IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v41y2013i4p965-988.html
   My bibliography  Save this article

Measuring the cohesiveness of preferences: an axiomatic analysis

Author

Listed:
  • Jorge Alcalde-Unzu
  • Marc Vorsatz

Abstract

In this paper, we axiomatically study how to measure the similarity of preferences in a group of individuals. For simplicity, we refer to this as the cohesiveness. First, we provide axioms that characterize a family of linear and additive measures whose intersection is a partial ordinal criterion similar to first order stochastic dominance. The introduction of some additional properties isolates a one-parameter subfamily. This parameter evaluates the effect on the cohesiveness if one individual changes his ranking on a single pair of objects, as a function of how many of the remaining individuals in the group rank the first object over the second and vice versa. Finally, we characterize the focal measures of this subfamily separately showing that they coincide with measures constructed using two, at first sight, totally different approaches suggested in the literature. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:41:y:2013:i:4:p:965-988
    DOI: 10.1007/s00355-012-0716-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00355-012-0716-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00355-012-0716-9?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. Robert Hutchens, 2004. "One Measure of Segregation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(2), pages 555-578, May.
    2. Blackorby,Charles & Bossert,Walter & Donaldson,David J., 2005. "Population Issues in Social Choice Theory, Welfare Economics, and Ethics," Cambridge Books, Cambridge University Press, number 9780521532587.
    3. Esteban, Joan & Ray, Debraj, 1994. "On the Measurement of Polarization," Econometrica, Econometric Society, vol. 62(4), pages 819-851, July.
    4. Daniel Eckert & Christian Klamler & Johann Mitlöhner & Christian Schlötterer, 2006. "A distance-based comparison of basic voting rules," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 14(4), pages 377-386, December.
    5. Kranich, Laurence, 1996. "Equitable Opportunities: An Axiomatic Approach," Journal of Economic Theory, Elsevier, vol. 71(1), pages 131-147, October.
    6. Wade D. Cook & Lawrence M. Seiford, 1982. "On the Borda-Kendall Consensus Method for Priority Ranking Problems," Management Science, INFORMS, vol. 28(6), pages 621-637, June.
    7. Wade D. Cook & Lawrence M. Seiford, 1978. "Priority Ranking and Consensus Formation," Management Science, INFORMS, vol. 24(16), pages 1721-1732, December.
    8. Baldiga, Katherine A. & Green, Jerry R., 2011. "Assent-maximizing social choice," Scholarly Articles 33927874, Harvard University Department of Economics.
    9. 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.
    10. Federico Echenique & Roland G. Fryer, 2007. "A Measure of Segregation Based on Social Interactions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(2), pages 441-485.
    11. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    12. Christian Klamler, 2008. "A distance measure for choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 419-425, April.
    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. 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.
    2. Matthew Gentzkow & Jesse M. Shapiro & Matt Taddy, 2019. "Measuring Group Differences in High‐Dimensional Choices: Method and Application to Congressional Speech," Econometrica, Econometric Society, vol. 87(4), pages 1307-1340, July.
    3. Mushtaq Abdal Rahem & Marjorie Darrah, 2018. "Using a Computational Approach for Generalizing a Consensus Measure to Likert Scales of Any Size," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2018, pages 1-7, July.
    4. Can, Burak, 2014. "Weighted distances between preferences," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 109-115.
    5. 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.
    6. 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.
    7. Salvatore Barbaro, 2021. "A social-choice perspective on authoritarianism and political polarization," Working Papers 2108, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    8. Peeters, R.J.A.P. & Wolk, K.L., 2015. "Forecasting with Colonel Blotto," Research Memorandum 025, Maastricht University, Graduate School of Business and Economics (GSBE).
    9. Rodríguez Alcantud, José Carlos & de Andrés Calle, Rocío & González-Arteaga, Teresa, 2013. "Codifications of complete preorders that are compatible with Mahalanobis disconsensus measures," MPRA Paper 50533, University Library of Munich, Germany.
    10. 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.
    11. Can, Burak & Ozkes, Ali Ihsan & Storcken, Ton, 2015. "Measuring polarization in preferences," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 76-79.
    12. Alexander Karpov, 2017. "Preference Diversity Orderings," Group Decision and Negotiation, Springer, vol. 26(4), pages 753-774, July.
    13. 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.

    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. Jorge Alcalde-Unzu & Marc Vorsatz, 2008. "The Measurement of Consensus: An Axiomatic Analysis," Working Papers 2008-28, FEDEA.
    2. Yoonseok Lee & Donggyun Shin, 2016. "Measuring Social Tension from Income Class Segregation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 457-471, July.
    3. J.C.R. Alcantud & R. de Andrés Calle & J.M. Cascón, 2013. "Consensus and the Act of Voting," Studies in Microeconomics, , vol. 1(1), pages 1-22, June.
    4. Tugce, Cuhadaroglu, 2013. "My Group Beats Your Group: Evaluating Non-Income Inequalities," SIRE Discussion Papers 2013-49, Scottish Institute for Research in Economics (SIRE).
    5. Hodler, Roland & Valsecchi, Michele & Vesperoni, Alberto, 2021. "Ethnic geography: Measurement and evidence," Journal of Public Economics, Elsevier, vol. 200(C).
    6. 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.
    7. I. Contreras, 2012. "Ordered Weighted Disagreement Functions," Group Decision and Negotiation, Springer, vol. 21(3), pages 345-361, May.
    8. Tugce Cuhadaroglu, 2013. "My Group Beats Your Group: Evaluating Non-Income Inequalities," Discussion Paper Series, School of Economics and Finance 201308, School of Economics and Finance, University of St Andrews.
    9. Asheim, Geir B. & Bossert, Walter & D'Ambrosio, Conchita & Vögele, Claus, 2020. "The measurement of resilience," Journal of Economic Theory, Elsevier, vol. 189(C).
    10. Ignacio Contreras, 2010. "A Distance-Based Consensus Model with Flexible Choice of Rank-Position Weights," Group Decision and Negotiation, Springer, vol. 19(5), pages 441-456, September.
    11. Oscar Volij, 2018. "Segregation: theoretical approaches," Chapters, in: Conchita D’Ambrosio (ed.), Handbook of Research on Economic and Social Well-Being, chapter 21, pages 480-503, Edward Elgar Publishing.
    12. Ferreira, Francisco H. G. & Peragine, Vito, 2015. "Equality of Opportunity: Theory and Evidence," IZA Discussion Papers 8994, Institute of Labor Economics (IZA).
    13. Jo Thori Lind & Karl Moene, 2011. "Miserly Developments," Journal of Development Studies, Taylor & Francis Journals, vol. 47(9), pages 1332-1352, June.
    14. Antonio Abatemarco & Massimo Aria & Sergio Beraldo & Michela Collaro, 2023. "Measuring Access and Inequality of Access to Health Care: a Policy-Oriented Decomposition," CSEF Working Papers 666, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    15. Chakravarty, Satya R. & Sarkar, Palash, 2022. "A synthesis of local and effective tax progressivity measurement," MPRA Paper 115180, University Library of Munich, Germany.
    16. Sanghamitra Bandyopadhyay, 2003. "Convergence Club Empirics: Some Dynamics and Explanations of Unequal Growth across Indian States," WIDER Working Paper Series DP2003-77, World Institute for Development Economic Research (UNU-WIDER).
    17. Frankel, David M. & Volij, Oscar, 2011. "Measuring school segregation," Journal of Economic Theory, Elsevier, vol. 146(1), pages 1-38, January.
    18. Clark, Andrew E. & D'Ambrosio, Conchita, 2014. "Attitudes to Income Inequality: Experimental and Survey Evidence," IZA Discussion Papers 8136, Institute of Labor Economics (IZA).
    19. Cascón, J.M. & González-Arteaga, T. & de Andrés Calle, R., 2019. "Reaching social consensus family budgets: The Spanish case," Omega, Elsevier, vol. 86(C), pages 28-41.
    20. Cockburn, John & Duclos, Jean-Yves & Zabsonré, Agnès, 2014. "Is global social welfare increasing? A critical-level enquiry," Journal of Public Economics, Elsevier, vol. 118(C), pages 151-162.

    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:41:y:2013:i:4:p:965-988. 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.