An impossibility theorem for secure implementation in discrete public good economies

This paper studies the possibility of secure implementation (Saijo, T., T. Sjostrom, and T. Yamato (2007) "Secure implementation," Theoretical Economics 2, pp.203-229) in discrete public good economies with quasi-linear preferences. We find that only constant social choice functions are securely implementable over the domains that satisfy partial dominance introduced in this paper. Partial dominance is a reasonable condition because the set of all strictly increasing and strictly concave valuation functions satisfies this condition.