More, better or different? Trade-offs between group size and competence development in jury theorems

Abstract: In many circumstances there is a trade off between the number of voters and the time they can be given before having to make a decision since both aspects are costly. An example is the hiring of a committee with a fixed salary budget: more people but a shorter time for each to develop their competence about the issue at hand or less people with a longer time for competence development? In this paper we investigate the interaction between the number of voters, the development of their competence over time and the final probability for an optimal majority decision. Among other things we consider how different learning profiles, or rates of relevant competence increase, for the members of a committee affects the optimal committee size. To the best of our knowledge, our model is the first that includes the potentially positive effects of having a heterogeneous group of voters on majority decisions in a satisfactory way. We also discuss how some earlier attempts fail to capture the effect of heterogeneity correctly.