Rescuing Collective Wisdom when the Average Group Opinion Is Wrong

The total knowledge contained within a collective supersedes the knowledge of even its most intelligent member. Yet the collective knowledge will remain unaccessible to us unless we are able to find efficient knowledge aggregation methods which produce reliable decisions based on the behavior or opinions of the collective's members. It is often stated that simple averaging of a pool of opinions is a good and in many cases the optimal way to extract knowledge from a crowd. The method of averaging has been applied to analysis of decision-making in very different fields such as forecasting, collective animal behavior, individual psychology and machine learning. Two mathematical theorems, Condorcet's theorem and Jensen's inequality, provide a general theoretical justification for the averaging procedure. Yet the necessary conditions which guarantee the applicability of these theorems are often not met in practice. Under such circumstances, averaging can lead to suboptimal and sometimes very poor performance. Practitioners in many different fields have independently developed procedures to counteract the failures of averaging. We review such knowledge aggregation procedures and interpret the methods in the light of a statistical decision theory framework to explain when their application is justified. Our analysis indicates that in the ideal case, there should be a matching between the aggregation procedure and the nature of the knowledge distribution, correlations and associated error costs. This leads us to explore how machine learning techniques can be used to extract near-optimal decision rules in a data-driven manner. We end with a discussion of open frontiers in the domain of knowledge aggregation and collective intelligence in general.