The Contributions of Diversity, Accuracy, and Group Size on Collective Accuracy

Abstract

In this paper, we characterize a group's collective accuracy on a classification problem as a function of its diversity, size, and its member's individual accuracies. We first derive necessary and sufficient conditions on the individuals' classification models for the existence of an aggregation function that produces perfect accuracy. We then characterize the set of possible group accuracies under majority rule. For majority rule, we show that increasing individual accuracy produces a setwise increase in collective accuracy. In contrast, increases in diversity and size have conditional effects. For groups with low diversity, increasing either diversity or size increases the set of possible group accuracies but does not change the set's midpoint. For highly diverse groups, increasing diversity weakly increases setwise accuracy, whereas increases in group size need not. In an extension, we consider a collection of classification models drawn from a population and derive a general condition for increasing group size to raise or lower expected accuracy.