Information Cascades and the Hung Jury Paradox
In the 1970 court case Williams v. Florida, the Supreme Court ruled that the 12 person jury, a legal fixture originating in at least the 14th century, is not constitutionally mandated. In response, several states swiftly shrunk the size of their juries. Florida, for example, chopped theirs in half: 6 people serve on all trials except capital cases. These changes were put in place under the assumption that small juries would result in fewer mistrials, thereby minimizing state costs. Surprisingly, jury size reductions have not produced the desired effect. There is no evidence of significant change in the proportion of unanimous decisions as a result of smaller juries. To help explain why, economists Barbara Luippi and Francesco Parisi published an article for The Journal of Legal Studies in which they describe a new, more accurate model for predicting unanimity by applying the theory of information cascades.
Luppi and Parisi claim that the previous models falsely predicted a reduction in mistrials because of one fatal assumption: that jury decisions are independent. Let’s begin by outlining the expected result of jury size reductions under this false assumption. If there are n jurors and p is the probability of a juror making the correct decision, then the probability of a unanimous ruling is simply p^n + (1-p)^n. Reducing jury size from 12 to 6 should lower the rate of hung juries from roughly 6% to 2.5%, but this is not empirically observed. To understand why, Luippi and Parisi drew on evidence from previous legal studies that suggests jurors are often influenced by other people’s decisions. This violates the independence assumption, so Luippi and Parasi drafted a new model to account for the interdependence of decision making. In their model, each juror’s voting preference is expressed as a function of their own self-confidence in their reasoning and the average vote of the jurors who preceded them. The first part of this function, the self-confidence factor, introduces a drift that increases the probability of unanimity compared to an independence model. Intuitively, any time a juror is swayed by others’ decisions there is a tendency towards convergence. The second aspect of the function, the average decision of the previous jurors, is like a combined signal that affects an individual’s decision. As values of n get larger, this cascade effect grows. Putting this into context, small juries have small values of n and are therefore less likely to converge on a decision. Big juries have a stronger cascade effect and therefore have a greater likelihood of making a unanimous decision. This tweak in the model helps explain why small juries don’t reduce mistrials after all.
Assuming this cascade model is correct, how does it impact the rate of wrongful convictions? How can this theory inform a state’s choice of jury size? The authors of this study point out that cascades don’t seem to increase wrongful convictions. The stronger cascade effects of 12 person juries are most likely to induce convergence towards a correct result and very unlikely to induce convergence towards an incorrect result. However, this research is only about information cascades and doesn’t account for other factors that should be considered in determining jury size. For example, it doesn’t account for other potential explanations for crowd behavior such as direct-benefit effects. Perhaps jurors believe they will gain an abstract social benefit by agreeing with others. Though judges are obviously not supposed to coerce a jury, it is still possible that people feel pressured to agree on a ruling even when they carry personal doubts. Another factor to consider is the extent to which hung juries are a problem and whether they are truly costly to the state. Additionally, a growing body of research suggests that small juries are less likely to be representative of their communities, which could increase the rate of wrongful convictions. The results of Luippi’s and Parisi’s study indicate why 6 person juries don’t have the cost benefits people thought they would, but they don’t tell us much more about the relative merits of different jury sizes. Further investigation is clearly needed to understand how the number of jurors impacts wrongful convictions and inequality so that size selection can be well-informed.
Jury Size and the Hung Jury Paradox by Luippi and Parisi: https://www.journals.uchicago.edu/doi/full/10.1086/670692
Additional resource: https://www.apa.org/monitor/2008/03/jn