IDEAS home Printed from https://ideas.repec.org/p/bge/wpaper/418.html
   My bibliography  Save this paper

Domains, Ranges and Strategy-Proofness: The Case of Single-dipped Preferences

Author

Listed:
  • Salvador Barberà
  • Dolors Berga
  • Bernardo Moreno

Abstract

We characterize the set of all individual and group strategy-proof rules on the domain of all single-dipped preferences on a line. For rules defined on this domain, and on several of its subdomains, we explore the implications of these strategy-proofness requirements on the maximum size of the rules' range. We show that when all single-dipped preferences are admissible, the range must contain two alternatives at most. But this bound changes as we consider different subclasses of single-dipped preferences: we provide examples of subdomains admitting strategy-proof rules with larger ranges. We establish exact bounds on the maximal size of strategy-proof functions on each of these domains, and prove that the relationship between the sizes of the subdomains and those of the ranges of strategy-proof functions on them need not be monotonic. Our results exhibit a sharp contrast between the structure of strategy-proof rules defined on subdomains of single-dipped preferences and those defined on subsets of single-peaked ones.

Suggested Citation

  • Salvador Barberà & Dolors Berga & Bernardo Moreno, 2009. "Domains, Ranges and Strategy-Proofness: The Case of Single-dipped Preferences," Working Papers 418, Barcelona School of Economics.
  • Handle: RePEc:bge:wpaper:418
    as

    Download full text from publisher

    File URL: http://www.barcelonagse.eu/sites/default/files/working_paper_pdfs/418_revised.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    2. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2012. "Group strategy-proof social choice functions with binary ranges and arbitrary domains: characterization results," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 791-808, November.
    3. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    4. Sen, Amartya & Pattanaik, Prasanta K., 1969. "Necessary and sufficient conditions for rational choice under majority decision," Journal of Economic Theory, Elsevier, vol. 1(2), pages 178-202, August.
    5. 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.
    6. Vikram Manjunath, 2014. "Efficient and strategy-proof social choice when preferences are single-dipped," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(3), pages 579-597, August.
    7. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    8. Larsson, Bo & Svensson, Lars-Gunnar, 2006. "Strategy-proof voting on the full preference domain," Mathematical Social Sciences, Elsevier, vol. 52(3), pages 272-287, December.
    9. 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.
    10. Saari, Donald G. & Valognes, Fabrice, 1999. "The geometry of Black's single peakedness and related conditions," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 429-456, December.
    11. Manjunath, Vikram, 2012. "Group strategy-proofness and voting between two alternatives," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 239-242.
    12. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    13. Klaus, Bettina & Peters, Hans & Storcken, Ton, 1997. "Strategy-proof division of a private good when preferences are single-dipped," Economics Letters, Elsevier, vol. 55(3), pages 339-346, September.
    Full references (including those not matched with items on IDEAS)

    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. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2022. "Restricted environments and incentive compatibility in interdependent values models," Games and Economic Behavior, Elsevier, vol. 131(C), pages 1-28.
    2. Vikram Manjunath, 2014. "Efficient and strategy-proof social choice when preferences are single-dipped," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(3), pages 579-597, August.
    3. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2012. "Group strategy-proof social choice functions with binary ranges and arbitrary domains: characterization results," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 791-808, November.
    4. Patrick Harless, 2015. "Reaching consensus: solidarity and strategic properties in binary social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(1), pages 97-121, June.
    5. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2018. "Strategy-proof location of public facilities," Games and Economic Behavior, Elsevier, vol. 112(C), pages 21-48.
    6. Qiaoming Han & Donglei Du & Dachuan Xu & Yicheng Xu, 2018. "Approximate efficiency and strategy-proofness for moneyless mechanisms on single-dipped policy domain," Journal of Global Optimization, Springer, vol. 70(4), pages 859-873, April.
    7. Manjunath, Vikram, 2012. "Group strategy-proofness and voting between two alternatives," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 239-242.
    8. 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.
    9. Achille Basile & Surekha Rao & K. P. S. Bhaskara Rao, 2022. "Binary strategy-proof social choice functions with indifference," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 807-826, April.
    10. Makoto Hagiwara & Hirofumi Yamamura, 2020. "Upper set rules with binary ranges," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(4), pages 657-666, April.
    11. Moulin, Hervé, 2017. "One dimensional mechanism design," Theoretical Economics, Econometric Society, vol. 12(2), May.
    12. Grisel Ayllón & Diego M. Caramuta, 2016. "Single-dipped preferences with satiation: strong group strategy-proofness and unanimity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 245-264, August.
    13. Basile, Achille & Rao, Surekha & Bhaskara Rao, K.P.S., 2022. "Anonymous, non-manipulable binary social choice," Games and Economic Behavior, Elsevier, vol. 133(C), pages 138-149.
    14. 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.
    15. Dolors Berga & Bernardo Moreno & Antonio Nicolò, 2023. "Undominated rules with three alternatives in an almost unrestricted domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(1), pages 65-74, January.
    16. 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.
    17. Arribillaga, R. Pablo & Bonifacio, Agustín G., 2024. "Obvious manipulations of tops-only voting rules," Games and Economic Behavior, Elsevier, vol. 143(C), pages 12-24.
    18. Berga, Dolors & Moreno, Bernardo, 2020. "Preference reversal and group strategy-proofness," Economics Letters, Elsevier, vol. 196(C).
    19. M. Sanver, 2009. "Strategy-proofness of the plurality rule over restricted domains," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 461-471, June.
    20. 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.

    More about this item

    Keywords

    Strategy-proof; group strategy-proof; binary range rules; single-dipped;
    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:bge:wpaper:418. 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: Bruno Guallar (email available below). General contact details of provider: https://edirc.repec.org/data/bargses.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.