The Roman metro problem: Dynamic voting and the limited power of commitment

A frequently heard explanation for the underdeveloped metro system in Rome is the following one: If we tried to build a new metro line, it would probably be stopped by archeological finds that are too valuable to destroy, so the investment would be wasted. This statement, which seems self-contradictory from the perspective of a single decision maker, can be rationalized in a voting model with diverse constituents. One would think that commitment to finishing the metro line (no matter what is discovered in the process) can resolve this inefficiency. We show, however, that a Condorcet cycle occurs among the plans of action one could feasibly commit to, precisely when the metro project is defeated in step-by-step voting (that is, when commitment is needed). More generally, we prove a theorem for binary-choice trees and arbitrary learning, establishing that no plan of action which is majority-preferred to the equilibrium play without commitment can be a Condorcet winner among all possible plans. Hence, surprisingly, commitment has no power in a large class of voting problems.