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Extreme Copulas and the Comparison of Ordered Lists

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  • B. Schuymer
  • H. Meyer
  • B. baets

Abstract

We introduce two extreme methods to pairwisely compare ordered lists of the same length, viz. the comonotonic and the countermonotonic comparison method, and show that these methods are, respectively, related to the copula T M (the minimum operator) and the Å\x81 ukasiewicz copula T L used to join marginal cumulative distribution functions into bivariate cumulative distribution functions. Given a collection of ordered lists of the same length, we generate by means of T M and T L two probabilistic relations Q M and Q L and identify their type of transitivity. Finally, it is shown that any probabilistic relation with rational elements on a 3-dimensional space of alternatives which possesses one of these types of transitivity, can be generated by three ordered lists and at least one of the two extreme comparison methods. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • B. Schuymer & H. Meyer & B. baets, 2007. "Extreme Copulas and the Comparison of Ordered Lists," Theory and Decision, Springer, vol. 62(3), pages 195-217, May.
    • Handle: RePEc:kap:theord:v:62:y:2007:i:3:p:195-217
    DOI: 10.1007/s11238-006-9012-4
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    References listed on IDEAS

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    1. B. Baets & H. Meyer & B. Schuymer, 2006. "Cyclic Evaluation of Transitivity of Reciprocal Relations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 217-238, April.
    2. B. De Schuymer & H. De Meyer & B. De Baets & S. Jenei, 2003. "On the Cycle-Transitivity of the Dice Model," Theory and Decision, Springer, vol. 54(3), pages 261-285, May.
    3. De Schuymer, B. & De Meyer, H. & De Baets, B., 2005. "Cycle-transitive comparison of independent random variables," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 352-373, October.
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