"Research on collective provision of private goods has focused on distributional considerations. This paper studies a class of problems of decision under uncertainty in which the argument for collective choice emerges from the mathematics of aggregating individual payoffs. Consider decision...

This paper studies an identification problem that arises when clinicians seek to personalize patient care by predicting health outcomes conditional on observed patient covariates. Let y be an outcome of interest and let (x=k, w=j) be observed patient covariates. Suppose a clinician wants to...