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Representation of strongly independent preorders by sets of scalar-valued functions

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  • McCarthy, David
  • Mikkola, Kalle
  • Thomas, Teruji

Abstract

We provide conditions under which an incomplete strongly independent preorder on a convex set X can be represented by a set of mixture preserving real-valued functions. We allow X to be infinite dimensional. The main continuity condition we focus on is mixture continuity. This is sufficient for such a representation provided X has countable dimension or satisfies a condition that we call Polarization.

Suggested Citation

  • McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2017. "Representation of strongly independent preorders by sets of scalar-valued functions," MPRA Paper 79284, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:79284
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    File URL: https://mpra.ub.uni-muenchen.de/79284/1/MPRA_paper_79284.pdf
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    References listed on IDEAS

    as
    1. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2016. "Utilitarianism with and without expected utility," MPRA Paper 72578, University Library of Munich, Germany.
    2. Karni, Edi, 2011. "Continuity, completeness and the definition of weak preferences," Mathematical Social Sciences, Elsevier, vol. 62(2), pages 123-125, September.
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    6. David, McCarthy & Kalle, Mikkola, 2017. "Continuity and completeness of strongly independent preorders," MPRA Paper 79755, University Library of Munich, Germany.
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    15. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2017. "Representation of strongly independent preorders by vector-valued functions," MPRA Paper 80806, University Library of Munich, Germany.
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    1. repec:eee:matsoc:v:93:y:2018:i:c:p:141-145 is not listed on IDEAS
    2. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2017. "Aggregation for general populations without continuity or completeness," MPRA Paper 80820, University Library of Munich, Germany.
    3. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2017. "Representation of strongly independent preorders by vector-valued functions," MPRA Paper 80806, University Library of Munich, Germany.

    More about this item

    Keywords

    Expected utility Multi-representation Incompleteness Mixture continuity;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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