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Measuring the cohesiveness of preferences: an axiomatic analysis

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  • Jorge Alcalde-Unzu

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  • Marc Vorsatz

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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
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    References listed on IDEAS

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    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.
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    5. Kranich, Laurence, 1996. "Equitable Opportunities: An Axiomatic Approach," Journal of Economic Theory, Elsevier, vol. 71(1), pages 131-147, October.
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    8. repec:hrv:faseco:33927874 is not listed on IDEAS
    9. Federico Echenique & Roland G. Fryer, 2007. "A Measure of Segregation Based on Social Interactions," The Quarterly Journal of Economics, Oxford University Press, vol. 122(2), pages 441-485.
    10. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
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    Citations

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    Cited by:

    1. Matthew Gentzkow & Jesse Shapiro & Matt Taddy, 2016. "Measuring Polarization in High-Dimensional Data: Method and Application to Congressional Speech," Working Papers id:11114, eSocialSciences.
    2. 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.
    3. 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.
    4. Alexander Karpov, 2017. "Preference Diversity Orderings," Group Decision and Negotiation, Springer, vol. 26(4), pages 753-774, July.
    5. 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.
    6. Can, Burak, 2014. "Weighted distances between preferences," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 109-115.
    7. 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.
    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. repec:spr:grdene:v:24:y:2015:i:5:d:10.1007_s10726-014-9415-5 is not listed on IDEAS
    10. Can, Burak & Ozkes, Ali Ihsan & Storcken, Ton, 2015. "Measuring polarization in preferences," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 76-79.

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