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An Alternative Proof for the Linear Utility Representation Theorem

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  • Trockel, Walter

Abstract

The paper presents an alternative short proof for the linear utility representation theorem. In particular a generalization of the theorem of Blackwell and Girshick (l954) and a special case of the theorem of Herstein and Milnor(1953) are proved by exploiting the topological group structure of finite-dimensional Euclidean vector space.

Suggested Citation

  • Trockel, Walter, 1992. "An Alternative Proof for the Linear Utility Representation Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 298-302, April.
    • Handle: RePEc:spr:joecth:v:2:y:1992:i:2:p:298-302
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    Cited by:

    1. René Van Den Brink & Agnieszka Rusinowska, 2023. "Degree Centrality, von Neumann-Morgenstern Expected Utility and Externalities in Networks," Documents de travail du Centre d'Economie de la Sorbonne 23012, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Mishra, Debasis & Sen, Arunava, 2012. "Robertsʼ Theorem with neutrality: A social welfare ordering approach," Games and Economic Behavior, Elsevier, vol. 75(1), pages 283-298.
    3. van den Brink, René & Rusinowska, Agnieszka, 2022. "The degree measure as utility function over positions in graphs and digraphs," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1033-1044.
    4. René van den Brink & Agnieszka Rusinowska, 2017. "The degree measure as utility function over positions in networks," Documents de travail du Centre d'Economie de la Sorbonne 17035, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Herden, Gerhard & Pallack, Andreas, 2002. "Consistency in ordinal data analysis I," Mathematical Social Sciences, Elsevier, vol. 43(1), pages 79-113, January.
    6. Candeal, Juan Carlos & Induráin, Esteban & Molina, José Alberto, 2007. "Interpersonal Comparisons of Utility: An Algebraic Characterization of Projective Preorders and Some Welfare Consequences," IZA Discussion Papers 2594, Institute of Labor Economics (IZA).
    7. José Faro, 2013. "Cobb-Douglas preferences under uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 273-285, October.
    8. Tapan Mitra & Kemal Ozbek, 2021. "Ranking by weighted sum," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 511-532, September.
    9. René Van Den Brink & Agnieszka Rusinowska, 2023. "Degree Centrality, von Neumann-Morgenstern Expected Utility and Externalities in Networks," Documents de travail du Centre d'Economie de la Sorbonne 23012r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jun 2024.

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