IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v109y2018icp413-435.html
   My bibliography  Save this article

On random social choice functions with the tops-only property

Author

Listed:
  • Chatterji, Shurojit
  • Zeng, Huaxia

Abstract

We study the standard voting model with randomization. A Random Social Choice Function (or RSCF) satisfies the tops-only property if the social lottery under each preference profile depends only on the peaks of voters' preferences. We identify a general condition on domains of preferences (the Interior Property and the Exterior Property) which ensures that every strategy-proof RSCF satisfying unanimity has the tops-only property. We show that our condition applies to important classes of voting domains which include restricted connected domains (Sato, 2013) and the multi-dimensional single-peaked domain (Barberà et al., 1993). As an application of our result, we show that every ex-post efficient and strategy-proof RSCF defined on the multi-dimensional single-peaked domain is a random dictatorship.

Suggested Citation

  • Chatterji, Shurojit & Zeng, Huaxia, 2018. "On random social choice functions with the tops-only property," Games and Economic Behavior, Elsevier, vol. 109(C), pages 413-435.
  • Handle: RePEc:eee:gamebe:v:109:y:2018:i:c:p:413-435
    DOI: 10.1016/j.geb.2017.11.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825617302427
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.geb.2017.11.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Saporiti, Alejandro, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
    2. Sato, Shin, 2013. "A sufficient condition for the equivalence of strategy-proofness and nonmanipulability by preferences adjacent to the sincere one," Journal of Economic Theory, Elsevier, vol. 148(1), pages 259-278.
    3. Salvador Barbera, 1979. "Majority and Positional Voting in a Probabilistic Framework," Review of Economic Studies, Oxford University Press, vol. 46(2), pages 379-389.
    4. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2012. "Domains, ranges and strategy-proofness: the case of single-dipped preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 335-352, July.
    5. 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.
    6. Bernard Monjardet, 2009. "Acyclic Domains of Linear Orders: A Survey," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 139-160, Springer.
    7. Barbera, Salvador & Masso, Jordi & Neme, Alejandro, 2005. "Voting by committees under constraints," Journal of Economic Theory, Elsevier, vol. 122(2), pages 185-205, June.
    8. Bhaskar Dutta & Hans Peters & Arunava Sen, 2008. "Strategy-proof cardinal decision schemes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(4), pages 701-702, May.
    9. John A. Weymark, 2008. "Strategy‐Proofness and the Tops‐Only Property," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(1), pages 7-26, February.
    10. Barbera, Salvador & Jackson, Matthew O. & Neme, Alejandro, 1997. "Strategy-Proof Allotment Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 1-21, January.
    11. Chatterji, Shurojit & Sen, Arunava & Zeng, Huaxia, 2014. "Random dictatorship domains," Games and Economic Behavior, Elsevier, vol. 86(C), pages 212-236.
    12. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-519, March.
    13. Mishra, Debasis & Roy, Souvik, 2012. "Strategy-proof partitioning," Games and Economic Behavior, Elsevier, vol. 76(1), pages 285-300.
    14. 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.
    15. Cho, Wonki Jo, 2016. "Incentive properties for ordinal mechanisms," Games and Economic Behavior, Elsevier, vol. 95(C), pages 168-177.
    16. 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.
    17. Dutta, Bhaskar & Peters, Hans & Sen, Arunava, 2002. "Strategy-Proof Probabilistic Mechanisms in Economies with Pure Public Goods," Journal of Economic Theory, Elsevier, vol. 106(2), pages 392-416, October.
    18. 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.
    19. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    20. Michel Le Breton & Arunava Sen, 1999. "Separable Preferences, Strategyproofness, and Decomposability," Econometrica, Econometric Society, vol. 67(3), pages 605-628, May.
    21. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    22. Reffgen, Alexander, 2015. "Strategy-proof social choice on multiple and multi-dimensional single-peaked domains," Journal of Economic Theory, Elsevier, vol. 157(C), pages 349-383.
    23. Peters, Hans & Roy, Souvik & Sen, Arunava & Storcken, Ton, 2014. "Probabilistic strategy-proof rules over single-peaked domains," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 123-127.
    24. Arribillaga, R. Pablo & Massó, Jordi, 2016. "Comparing generalized median voter schemes according to their manipulability," Theoretical Economics, Econometric Society, vol. 11(2), May.
    25. Gabriel Carroll, 2012. "When Are Local Incentive Constraints Sufficient?," Econometrica, Econometric Society, vol. 80(2), pages 661-686, March.
    26. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    27. Lin Zhou, 1991. "Impossibility of Strategy-Proof Mechanisms in Economies with Pure Public Goods," Review of Economic Studies, Oxford University Press, vol. 58(1), pages 107-119.
    28. Arunava Sen, 2011. "The Gibbard random dictatorship theorem: a generalization and a new proof," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(4), pages 515-527, December.
    29. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 389-396, December.
    30. Nehring, Klaus & Puppe, Clemens, 2007. "The structure of strategy-proof social choice -- Part I: General characterization and possibility results on median spaces," Journal of Economic Theory, Elsevier, vol. 135(1), pages 269-305, July.
    31. Alexander Reffgen, 2011. "Generalizing the Gibbard–Satterthwaite theorem: partial preferences, the degree of manipulation, and multi-valuedness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(1), pages 39-59, June.
    32. Yves Sprumont, 1995. "Strategyproof Collective Choice in Economic and Political Environments," Canadian Journal of Economics, Canadian Economics Association, vol. 28(1), pages 68-107, February.
    33. Barbera, Salvador & Masso, Jordi & Neme, Alejandro, 1997. "Voting under Constraints," Journal of Economic Theory, Elsevier, vol. 76(2), pages 298-321, October.
    34. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    35. 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.
    36. Shurojit Chatterji & Arunava Sen, 2011. "Tops-only domains," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(2), pages 255-282, February.
    37. Pycia, Marek & Ünver, M. Utku, 2015. "Decomposing random mechanisms," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 21-33.
    38. Kelly, Jerry S., 1989. "A new informational base for social choice," Mathematical Social Sciences, Elsevier, vol. 17(2), pages 177-188, April.
    39. Navin Aswal & Shurojit Chatterji & Arunava Sen, 2003. "Dictatorial domains," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(1), pages 45-62, August.
    40. 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.
    41. Florian Brandl & Felix Brandt & Hans Georg Seedig, 2016. "Consistent Probabilistic Social Choice," Econometrica, Econometric Society, vol. 84, pages 1839-1880, September.
    42. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kumar, Ujjwal & Roy, Souvik & Sen, Arunava & Yadav, Sonal & Zeng, Huaxia, 2021. "Local global equivalence for unanimous social choice functions," Games and Economic Behavior, Elsevier, vol. 130(C), pages 299-308.
    2. Roy, Souvik & Sadhukhan, Soumyarup, 2021. "A unified characterization of the randomized strategy-proof rules," Journal of Economic Theory, Elsevier, vol. 197(C).
    3. Souvik Roy & Soumyarup Sadhukhan, 2019. "A characterization of random min–max domains and its applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(4), pages 887-906, November.
    4. Gopakumar Achuthankutty & Souvik Roy, 2018. "On single-peaked domains and min–max rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 753-772, December.
    5. Roy, Souvik & Sadhukhan, Soumyarup, 2022. "On the equivalence of strategy-proofness and upper contour strategy-proofness for randomized social choice functions," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    6. Chatterji, Shurojit & Zeng, Huaxia, 2019. "Random mechanism design on multidimensional domains," Journal of Economic Theory, Elsevier, vol. 182(C), pages 25-105.
    7. Bonifacio, Agustín G. & Massó, Jordi, 2020. "On strategy-proofness and semilattice single-peakedness," Games and Economic Behavior, Elsevier, vol. 124(C), pages 219-238.
    8. Chatterji, Shurojit & Roy, Souvik & Sadhukhan, Soumyarup & Sen, Arunava & Zeng, Huaxia, 2022. "Probabilistic fixed ballot rules and hybrid domains," Journal of Mathematical Economics, Elsevier, vol. 100(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chatterji, Shurojit & Zeng, Huaxia, 2019. "Random mechanism design on multidimensional domains," Journal of Economic Theory, Elsevier, vol. 182(C), pages 25-105.
    2. Chatterji, Shurojit & Roy, Souvik & Sadhukhan, Soumyarup & Sen, Arunava & Zeng, Huaxia, 2022. "Probabilistic fixed ballot rules and hybrid domains," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    3. 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.
    4. Chatterji, Shurojit & Sen, Arunava & Zeng, Huaxia, 2014. "Random dictatorship domains," Games and Economic Behavior, Elsevier, vol. 86(C), pages 212-236.
    5. Roy, Souvik & Sadhukhan, Soumyarup, 2021. "A unified characterization of the randomized strategy-proof rules," Journal of Economic Theory, Elsevier, vol. 197(C).
    6. Shurojit Chatterji & Souvik Roy & Soumyarup Sadhukhan & Arunava Sen & Huaxia Zeng, 2021. "Probabilistic Fixed Ballot Rules and Hybrid Domains," Papers 2105.10677, arXiv.org, revised Jan 2022.
    7. Shurojit Chatterji & Huaxia Zeng, 2022. "A Taxonomy of Non-dictatorial Unidimensional Domains," Papers 2201.00496, arXiv.org, revised Jul 2022.
    8. Shurojit Chatterji & Arunava Sen, 2011. "Tops-only domains," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(2), pages 255-282, February.
    9. Bonifacio, Agustín G. & Massó, Jordi, 2020. "On strategy-proofness and semilattice single-peakedness," Games and Economic Behavior, Elsevier, vol. 124(C), pages 219-238.
    10. Reffgen, Alexander, 2015. "Strategy-proof social choice on multiple and multi-dimensional single-peaked domains," Journal of Economic Theory, Elsevier, vol. 157(C), pages 349-383.
    11. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2017. "Optimal Voting Rules," Review of Economic Studies, Oxford University Press, vol. 84(2), pages 688-717.
    12. John A. Weymark, 2008. "Strategy‐Proofness and the Tops‐Only Property," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(1), pages 7-26, February.
    13. Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    14. Pycia, Marek & Ünver, M. Utku, 2015. "Decomposing random mechanisms," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 21-33.
    15. Barbera, S. & Masso, J. & Serizawa, S., 1998. "Strategy-Proof Voting on Compact Ranges," Games and Economic Behavior, Elsevier, vol. 25(2), pages 272-291, November.
    16. Gopakumar Achuthankutty & Souvik Roy, 2018. "On single-peaked domains and min–max rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 753-772, December.
    17. Salvador Barberà, 2010. "Strategy-proof social choice," Working Papers 420, Barcelona School of Economics.
    18. Souvik Roy & Soumyarup Sadhukhan, 2019. "A characterization of random min–max domains and its applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(4), pages 887-906, November.
    19. Peters, Hans & Roy, Souvik & Sen, Arunava & Storcken, Ton, 2014. "Probabilistic strategy-proof rules over single-peaked domains," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 123-127.
    20. Lars-Gunnar Svensson & Pär Torstensson, 2008. "Strategy-proof allocation of multiple public goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(2), pages 181-196, February.

    More about this item

    Keywords

    Random social choice functions; Unanimity; Strategy-proofness; The tops-only property; The interior property; The exterior property;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:109:y:2018:i:c:p:413-435. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.