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Two preference metrics provide settings for the study of properties of binary relations

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  • Vicki Knoblauch

Abstract

The topological structures imposed on the collection of binary relations on a given set by the symmetric difference metric and the Hausdorff metric provide opportunities for learning about how collections of binary relations with various properties fit into the collection of all binary relations. For example, there is some agreement and some disagreement between conclusions drawn about the rarity of certain properties of binary relations using first the symmetric difference metric and then the Hausdorff metric. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Vicki Knoblauch, 2015. "Two preference metrics provide settings for the study of properties of binary relations," Theory and Decision, Springer, vol. 79(4), pages 615-625, December.
    • Handle: RePEc:kap:theord:v:79:y:2015:i:4:p:615-625
    DOI: 10.1007/s11238-015-9487-y
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    References listed on IDEAS

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    1. Vicki Knoblauch, 2014. "Preference, topology and measure," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 507-514, August.
    2. Balasko, Yves & Cres, Herve, 1997. "The Probability of Condorcet Cycles and Super Majority Rules," Journal of Economic Theory, Elsevier, vol. 75(2), pages 237-270, August.
    3. Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
    4. Paras Mehta, 1997. "Topological methods in social choice: an overview," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 233-243.
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    Cited by:

    1. Knoblauch, Vicki, 2023. "Lexicographic preference representation: Intrinsic length of linear orders on infinite sets," Journal of Mathematical Economics, Elsevier, vol. 105(C).

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