Maximization of Relative Social Welfare on Truthful Cardinal Voting Schemes

TL;DR

This paper investigates truthful voting schemes that approximate the social welfare of range voting, providing bounds on their performance and demonstrating the optimality of the proposed scheme.

Contribution

It introduces a truthful voting scheme that achieves a near-optimal ratio of social welfare compared to range voting, with tight asymptotic bounds.

Findings

Achieves a social welfare ratio of  m^{-2/3}

Proves the bound is asymptotically tight

No better truthful scheme can surpass this ratio

Abstract

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.