IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/79363.html
   My bibliography  Save this paper

A Unified Characterization of Randomized Strategy-proof Rules

Author

Listed:
  • Roy, Souvik
  • Sadhukhan, Soumyarup

Abstract

This paper presents a unified characterization of the unanimous and strategy-proof random rules on a class of domains that are based on some prior ordering over the alternatives. It identifies a condition called top-richness so that, if a domain satisfies top-richness, then an RSCF on it is unanimous and strategy-proof if and only if it is a convex combination of tops-restricted min-max rules. Well-known domains like single-crossing, single-peaked, single-dipped etc. satisfy top-richness. This paper also provides a characterization of the random min-max domains. Furthermore, it offers a characterization of the tops-only and strategy-proof random rules on top-rich domains satisfying top-connectedness. Finally, it presents a characterization of the unanimous (tops-only) and group strategy-proof random rules on those domains.

Suggested Citation

  • Roy, Souvik & Sadhukhan, Soumyarup, 2017. "A Unified Characterization of Randomized Strategy-proof Rules," MPRA Paper 79363, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:79363
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/79363/1/MPRA_paper_79363.pdf
    File Function: original version
    Download Restriction: no
    File URL: https://mpra.ub.uni-muenchen.de/104406/1/MPRA_paper_104406.pdf
    File Function: revised version
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. 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. 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.
    4. Epple, Dennis & Platt, Glenn J., 1998. "Equilibrium and Local Redistribution in an Urban Economy when Households Differ in both Preferences and Incomes," Journal of Urban Economics, Elsevier, vol. 43(1), pages 23-51, January.
    5. Anup Pramanik & Arunava Sen, 2016. "Pairwise partition graphs and strategy-proof social choice in the exogenous indifference class model," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(1), pages 1-24, June.
    6. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2010. "Individual versus group strategy-proofness: When do they coincide?," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1648-1674, September.
    7. 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.
    8. Stiglitz, J. E., 1974. "The demand for education in public and private school systems," Journal of Public Economics, Elsevier, vol. 3(4), pages 349-385, November.
    9. 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.
    10. Salvador Barbera & Matthew O. Jackson, 2004. "Choosing How to Choose: Self-Stable Majority Rules and Constitutions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(3), pages 1011-1048.
    11. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2017. "Optimal Voting Rules," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(2), pages 688-717.
    12. 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.
    13. Lahiri, Abhinaba & Peters, Hans & Storcken, Ton, 2017. "Strategy-proof location of public bads in a two-country model," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 150-159.
    14. Peter Bearse & Gerhard Glomm & Eckhard Janeba, 2001. "Composition of Government Budget, Non‐Single Peakedness, and Majority Voting," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 3(4), pages 471-481, October.
    15. Ireland, Norman J., 1990. "The mix of social and private provision of goods and services," Journal of Public Economics, Elsevier, vol. 43(2), pages 201-219, November.
    16. Shurojit Chatterji & Huaxia Zeng, 2015. "On Random Social Choice Functions with the Tops-only Property," Working Papers 11-2015, Singapore Management University, School of Economics.
    17. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January.
    18. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    19. 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.
    20. 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.
    21. Shurojit Chatterji & Jordi Massó, 2018. "On Strategy†Proofness And The Salience Of Single†Peakedness," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(1), pages 163-189, February.
    22. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    23. Fan‐Chin Kung, 2006. "An Algorithm for Stable and Equitable Coalition Structures with Public Goods," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 8(3), pages 345-355, August.
    24. Roberts, Kevin W. S., 1977. "Voting over income tax schedules," Journal of Public Economics, Elsevier, vol. 8(3), pages 329-340, December.
    25. Meltzer, Allan H & Richard, Scott F, 1981. "A Rational Theory of the Size of Government," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 914-927, October.
    26. Berga, Dolors, 1998. "Strategy-proofness and single-plateaued preferences," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 105-120, March.
    27. Kim C. Border & J. S. Jordan, 1983. "Straightforward Elections, Unanimity and Phantom Voters," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 153-170.
    28. Dennis Epple & Thomas Romer & Holger Sieg, 2001. "Interjurisdictional Sorting and Majority Rule: An Empirical Analysis," Econometrica, Econometric Society, vol. 69(6), pages 1437-1465, November.
    29. ,, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
    30. Murat Öztürk & Hans Peters & Ton Storcken, 2014. "On the location of public bads: strategy-proofness under two-dimensional single-dipped preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 83-108, May.
    31. Cho, Wonki Jo, 2016. "Incentive properties for ordinal mechanisms," Games and Economic Behavior, Elsevier, vol. 95(C), pages 168-177.
    32. Barberà, Salvador & Moreno, Bernardo, 2011. "Top monotonicity: A common root for single peakedness, single crossing and the median voter result," Games and Economic Behavior, Elsevier, vol. 73(2), pages 345-359.
    33. Romer, Thomas, 1975. "Individual welfare, majority voting, and the properties of a linear income tax," Journal of Public Economics, Elsevier, vol. 4(2), pages 163-185, February.
    34. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    35. Epple, Dennis & Romano, Richard E, 1996. "Public Provision of Private Goods," Journal of Political Economy, University of Chicago Press, vol. 104(1), pages 57-84, February.
    36. Anderberg, Dan, 1999. "Determining the mix of public and private provision of insurance by majority rule," European Journal of Political Economy, Elsevier, vol. 15(3), pages 417-440, September.
    37. 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.
    38. Westhoff, Frank, 1977. "Existence of equilibria in economies with a local public good," Journal of Economic Theory, Elsevier, vol. 14(1), pages 84-112, February.
    39. Dennis Epple & Richard Romano & Holger Sieg, 2006. "Admission, Tuition, and Financial Aid Policies in the Market for Higher Education," Econometrica, Econometric Society, vol. 74(4), pages 885-928, July.
    40. Gabriel Carroll, 2012. "When Are Local Incentive Constraints Sufficient?," Econometrica, Econometric Society, vol. 80(2), pages 661-686, March.
    41. 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.
    42. repec:bla:jpbect:v:3:y:2001:i:4:p:471-81 is not listed on IDEAS
    43. Nehring, Klaus & Puppe, Clemens, 2007. "Efficient and strategy-proof voting rules: A characterization," Games and Economic Behavior, Elsevier, vol. 59(1), pages 132-153, April.
    44. 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.
    45. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2018. "Strategy-proof location of public facilities," Games and Economic Behavior, Elsevier, vol. 112(C), pages 21-48.
    46. Saporiti, Alejandro, 2014. "Securely implementable social choice rules with partially honest agents," Journal of Economic Theory, Elsevier, vol. 154(C), pages 216-228.
    47. Barzel, Yoram, 1973. "Private Schools and Public School Finance," Journal of Political Economy, University of Chicago Press, vol. 81(1), pages 174-186, Jan.-Feb..
    48. Pycia, Marek & Ünver, M. Utku, 2015. "Decomposing random mechanisms," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 21-33.
    49. Schummer, James & Vohra, Rakesh V., 2002. "Strategy-proof Location on a Network," Journal of Economic Theory, Elsevier, vol. 104(2), pages 405-428, June.
    50. Davis, Otto A. & Hinich, Melvin J. & Ordeshook, Peter C., 1970. "An Expository Development of a Mathematical Model of the Electoral Process," American Political Science Review, Cambridge University Press, vol. 64(2), pages 426-448, June.
    51. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    52. Raquel Fernandez & Richard Rogerson, 1995. "On the Political Economy of Education Subsidies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(2), pages 249-262.
    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. Karmokar, Madhuparna & Roy, Souvik, 2020. "The structure of (local) ordinal Bayesian incentive compatible random rules," MPRA Paper 103494, University Library of Munich, Germany.
    2. 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).

    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. 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.
    2. 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.
    3. 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.
    4. ,, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
    5. Chatterji, Shurojit & Zeng, Huaxia, 2019. "Random mechanism design on multidimensional domains," Journal of Economic Theory, Elsevier, vol. 182(C), pages 25-105.
    6. Achuthankutty, Gopakumar & Roy, Souvik, 2017. "On Top-connected Single-peaked and Partially Single-peaked Domains," MPRA Paper 78102, University Library of Munich, Germany.
    7. 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).
    8. Alejandro Saporiti, 2006. "Strategic voting on single-crossing domains," Economics Discussion Paper Series 0617, Economics, The University of Manchester.
    9. Achuthankutty, Gopakumar & Roy, Souvik, 2017. "Strategy-proof Rules on Partially Single-peaked Domains," MPRA Paper 82267, University Library of Munich, Germany.
    10. 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.
    11. 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).
    12. Chatterji, Shurojit & Zeng, Huaxia, 2023. "A taxonomy of non-dictatorial unidimensional domains," Games and Economic Behavior, Elsevier, vol. 137(C), pages 228-269.
    13. Robert Bredereck & Jiehua Chen & Gerhard Woeginger, 2013. "A characterization of the single-crossing domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 989-998, October.
    14. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2017. "Optimal Voting Rules," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(2), pages 688-717.
    15. Felix Brand & Patrick Lederer & Sascha Tausch, 2023. "Strategyproof Social Decision Schemes on Super Condorcet Domains," Papers 2302.12140, arXiv.org.
    16. Shurojit Chatterji & Huaxia Zeng, 2022. "A Taxonomy of Non-dictatorial Unidimensional Domains," Papers 2201.00496, arXiv.org, revised Oct 2022.
    17. Madhuparna Karmokar & Souvik Roy, 2023. "The structure of (local) ordinal Bayesian incentive compatible random rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 111-152, July.
    18. Bonifacio, Agustín G. & Massó, Jordi, 2020. "On strategy-proofness and semilattice single-peakedness," Games and Economic Behavior, Elsevier, vol. 124(C), pages 219-238.
    19. Hans Peters & Souvik Roy & Soumyarup Sadhukhan, 2021. "Unanimous and Strategy-Proof Probabilistic Rules for Single-Peaked Preference Profiles on Graphs," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 811-833, May.
    20. Gogulapati Sreedurga & Soumyarup Sadhukhan & Souvik Roy & Yadati Narahari, 2022. "Characterization of Group-Fair Social Choice Rules under Single-Peaked Preferences," Papers 2207.07984, arXiv.org.

    More about this item

    Keywords

    Random Social Choice Functions; Unanimity; Strategy-proofness; Tops-onlyness; Uncompromisingness; Random min-max Rules; Single-crossing Domains.;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:pra:mprapa:79363. See general information about how to correct material in RePEc.

    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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.