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Classifying interdependence in multidimensional binary preferences


  • Hodge, Jonathan K.
  • TerHaar, Micah


When individual preferences over multiple dimensions are interdependent, the resulting collective decisions can be unsatisfactory and even paradoxical. The notion of separability formalizes this idea of interdependence, and preferences that are completely free from interdependence are said to be separable. In this paper, we develop a mechanism for classifying preferences according to the extent to which they achieve or fail to achieve the desirable property of separability. We show that binary preferences over multiple dimensions are surprisingly complex, in that their interdependence structures defy the most natural attempts at characterization. We also extend previous results pertaining to the rarity of separable preferences by showing that the probability of complete nonseparability approaches 1 as the number of dimensions increases without bound.

Suggested Citation

  • Hodge, Jonathan K. & TerHaar, Micah, 2008. "Classifying interdependence in multidimensional binary preferences," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 190-204, March.
  • Handle: RePEc:eee:matsoc:v:55:y:2008:i:2:p:190-204

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    References listed on IDEAS

    1. W. M. Gorman, 1968. "The Structure of Utility Functions," Review of Economic Studies, Oxford University Press, vol. 35(4), pages 367-390.
    2. Bradley, W. James & Hodge, Jonathan K. & Kilgour, D. Marc, 2005. "Separable discrete preferences," Mathematical Social Sciences, Elsevier, vol. 49(3), pages 335-353, May.
    3. F. P. Murphy, 1981. "A Note on Weak Separability," Review of Economic Studies, Oxford University Press, vol. 48(4), pages 671-672.
    4. Jonathan Hodge & Peter Schwallier, 2006. "How Does Separability Affect The Desirability Of Referendum Election Outcomes?," Theory and Decision, Springer, vol. 61(3), pages 251-276, November.
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    Cited by:

    1. Clark Bowman & Jonathan Hodge & Ada Yu, 2014. "The potential of iterative voting to solve the separability problem in referendum elections," Theory and Decision, Springer, vol. 77(1), pages 111-124, June.
    2. Lang, Jrme & Xia, Lirong, 2009. "Sequential composition of voting rules in multi-issue domains," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 304-324, May.

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