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Maskin-monotonic scoring rules

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Abstract

We characterize which scoring rules are Maskin-monotonic for each social choice problem as a function of the number of agents and the number of alternatives. We show that a scoring rule is Maskin-monotonic if and only if it satisfies a certain unanimity condition. Since scoring rules are neutral, Maskin-monotonicity turns out to be equivalent to Nash-implementability within the class of scoring rules. We propose a class of mechanisms such that each Nash-implementable scoring rule can be implemented via a mechanism in that class. Moreover, we investigate the class of generalized scoring rules and show that with a restriction on score vectors, our results for the standard case are still valid.

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Notes

  1. A linear order is a transitive, anti-symmetric and complete binary relation.

  2. \(\lfloor x\rfloor \) denotes the maximal integer that does not exceed \(x\).

  3. The result is Lemma 4 in Chapter 3 of Moulin (1983).

  4. The result is Theorem 2.3.22 of Peleg (1984).

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Acknowledgments

We would like to thank William Thomson and an anonymous referee for their careful reading of the paper and many helpful comments.

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Authors and Affiliations

  1. University of Rochester, Rochester, NY, USA

    Battal Doğan

  2. Bilkent University, Ankara, Turkey

    Semih Koray

Authors
  1. Battal Doğan
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  2. Semih Koray
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Correspondence to Battal Doğan.

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Doğan, B., Koray, S. Maskin-monotonic scoring rules. Soc Choice Welf 44, 423–432 (2015). https://doi.org/10.1007/s00355-014-0835-6

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  • DOI: https://doi.org/10.1007/s00355-014-0835-6

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