Maximization of Relative Social Welfare on Truthful Cardinal Voting Schemes

Consider the the problem of maximizing the relative social welfare of truthful single-winner voting schemes with cardinal preferences compared to the classical range voting scheme. The range voting scheme is a simple and straightforward mechanism which deterministically maximizes the social welfare. However, the scheme that is known to be non-truthful and we studied the truthful mechanism that maximize the ratio of its expected social welfare to the social welfare achieved by the range voting scheme. We provide a scheme which achieve a ratio of $\Omega(m^{-2/3})$ in this paper. It is proved that this bound is tight asymptotically and it is impossible to find a better voting scheme.