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Preference, topology and measure

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  • Vicki Knoblauch

Abstract

A symmetric difference metric topology on the collection of binary relations on a countably infinite set provides a new setting for the study of properties of preferences and, as an illustration, is used to lend credence and meaning to some simple intuitions about properties of binary relations. A finite measure on a $$\sigma $$ σ -algebra over the same collection of binary relations is used to provide support for the topological results. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:43:y:2014:i:2:p:507-514
    DOI: 10.1007/s00355-013-0788-1
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    References listed on IDEAS

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    1. 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.
    2. Nick Baigent & Christian Klamler, 2003. "Transitive closure, proximity and intransitivities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(1), pages 175-181, December.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Ram Sewak Dubey & Giorgio Laguzzi, 2022. "How rare are the properties of binary relations?," Papers 2202.05229, arXiv.org.
    2. Knoblauch, Vicki, 2023. "Lexicographic preference representation: Intrinsic length of linear orders on infinite sets," Journal of Mathematical Economics, Elsevier, vol. 105(C).
    3. 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.

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    More about this item

    Keywords

    Binary relation; Symmetric difference metric space ; Measure space; D11; C65;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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