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Multiutility representations for incomplete difference preorders

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  • Pivato, Marcus

Abstract

A ``difference preorder'' is a (possibly incomplete) preorder on a space of state changes (rather than the states themselves); it encodes information about preference intensity, in addition to ordinal preferences. We find necessary and sufficient conditions for a difference preorder to be representable by a family of cardinal utility functions which take values in linearly ordered abelian groups. This has applications to interpersonal comparisons, social welfare, and decisions under uncertainty.

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  • Pivato, Marcus, 2012. "Multiutility representations for incomplete difference preorders," MPRA Paper 41182, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:41182
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    Cited by:

    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. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2021. "Expected utility theory on mixture spaces without the completeness axiom," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    3. Marcus Pivato, 2015. "Social choice with approximate interpersonal comparison of welfare gains," Theory and Decision, Springer, vol. 79(2), pages 181-216, September.
    4. Marcus Pivato, 2020. "Subjective expected utility with a spectral state space," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 249-313, March.
    5. Bosi, Gianni & Herden, Gerhard, 2014. "Topological spaces for which every closed and semi-closed preorder respectively admits a continuous multi-utility representation," MPRA Paper 53404, University Library of Munich, Germany.

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    More about this item

    Keywords

    Preference intensity; cardinal utility; linearly ordered abelian group; social welfare; uncertainty;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D60 - Microeconomics - - Welfare Economics - - - General

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