Secret ballots and costly information gathering: The jury size problem revisited

Abstract

Suppose paying attention during jury trials is costly, but that jurors do not pool information (as in contemporary Brazil, or ancient Athens). If inattentive jurors are as likely to be wrong as right, Ifind that small jury panels work better as long as identical jurors behave symmetrically. If not paying attention makes error more likely than not, jurors may co-ordinate on two different symmetric outcomes: a "high-attention" one or a "low attention" one. If social norms stigmatize shirking, jurors co-ordinate on the high-attention equilibrium, and a smaller jury yields better outcomes. However, increasing the jury up to a finite bound works better if norms are tolerant of shirking, in which case co-ordination on the low-attention outcome results. If the cost of attention is high, a bare majority of jurors pay attention, and efficiency increases in jury size up to a bound. The model also applies to elections and referendums.

Should Jurors Deliberate?

“…As shown in Guha (2016), and as our numerical examples will illustrate later, both σND and decrease in jury size, n. Intuitively, a larger panel reduces the probability, fixing σ, that an individual juror will be pivotal, tending to reduce his expected benefit from paying attention below his cost of doing so. To restore the equality, and thereby induce him to pay attention with at least some probability, it is necessary that all the other jurors be less attentive when the panel size goes up, so that the probability that some of them are incorrect, resulting in a tie, increasesthus pushing up the pivotal probability again.…”

“…Had we focused instead on asymmetric pure strategy equilibria, we would have found one in the model without deliberation where a bare majority of jurors (exactly (n+1)/2 out of n) pays attention and delivers the correct verdict with probability 1 (see Guha (2016)) and one in the deliberation model where exactly one juror out of n pays attention, again delivering the correct verdict with probability 1. However, equilibrium selection is a real issue in both models.…”

“…Moreover, this solution is well-defined as long as the expression in the square root is non-negative, which is the case if 2/( −1) < . As shown in Guha (2016), the RHS of this restriction is decreasing in n, and there is therefore some maximum odd integer n* which satisfies this restriction. Moreover, this integer is at least 3, because the RHS of the restriction for n = 3 is ¼, and we always have c<1/4.…”

“…Models with costly juror participation include Mukhopadhyaya (2003) and Guha (2016). The first of these focuses on optimal jury size when deliberation is a part of jury trials, and shows that small panels generally work best.…”