Daniel Barkoczi, Mirta Galesic, Konstantinos Katsikopoulos

Paper #: 15-12-051

Decisions about political, economic, legal, and health issues are often made by simple majority voting in groups that rarely exceed 30-40 members and are typically much smaller. Given that wisdom is usually attributed to large crowds, and that technological advances make group meetings easier than ever before, shouldn’t committees be larger? In many real-life situations, expert groups encounter a number of different tasks. Most are easy, with average individual accuracy is above chance, but some are surprisingly difficult, with most group members being wrong. Examples of the latter are elections with unexpected outcomes, sudden turns in financial trends, or tricky knowledge questions. Most of the time, groups cannot predict in advance whether the next task will be easy or difficult. We show that in these circumstances moderate-sized groups can achieve higher average accuracy across all tasks than larger groups or individuals. This happens because an increase in group size can lead to a decrease in group accuracy for difficult tasks which is larger than the corresponding increase in accuracy for easy tasks. We derive this non-monotonic relationship between group size and accuracy from Condorcet Jury Theorem and use simulations and further analyses to show that it holds under a variety of assumptions, including two or more task difficulties, tasks with two and more options, independent and correlated votes, and sampling from either infinite populations or from finite populations without replacement. We further show that situations favoring moderate-sized groups occur in a variety of real-life domains including political, medical, and financial decisions, and general knowledge tests. We discuss implications for the design of decision-making bodies at all levels of policy.