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Measuring the cohesiveness of preferences: an axiomatic analysis

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  • 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

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  • 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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    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. 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.
    5. Alexander Karpov, 2017. "Preference Diversity Orderings," Group Decision and Negotiation, Springer, vol. 26(4), pages 753-774, July.
    6. Can, Burak, 2014. "Weighted distances between preferences," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 109-115.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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).
    12. 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.
    13. 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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