Manipulation and Single-Peakedness: A General Result

This article considers environments in which individual preferences are single-peaked with respect to an unspecified, but unidimensional, ordering of the alternative space. We show that in these environments, any institution that is coalitionally strategy-proof must be dictatorial. Thus, any nondictatorial institutional environment that does not explicitly utilize an a priori ordering over alternatives in order to render a collective decision is necessarily prone to the strategic misrepresentation of preferences by an individual or a group. Moreover, we prove in this environment that for any nondictatorial institution, the truthful revelation of preferences can never be a dominant strategy equilibrium. Accordingly, an incentive to behave insincerely is inherent to the vast majority of real-world lawmaking systems, even when the policy space is unidimensional and the core is nonempty.