Abstract
We consider the fundamental mechanism design problem of approximate social welfare maximization under general cardinal preferences on a finite number of alternatives and without money. The well-known range voting scheme can be thought of as a non-truthful mechanism for exact social welfare maximization in this setting. With m being the number of alternatives, we exhibit a randomized truthful-in-expectation ordinal mechanism with approximation ratio Ω(m − 3/4). On the other hand, we show that for sufficiently many agents, the approximation ratio of any truthful-in-expectation ordinal mechanism is O(m − 2/3). We supplement our results with an upper bound for any truthful-in-expectation mechanism. We get tighter bounds for the natural special case of m = 3, and in that case furthermore obtain separation results concerning the approximation ratios achievable by natural restricted classes of truthful-in-expectation mechanisms. In particular, we show that the best cardinal truthful mechanism strictly outperforms all ordinal ones.
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Filos-Ratsikas, A., Miltersen, P.B. (2014). Truthful Approximations to Range Voting. In: Liu, TY., Qi, Q., Ye, Y. (eds) Web and Internet Economics. WINE 2014. Lecture Notes in Computer Science, vol 8877. Springer, Cham. https://doi.org/10.1007/978-3-319-13129-0_13
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DOI: https://doi.org/10.1007/978-3-319-13129-0_13
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