, using the majority-vote model, we show that such jury sizes achieve the best balance between the accuracy of verdicts and the time spent for unanimous decision-making. First, we identify two determinants of the efficient jury size: the opinion homogeneity in a community decreases the optimal jury size by affecting the accuracy of verdicts; the anti-conformity tendency in the community also reduces the efficient jury size by prolonging the time to reach unanimous verdicts. Moreover, we find an inverse correlation between these two determinants, which prevents over-shrinking and excessive expansion of the efficient jury size. Finally, by applying these findings into real-life settings, we narrow down the efficient jury size to 11.8 ± 3.0. Given that such a simple toy model can explain the jury sizes in the actual societies, the number of jurors may have been implicitly optimised for efficient unanimous decision-making throughout human history.