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Probabilistic Strategy-Proof Rules over Single-Peaked Domains

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Listed:
  • Storcken A.J.A.
  • Peters H.J.M.
  • Roy S.
  • Sen A.

    (GSBE)

Abstract

It is proved that every strategy-proof, peaks-only or unanimous, probabilistic rule defined over a minimally rich domain of single-peaked preferences is a probability mixture of strategy-proof, peaks-only or unanimous, deterministic rules over the same domain. The proof employs Farkas Lemma and the max-flow min-cut theorem for capacitated networks.

Suggested Citation

  • Storcken A.J.A. & Peters H.J.M. & Roy S. & Sen A., 2013. "Probabilistic Strategy-Proof Rules over Single-Peaked Domains," Research Memorandum 040, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2013040
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    References listed on IDEAS

    as
    1. John Weymark, 2011. "A unified approach to strategy-proofness for single-peaked preferences," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(4), pages 529-550, December.
    2. Duggan, John, 1996. "A Geometric Proof of Gibbard's Random Dictatorship Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 365-369, February.
    3. Chatterji, Shurojit & Roy, Souvik & Sen, Arunava, 2012. "The structure of strategy-proof random social choice functions over product domains and lexicographically separable preferences," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 353-366.
    4. Picot, Jérémy & Sen, Arunava, 2012. "An extreme point characterization of random strategy-proof social choice functions: The two alternative case," Economics Letters, Elsevier, vol. 115(1), pages 49-52.
    5. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    6. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    7. Ehlers, Lars & Peters, Hans & Storcken, Ton, 2002. "Strategy-Proof Probabilistic Decision Schemes for One-Dimensional Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 105(2), pages 408-434, August.
    8. Shurojit Chatterji & Arunava Sen & Huaxia Zeng, 2012. "Random Dictatorship Domains," Working Papers 27-2012, Singapore Management University, School of Economics.
    9. Barbera Salvador & Gul Faruk & Stacchetti Ennio, 1993. "Generalized Median Voter Schemes and Committees," Journal of Economic Theory, Elsevier, vol. 61(2), pages 262-289, December.
    10. Kim C. Border & J. S. Jordan, 1983. "Straightforward Elections, Unanimity and Phantom Voters," Review of Economic Studies, Oxford University Press, vol. 50(1), pages 153-170.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Stefano Vannucci, 2017. "Tree-Wise Single Peaked Domains," Department of Economics University of Siena 770, Department of Economics, University of Siena.
    2. Aytek Erdil, 2013. "Strategy-Proof Stochastic Assignment," Cambridge Working Papers in Economics 1333, Faculty of Economics, University of Cambridge.
    3. Erdil, Aytek, 2014. "Strategy-proof stochastic assignment," Journal of Economic Theory, Elsevier, vol. 151(C), pages 146-162.
    4. repec:oup:restud:v:84:y:2017:i:2:p:688-717. is not listed on IDEAS
    5. Pycia, Marek & Ünver, M. Utku, 2015. "Decomposing random mechanisms," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 21-33.
    6. Chatterji, Shurojit & Sen, Arunava & Zeng, Huaxia, 2014. "Random dictatorship domains," Games and Economic Behavior, Elsevier, vol. 86(C), pages 212-236.
    7. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2017. "Optimal Voting Rules," Review of Economic Studies, Oxford University Press, vol. 84(2), pages 688-717.
    8. Lars EHLERS & Dipjyoti MAJUMDAR & Debasis MISHRA & Arunava SEN, 2016. "Continuity and Incentive Compatibility in Cardinal Voting Mechanisms," Cahiers de recherche 04-2016, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    9. Chatterji, Shurojit & Sen, Arunava & Zeng, Huaxia, 2016. "A characterization of single-peaked preferences via random social choice functions," Theoretical Economics, Econometric Society, vol. 11(2), May.
    10. Achuthankutty, Gopakumar & Roy, Souvik, 2017. "On Single-peaked Domains and Min-max Rules," MPRA Paper 81375, University Library of Munich, Germany.
    11. Peters, Hans & Roy, Souvik & Sadhukhan, Soumyarup & Storcken, Ton, 2017. "An extreme point characterization of strategy-proof and unanimous probabilistic rules over binary restricted domains," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 84-90.
    12. Roy, Souvik & Sadhukhan, Soumyarup, 2017. "A Unified Characterization of Randomized Strategy-proof Rules," MPRA Paper 79363, University Library of Munich, Germany.
    13. repec:eee:matsoc:v:90:y:2017:i:c:p:28-34 is not listed on IDEAS
    14. Núñez, Matías, 2015. "Threshold voting leads to Type-Revelation," Economics Letters, Elsevier, vol. 136(C), pages 211-213.
    15. Shurojit Chatterji & Arunava Sen & Huaxia Zeng, 2014. "A CHaracterization of Single-Peaked Preferences via Random Social Choice Functions," Working Papers 13-2014, Singapore Management University, School of Economics.

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