The replacement principle for the provision of multiple public goods on tree networks

We study the problem of providing two public goods on tree networks, in which each agent has a single-peaked preference. We show that if the number of agents is at least four, then there exists no social choice rule that satisfies efficiency and replacement– domination. In fact, it is shown that these two properties are incompatible even if agents’ preferences are restricted to a smaller domain of symmetric single-peaked preferences. On the other hand, for rules on an interval, we prove that Miyagawa’s (2001) characterization that only the left-peaks rule and the right-peaks rule satisfy these two properties also holds on the domain of symmetric single-peaked preferences. Moreover, if agents’ peak locations are restricted to either the nodes or the endpoints of trees, rules exist on a subclass of trees. We provide a characterization of a family of such rules. JEL classification: C79; D71; H41.