IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v54y2020i1d10.1007_s00355-019-01216-3.html
   My bibliography  Save this article

A characterization of the single-peaked single-crossing domain

Author

Listed:
  • Edith Elkind

    (University of Oxford)

  • Piotr Faliszewski

    (AGH University)

  • Piotr Skowron

    (University of Warsaw)

Abstract

We characterize elections that are simultaneously single-peaked and single-crossing (SPSC), by establishing a connection between this domain and that of minimally rich elections, i.e., elections where each candidate is ranked first by at least one voter. Specifically, we show that an election is both single-peaked and single-crossing if and only if it can be obtained from a minimally rich single-crossing election by deleting voters.

Suggested Citation

  • Edith Elkind & Piotr Faliszewski & Piotr Skowron, 2020. "A characterization of the single-peaked single-crossing domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(1), pages 167-181, January.
    • Handle: RePEc:spr:sochwe:v:54:y:2020:i:1:d:10.1007_s00355-019-01216-3
    DOI: 10.1007/s00355-019-01216-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00355-019-01216-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00355-019-01216-3?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. ,, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
    2. Puppe, Clemens, 2018. "The single-peaked domain revisited: A simple global characterization," Journal of Economic Theory, Elsevier, vol. 176(C), pages 55-80.
    3. Alejandro Saporiti & Fernando Tohmé, 2006. "Single-Crossing, Strategic Voting and the Median Choice Rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 363-383, April.
    4. Inada, Ken-Ichi, 1969. "The Simple Majority Decision Rule," Econometrica, Econometric Society, vol. 37(3), pages 490-506, July.
    5. 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.
    6. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January.
    7. 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.
    8. Knoblauch, Vicki, 2010. "Recognizing one-dimensional Euclidean preference profiles," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 1-5, January.
    9. Jiehua Chen & Kirk R. Pruhs & Gerhard J. Woeginger, 2017. "The one-dimensional Euclidean domain: finitely many obstructions are not enough," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 409-432, February.
    10. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    11. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    12. Roberts, Kevin W. S., 1977. "Voting over income tax schedules," Journal of Public Economics, Elsevier, vol. 8(3), pages 329-340, December.
    13. 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.
    14. Miguel Ballester & Guillaume Haeringer, 2011. "A characterization of the single-peaked domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(2), pages 305-322, February.
    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. 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.
    2. Jiehua Chen & Kirk R. Pruhs & Gerhard J. Woeginger, 2017. "The one-dimensional Euclidean domain: finitely many obstructions are not enough," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 409-432, February.
    3. Puppe, Clemens & Slinko, Arkadii, 2024. "Maximal Condorcet domains. A further progress report," Games and Economic Behavior, Elsevier, vol. 145(C), pages 426-450.
    4. Tanguiane, Andranick S., 2022. "Analysis of the 2021 Bundestag elections. 2/4. Political spectrum," Working Paper Series in Economics 152, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    5. Roy, Souvik & Sadhukhan, Soumyarup, 2021. "A unified characterization of the randomized strategy-proof rules," Journal of Economic Theory, Elsevier, vol. 197(C).
    6. 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.
    7. Puppe, Clemens & Slinko, Arkadii, 2022. "Maximal Condorcet domains: A further progress report," Working Paper Series in Economics 159, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    8. Bredereck, Robert & Chen, Jiehua & Woeginger, Gerhard J., 2016. "Are there any nicely structured preference profiles nearby?," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 61-73.
    9. Fan-Chin Kung, 2015. "Sorting out single-crossing preferences on networks," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 663-672, March.
    10. 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.
    11. Puppe, Clemens, 2018. "The single-peaked domain revisited: A simple global characterization," Journal of Economic Theory, Elsevier, vol. 176(C), pages 55-80.
    12. ,, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
    13. Alejandro Saporiti, 2006. "Strategic voting on single-crossing domains," Economics Discussion Paper Series 0617, Economics, The University of Manchester.
    14. 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.
    15. Slinko, Arkadii & Wu, Qinggong & Wu, Xingye, 2021. "A characterization of preference domains that are single-crossing and maximal Condorcet," Economics Letters, Elsevier, vol. 204(C).
    16. Marie-Louise Lackner & Martin Lackner, 2017. "On the likelihood of single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 717-745, April.
    17. Jiehua Chen & Sven Grottke, 2021. "Small one-dimensional Euclidean preference profiles," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 117-144, July.
    18. Gabrielle Demange, 2012. "Majority relation and median representative ordering," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 95-109, March.
    19. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2020. "Arrow on domain conditions: a fruitful road to travel," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 237-258, March.
    20. Chatterji, Shurojit & Zeng, Huaxia, 2023. "A taxonomy of non-dictatorial unidimensional domains," Games and Economic Behavior, Elsevier, vol. 137(C), pages 228-269.

    More about this item

    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:spr:sochwe:v:54:y:2020:i:1:d:10.1007_s00355-019-01216-3. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.