Interdependent Public Projects

TL;DR

This paper studies public project decision-making under interdependent values, providing a characterization of truthful mechanisms for a broad class of valuations and revealing fundamental limits and possibilities for welfare approximation.

Contribution

It introduces a characterization of truthful mechanisms for decomposable valuations and analyzes welfare approximation limits and opportunities for SOS valuations in public projects.

Findings

No universally truthful mechanism outperforms random choice for SOS valuations.

Constant factor welfare approximation is achievable for excludable public projects with SOS.

Exclusion may be crucial for welfare guarantees in the interdependent values model.

Abstract

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 setting of public projects. The IDV model is very challenging relative to standard independent private values, and welfare guarantees have been achieved through two alternative conditions known as {\em single-crossing} and {\em 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 workable characterization of truthfulness for IDV public projects for the largest class of valuations for which such a characterization exists, and term this class \emph{decomposable valuations}; (ii) 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 {\em 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.