Fully Bayesian Aggregation
27 Pages Posted: 18 Feb 2021 Last revised: 9 Apr 2021
Date Written: January 1, 2021
Can a group be an orthodox rational agent? This requires the group's aggregate preferences to follow expected utility (static rationality) and to evolve by Bayesian updating (dynamic rationality). Group rationality is possible, but the only preference aggregation rules which achieve it (and are minimally Paretian and continuous) are the linear-geometric rules, which combine individual values linearly and combine individual beliefs geometrically. Linear-geometric preference aggregation contrasts with classic linear-linear preference aggregation, which combines both values and beliefs linearly, but achieves only static rationality. Our characterisation of linear-geometric preference aggregation has two corollaries: a characterisation of linear aggregation of values (Harsanyi's Theorem) and a characterisation of geometric aggregation of beliefs.
Keywords: Rational Group Agent, Uncertainty, Preference Aggregation, Values aggregation and Harsanyi's Theorem, Opinion Pooling, Static Versus Dynamic Rationality, Expected-Utility Hypothesis, Bayesianism, Group Rationality Versus Paretianism, Spurious Unanimity, Ex-Ante Versus Ex-Post Pareto
JEL Classification: D7, D8
Suggested Citation: Suggested Citation