Interdependent Public Projects

In the interdependent values (IDV) model introduced by Milgrom and Weber [1982], agents have private signals that capture their information about different social alternatives, and the valuation of every agent is a function of all agent signals. While interdependence has been mainly studied for auctions, it is extremely relevant for a large variety of social choice settings, including the canonical and practically important setting of public projects. The IDV model is much more realistic but also very challenging relative to the standard independent private values model. Welfare guarantees for IDV have been achieved mainly through two alternative conditions known as single-crossing and submodularity over signals (SOS). In either case, the existing theory falls short of solving the public projects setting. Our contribution is twofold: (i) We give a useful characterization of truthfulness for IDV public projects, parallel to the known characterization for independent private values, and identify the domain frontier for which this characterization applies; (ii) Using this characterization, we provide possibility and impossibility results for welfare approximation in public projects with SOS valuations. Our main impossibility result is that, in contrast to auctions, no universally truthful mechanism performs better for public projects with SOS valuations than choosing a project at random. Our main positive result applies to excludable public projects with SOS, for which we establish a constant factor approximation similar to auctions. Our results suggest that exclusion may be a key tool for achieving welfare guarantees in the IDV model.