Utilitarian Cooperation under Incomplete Information∗

A theory of cooperative choice under incomplete information is developed in which agents possess private information at the time of contracting. It is assumed that the group of cooperating agents has agreed on a utilitarian “standard of fairness” (group preference ordering) governing choices under complete information. The task is to extend this standard to choices whose consequences depend on agents’ private information. It is accomplished by formulating appropriate axioms of Bayesian coherence at the group level. Assuming the existence of a common prior, the first main result generalizes Harsanyi’s (1955) classical characterization of utilitarian preference aggregation to incomplete information. We then show that Bayesian coherence of group preferences is compatible with Interim Pareto Dominance only if a common prior exists. This second result generalizes and corrects the classical literature on consistent Bayesian preference aggregation under complete information: allowing for incompleteness of information, consistent Bayesian aggregation turns out to be possible even if agents’ beliefs differ, as long as differences in beliefs can be attributed to differences in information. We finally relax the assumption that the standard of fairness is complete. In the extreme case in which no interpersonal utility-comparisons are made, this leads to an ex-interim justification of ex-ante Pareto efficiency as a criterion of welfare evaluation.