Confidence, consensus and aggregation
Abstract
This paper develops and defends a new approach to belief aggregation, involving confidence in beliefs. It is characterised by a variant of the Pareto condition that enjoins respecting consensuses borne of compromise. Confidence aggregation recoups standard probability aggregation rules, such as linear pooling, as special cases, whilst avoiding the spurious unanimity issues that have plagued such rules. Moreover, it generates a new family of probability aggregation rules that can faithfully accommodate within-person expertise diversity, hence resolving a longstanding challenge. Confidence aggregation also outperforms linear aggregation: the group beliefs it provides are closer to the truth, in expectation. Finally, confidence aggregation is dynamically rational: it commutes with update.