The Roman Metro Problem

In Rome, if you start digging, chances are you will find things. We consider a famous complaint that justifies the underdeveloped Roman metro system: "if we tried to build a new metro line, it would probably be stopped by archeological finds that are too valuable to destroy, so we would have wasted the money." Although this statement appears to be self-contradictory, we show that it can be rationalized in a voting model with diverse constituents. Even when there is a majority preference for a metro line, and discovery of an antiquity has the character of a positive option, a majority may oppose construction. We give sufficient conditions for this inefficiency to occur. One might think it arises from the inability to commit to finishing the metro (no matter what is discovered in the process). We show, however, that the inefficient choice is made in voting over immediate actions precisely when there is no Condorcet winner in voting over contingent plans with commitment. Hence, surprisingly, commitment cannot really solve the problem. Our results extend to other common dynamic voting scenarios, such as the academic job market, which share the essential features of the Roman metro game.