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Elections generate all binary relations on infinite sets

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  • Knoblauch, Vicki

Abstract

Every binary relation on an infinite set can be represented by an election in which each voter’s preferences are quasi-transitive and complete (except possibly not reflexive) and in which the electorate has smaller cardinality than or the same cardinality as the set of alternatives, depending on the cardinality of that set.

Suggested Citation

  • Knoblauch, Vicki, 2016. "Elections generate all binary relations on infinite sets," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 105-108.
    • Handle: RePEc:eee:matsoc:v:84:y:2016:i:c:p:105-108
    DOI: 10.1016/j.mathsocsci.2016.10.002
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    References listed on IDEAS

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    1. Bosi, Gianni & Herden, Gerhard, 2016. "On continuous multi-utility representations of semi-closed and closed preorders," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 20-29.
    2. Beardon, Alan F. & Candeal, Juan C. & Herden, Gerhard & Indurain, Esteban & Mehta, Ghanshyam B., 2002. "The non-existence of a utility function and the structure of non-representable preference relations," Journal of Mathematical Economics, Elsevier, vol. 37(1), pages 17-38, February.
    3. 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.
    4. Mark Fey, 2004. "May’s Theorem with an infinite population," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(2), pages 275-293, October.
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    Cited by:

    1. Vicki Knoblauch, 2020. "Von Neumann–Morgenstern stable set rationalization of choice functions," Theory and Decision, Springer, vol. 89(3), pages 369-381, October.

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