Fig 1.
(a) The mean deliberation time versus the fraction of jurors voting for the plaintiff. (b) The mean deliberation time versus the trial time across several datasets. (c) The distribution of the fraction of jurors voting for the plaintiff in the final vote, , and (d) the complementary cumulative distribution of deliberation. Error bars represent 90% confidence intervals in the mean.
Table 1.
Variable descriptions.
Table 2.
Data summary.
Fig 2.
Schematic of the influence with stubbornness model.
Solid lines correspond to deterministic transitions, while dashed lines correspond to probabilistic transitions. Jurors are first initialized to have one of two opinions (for the plaintiff or defendant). At each timestep, a random juror is picked and considers re-evaluating their opinion with probability 1 − s, where s is “stubbornness”. If they do re-evaluate, they pick the majority opinion with probability p, and the minority with probability 1 − p. At the end of each timestep, the jury stops deliberating with probability q. See (1), (2), and (3) for definitions of s and q.
Table 3.
Tuned model parameters.
Table 4.
Fixed model parameters.
Fig 3.
Normalized log-likelihoods for the null models and the influence with stubbornness model variants. Models above -1 explain the data better than the influence with stubbornness model, while those below -1 perform worse. (a) The relative fit of the one-mode, two-mode, and two-timescale null models, along with “no herding” model, in which p = 0.5, “no stubbornness” model, in which μ = 0, “no vote dependence” model, in which the model dynamics do not depend on the number of jurors voting for the plaintiff, and the “no hung conditions” model, in which jury dynamics do not depend on whether the jury is currently hung. (b) In a zoomed-in graph, the influence with stubbornness model variants seen in (a) perform worse than the full model.
Fig 4.
Comparing the influence with stubbornness model to null models.
We compare the influence with stubbornness model fit to the one- and two-mode null models and the two-timescale model for the CA 12-juror data with Ttrial equal to 6-8 hours. These figures serve as examples of the typical fit quality. (a) versus
, (b) Pr(T ≥ Tdelib) versus Tdelib, and (c) 〈Tdelib〉 versus
.
Fig 5.
The scaling of the stopping rate versus the trial time.
Solid line is α ∼ (Ttrial)−1/2, and error bars represent 90% confidence intervals in the mean.