Maximal domain for strategy-proof rules with one public good
In the context of a single public good, the Gibbard-Satterthwaite theorem shows that there are no strategy-proof nondictatorial social choice functions on unrestricted preference domains. On the other hand, Moulin showed that generalized median voter schemes are strategy-proof on single-peaked domains. The authors extend these results in two directions. First, they introduce the concept of a `minimally-rich' preference domain. Minimally-rich domains are smaller than single-peaked domains and the authors' first main result (Theorem 1) states that a social choice function on a minimally-rich domain is strategy-proof if and only if it is a generalized median voter scheme. Turning to the question of maximality of domain, the authors introduce a `no-vetoer' axiom to avoid the trivial dictatorial case. Under this condition, the authors obtain the following result (Theorem 2): The unique maximal domain containing a minimally-rich domain for strategy-proofness is the domain of convex preferences. Relaxing the no-vetoer condition, the authors give an example of a non-convex preference domain with a non-dictatorial strategy-proof social choice function with vetoers.
scientific article; zbMATH DE number 1445568