Bribe-proofness for single-peaked preferences: characterizations and maximality-of-domains results

This paper considers the problem of allocating an amount of a perfectly divisible resource among agents. We are interested in rules eliminating the possibility that an agent can compensate another to misrepresent her preferences, making both agents strictly better off. Such rules are said to be bribe-proof (Schummer in J Econ Theory 91:180-198, 2000). We first provide necessary and sufficient conditions for any rule defined on the single-peaked domain to be bribe-proof. By invoking this and Ching's (Soc Choice Welf 11:131-136, 1994) result, we obtain the uniform rule as the unique bribe-proof and symmetric rule on the single-peaked domain. Furthermore, we examine how large a domain can be to allow for the existence of bribe-proof and symmetric rules and show that the convex domain is such a unique maximal domain.