Strategy-proof partitioning

We consider the problem of choosing a partition of a set of objects by a set of agents. The private information of each agent is a strict ordering over the set of partitions of the objects. A social choice function chooses a partition given the reported preferences of the agents. We impose a natural restriction on the allowable set of strict orderings over the set of partitions, which we call an intermediate domain. Our main result is a complete characterization of strategy-proof and tops-only social choice functions in the intermediate domain. We also show that a social choice function is strategy-proof and unanimous if and only if it is a meet social choice function.