IDEAS home Printed from https://ideas.repec.org/a/spr/grdene/v26y2017i4d10.1007_s10726-017-9532-z.html
   My bibliography  Save this article

Preference Diversity Orderings

Author

Listed:
  • Alexander Karpov

    (National Research University Higher School of Economics)

Abstract

Applying new preference diversity axiomatics, a generalization of the Alcalde-Unzu and Vorsatz (Soc Choice Welf 41(4):965–988, 2013) criterion is developed. It is shown that all previously used indices violate this criterion. Two new indices (geometric mean-based and leximax-based) that satisfy a new criterion are developed. Leximax-based orders act as a polarization index and are compared to the polarization index of Can et al. (Math Soc Sci 78:76–79, 2015). New impossibility results are obtained.

Suggested Citation

  • Alexander Karpov, 2017. "Preference Diversity Orderings," Group Decision and Negotiation, Springer, vol. 26(4), pages 753-774, July.
    • Handle: RePEc:spr:grdene:v:26:y:2017:i:4:d:10.1007_s10726-017-9532-z
    DOI: 10.1007/s10726-017-9532-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10726-017-9532-z
    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/s10726-017-9532-z?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Can, Burak & Ozkes, Ali Ihsan & Storcken, Ton, 2015. "Measuring polarization in preferences," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 76-79.
    2. Anand, Paul & Pattanaik, Prasanta & Puppe, Clemens (ed.), 2009. "The Handbook of Rational and Social Choice," OUP Catalogue, Oxford University Press, number 9780199290420.
    3. Tommi Meskanen & Hannu Nurmi, 2008. "Closeness Counts in Social Choice," Springer Books, in: Matthew Braham & Frank Steffen (ed.), Power, Freedom, and Voting, chapter 15, pages 289-306, Springer.
    4. Lepelley, Dominique & Valognes, Fabrice, 2003. "Voting Rules, Manipulability and Social Homogeneity," Public Choice, Springer, vol. 116(1-2), pages 165-184, 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. William V. Gehrlein & Dominique Lepelley, 2011. "Voting paradoxes and group coherence: the condorcet efficiency of voting rules," Post-Print hal-01243452, HAL.
    7. Gehrlein, William V. & Moyouwou, Issofa & Lepelley, Dominique, 2013. "The impact of voters’ preference diversity on the probability of some electoral outcomes," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 352-365.
    8. William V. Gehrlein & Dominique Lepelley, 2011. "Voting Paradoxes and Group Coherence," Studies in Choice and Welfare, Springer, number 978-3-642-03107-6, December.
    9. Chakraborty, Archishman & Citanna, Alessandro & Ostrovsky, Michael, 2010. "Two-sided matching with interdependent values," Journal of Economic Theory, Elsevier, vol. 145(1), pages 85-105, January.
    10. Can, Burak, 2014. "Weighted distances between preferences," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 109-115.
    11. Edith Elkind & Piotr Faliszewski & Arkadii Slinko, 2015. "Distance rationalization of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 345-377, September.
    12. Jorge Alcalde-Unzu & Marc Vorsatz, 2016. "Do we agree? Measuring the cohesiveness of preferences," Theory and Decision, Springer, vol. 80(2), pages 313-339, February.
    13. Jorge Alcalde-Unzu & Marc Vorsatz, 2016. "Do we agree? Measuring the cohesiveness of preferences," Theory and Decision, Springer, vol. 80(2), pages 313-339, February.
    14. Yuliya Veselova, 2016. "The difference between manipulability indices in the IC and IANC models," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(3), pages 609-638, March.
    15. Klaus Nehring & Clemens Puppe, 2002. "A Theory of Diversity," Econometrica, Econometric Society, vol. 70(3), pages 1155-1198, May.
    16. Bubboloni, Daniela & Gori, Michele, 2015. "Symmetric majority rules," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 73-86.
    17. ,, 2009. "Asymptotic ordinal inefficiency of random serial dictatorship," Theoretical Economics, Econometric Society, vol. 4(2), June.
    18. 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.
    19. James Boudreau & Vicki Knoblauch, 2013. "Preferences and the price of stability in matching markets," Theory and Decision, Springer, vol. 74(4), pages 565-589, April.
    20. William V. Gehrlein & Dominique Lepelley, 2015. "Refining measures of group mutual coherence," Post-Print hal-01243405, HAL.
    21. J. C. R. Alcantud & R. Andrés Calle & J. M. Cascón, 2015. "Pairwise Dichotomous Cohesiveness Measures," Group Decision and Negotiation, Springer, vol. 24(5), pages 833-854, September.
    22. Jorge Alcalde-Unzu & Marc Vorsatz, 2013. "Measuring the cohesiveness of preferences: an axiomatic analysis," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 965-988, October.
    23. Onur B. Celik & Vicki Knoblauch, 2007. "Marriage Matching with Correlated Preferences," Working papers 2007-16, University of Connecticut, Department of Economics.
    24. 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)

    Citations

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


    Cited by:

    1. Burak Can & Ali Ihsan Ozkes & Ton Storcken, 2017. "Generalized Measures of Polarization in Preferences," Working Papers halshs-01597720, HAL.
    2. Alexander V. Karpov, 2018. "An Informational Basis for Voting Rules," HSE Working papers WP BRP 188/EC/2018, National Research University Higher School of Economics.
    3. 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.

    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. 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. Huremović, Kenan & Ozkes, Ali I., 2022. "Polarization in networks: Identification–alienation framework," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    3. 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.
    4. Maurice Salles, 2014. "‘Social choice and welfare’ at 30: its role in the development of social choice theory and welfare economics," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 1-16, January.
    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. Diss, Mostapha & Tsvelikhovskiy, Boris, 2021. "Manipulable outcomes within the class of scoring voting rules," Mathematical Social Sciences, Elsevier, vol. 111(C), pages 11-18.
    7. 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.
    8. 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.
    9. Jansen, C. & Schollmeyer, G. & Augustin, T., 2018. "A probabilistic evaluation framework for preference aggregation reflecting group homogeneity," Mathematical Social Sciences, Elsevier, vol. 96(C), pages 49-62.
    10. José Carlos R. Alcantud & María José M. Torrecillas, 2017. "Consensus measures for various informational bases. Three new proposals and two case studies from political science," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(1), pages 285-306, January.
    11. Smeulders, B., 2018. "Testing a mixture model of single-peaked preferences," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 101-113.
    12. Mostapha Diss & Eric Kamwa & Issofa Moyouwou & Hatem Smaoui, 2021. "Condorcet Efficiency of General Weighted Scoring Rules Under IAC: Indifference and Abstention," Studies in Choice and Welfare, in: Mostapha Diss & Vincent Merlin (ed.), Evaluating Voting Systems with Probability Models, pages 55-73, Springer.
    13. Gehrlein, William V. & Moyouwou, Issofa & Lepelley, Dominique, 2013. "The impact of voters’ preference diversity on the probability of some electoral outcomes," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 352-365.
    14. Brandl, Florian & Brandt, Felix, 0. "A natural adaptive process for collective decision-making," Theoretical Economics, Econometric Society.
    15. Eric Kamwa, 2019. "On the Likelihood of the Borda Effect: The Overall Probabilities for General Weighted Scoring Rules and Scoring Runoff Rules," Group Decision and Negotiation, Springer, vol. 28(3), pages 519-541, June.
    16. González-Arteaga, T. & Alcantud, J.C.R. & de Andrés Calle, R., 2016. "A cardinal dissensus measure based on the Mahalanobis distance," European Journal of Operational Research, Elsevier, vol. 251(2), pages 575-585.
    17. Harrison-Trainor, Matthew, 2022. "An analysis of random elections with large numbers of voters," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 68-84.
    18. Tanguiane, Andranick S., 2022. "Analysis of the 2021 Bundestag elections. 4/4. The third vote application," Working Paper Series in Economics 154, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    19. Jimena Galindo & Levent Ülkü, 2020. "Diversity relations over menus," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(2), pages 229-242, August.
    20. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 581-630, February.

    More about this item

    Keywords

    Polarization; Cohesiveness; Leximax; Borda;
    All these keywords.

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

    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:grdene:v:26:y:2017:i:4:d:10.1007_s10726-017-9532-z. 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.