The Roman Metro Problem
In Rome, if you start digging, chances are you will nd things. We consider a famous complaint that justi es the underdeveloped Roman metro system: \if we tried to build a new metro line, it would probably be stopped by archeological nds 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 sucient conditions for this ineciency to occur. One might think it arises from the inability to commit to nishing the metro (no matter what is discovered in the process). We show, however, that the inecient 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.
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