IDEAS home Printed from https://ideas.repec.org/a/spr/grdene/v28y2019i3d10.1007_s10726-019-09621-w.html
   My bibliography  Save this article

On the Number of Group-Separable Preference Profiles

Author

Listed:
  • Alexander Karpov

    (National Research University Higher School of Economics
    Russian Academy of Science)

Abstract

The paper studies group-separable preference profiles. Such a profile is group-separable if for each subset of alternatives there is a partition in two parts such that each voter prefers each alternative in one part to each alternative in the other part. We develop a parenthesization representation of group-separable domain. The precise formula for the number of group-separable preference profiles is obtained. The recursive formula for the number of narcissistic group-separable preference profiles is obtained. Such a profile is narcissistic group-separable if it is group-separable and each alternative is preferred the most by exactly one voter.

Suggested Citation

  • Alexander Karpov, 2019. "On the Number of Group-Separable Preference Profiles," Group Decision and Negotiation, Springer, vol. 28(3), pages 501-517, June.
    • Handle: RePEc:spr:grdene:v:28:y:2019:i:3:d:10.1007_s10726-019-09621-w
    DOI: 10.1007/s10726-019-09621-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10726-019-09621-w
    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/s10726-019-09621-w?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. 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.
    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. Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), 2009. "The Mathematics of Preference, Choice and Order," Studies in Choice and Welfare, Springer, number 978-3-540-79128-7, June.
    4. Inada, Ken-Ichi, 1969. "The Simple Majority Decision Rule," Econometrica, Econometric Society, vol. 37(3), pages 490-506, July.
    5. 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.
    6. Adrian Deemen, 2014. "On the empirical relevance of Condorcet’s paradox," Public Choice, Springer, vol. 158(3), pages 311-330, March.
    7. 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.
    8. Campbell, Donald E. & Kelly, Jerry S., 2002. "Impossibility theorems in the arrovian framework," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 1, pages 35-94, Elsevier.
    9. 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.
    10. Gehrlein, William V. & Fishburn, Peter C., 1976. "The probability of the paradox of voting: A computable solution," Journal of Economic Theory, Elsevier, vol. 13(1), pages 14-25, August.
    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. Alexander Karpov, 2020. "The likelihood of single-peaked preferences under classic and new probability distribution assumptions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(4), pages 629-644, December.
    2. Niclas Boehmer & Piotr Faliszewski & Rolf Niedermeier & Stanis{l}aw Szufa & Tomasz Wk{a}s, 2022. "Understanding Distance Measures Among Elections," Papers 2205.00492, arXiv.org.

    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. Puppe, Clemens, 2018. "The single-peaked domain revisited: A simple global characterization," Journal of Economic Theory, Elsevier, vol. 176(C), pages 55-80.
    2. Slinko, Arkadii, 2019. "Condorcet domains satisfying Arrow’s single-peakedness," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 166-175.
    3. Smeulders, B., 2018. "Testing a mixture model of single-peaked preferences," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 101-113.
    4. Alexander Karpov, 2020. "The likelihood of single-peaked preferences under classic and new probability distribution assumptions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(4), pages 629-644, December.
    5. 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.
    6. Li, Guanhao & Puppe, Clemens & Slinko, Arkadii, 2021. "Towards a classification of maximal peak-pit Condorcet domains," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 191-202.
    7. 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.
    8. Ping Zhan, 2019. "A simple construction of complete single-peaked domains by recursive tiling," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(3), pages 477-488, December.
    9. Li, Guanhao & Puppe, Clemens & Slinko, Arkadii, 2020. "Towards a classification of maximal peak-pit Condorcet domains," Working Paper Series in Economics 144, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    10. Wesley H. Holliday & Eric Pacuit, 2021. "Axioms for defeat in democratic elections," Journal of Theoretical Politics, , vol. 33(4), pages 475-524, October.
    11. Puppe, Clemens & Slinko, Arkadii, 2024. "Maximal Condorcet domains. A further progress report," Games and Economic Behavior, Elsevier, vol. 145(C), pages 426-450.
    12. Li, Guanhao, 2023. "A classification of peak-pit maximal Condorcet domains," Mathematical Social Sciences, Elsevier, vol. 125(C), pages 42-57.
    13. 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.
    14. 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.
    15. Arlegi, Ricardo & Teschl, Miriam, 2022. "Pareto rationalizability by two single-peaked preferences," Mathematical Social Sciences, Elsevier, vol. 118(C), pages 1-11.
    16. Bossert, Walter & Peters, Hans, 2014. "Single-basined choice," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 162-168.
    17. Eric Kamwa, 2023. "On two voting systems that combine approval and preferences: fallback voting and preference approval voting," Public Choice, Springer, vol. 196(1), pages 169-205, July.
    18. Kurrild-Klitgaard, Peter, 2018. "Trump, Condorcet and Borda: Voting paradoxes in the 2016 Republican presidential primaries," European Journal of Political Economy, Elsevier, vol. 55(C), pages 29-35.
    19. Harrison-Trainor, Matthew, 2022. "An analysis of random elections with large numbers of voters," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 68-84.
    20. Alexander Karpov, 2017. "Preference Diversity Orderings," Group Decision and Negotiation, Springer, vol. 26(4), pages 753-774, July.

    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:grdene:v:28:y:2019:i:3:d:10.1007_s10726-019-09621-w. 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.