Reliable Methods of Judgement Aggregation

Abstract

The aggregation of consistent individual judgements on logically interconnected propositions into a collective judgement on the same propositions has recently drawn much attention. Seemingly reasonable aggregation procedures, such as propositionwise majority voting, cannot ensure an equally consistent collective conclusion. The literature on judgement aggregation refers to such a problem as the discursive dilemma. In this article we assume that the decision which the group is trying to reach is factually right or wrong. Hence, we address the question of how good various approaches are at selecting the right conclusion. We focus on two approaches: distance-based procedures and a Bayesian analysis. They correspond to group-internal and group external decision making, respectively. We compare those methods in a probabilistic model whose assumptions are subsequently relaxed. Our findings have two general implications for judgement aggregation problems: first, in a voting procedure, reasons should carry higher weight than the conclusion, and second, considering members of an advisory board to be highly competent is a better strategy than discounting their advice.