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A simple voting scheme generates all binary relations on finite sets

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  • Knoblauch, Vicki

Abstract

A simple head-to-head voting scheme in which voters hold complete and transitive preferences over alternatives generates all binary relations on finite sets. The minimal number of voters required to generate a binary relation provides a measure of complexity for binary relations. Complexity so defined tells us, by how much a given binary relation fails to qualify as a total preorder.

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  • Knoblauch, Vicki, 2013. "A simple voting scheme generates all binary relations on finite sets," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 230-233.
    • Handle: RePEc:eee:mateco:v:49:y:2013:i:3:p:230-233
    DOI: 10.1016/j.jmateco.2013.01.002
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    References listed on IDEAS

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    1. Duggan, John, 1999. "A General Extension Theorem for Binary Relations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 1-16, May.
    2. Amartya Sen, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 381-393.
    3. Rubinstein, Ariel, 1996. "Why Are Certain Properties of Binary Relations Relatively More Common in Natural Language?," Econometrica, Econometric Society, vol. 64(2), pages 343-355, March.
    4. Peleg, Bezalel, 1970. "Utility Functions for Partially Ordered Topological Spaces," Econometrica, Econometric Society, vol. 38(1), pages 93-96, January.
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    Cited by:

    1. Knoblauch, Vicki, 2016. "Elections generate all binary relations on infinite sets," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 105-108.
    2. Shaofang Qi, 2016. "A characterization of the n-agent Pareto dominance relation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(3), pages 695-706, March.
    3. Knoblauch, Vicki, 2015. "Probabilistic evaluations: A universal representation for preferences over countable sets," Journal of Mathematical Economics, Elsevier, vol. 57(C), pages 25-27.

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    Keywords

    Binary relations; Elections;

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