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Cardinality versus Ordinality: A Suggested Compromise

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  • Michael Mandler

Abstract

By taking sets of utility functions as primitive, we define an ordering over assumptions on utility functions that gauges their measurement requirements. Cardinal and ordinal assumptions constitute two levels of measurability, but other assumptions lie between these extremes. We apply the ordering to explanations of why preferences should be convex. The assumption that utility is concave qualifies as a compromise between cardinality and ordinality, while the Arrow-Koopmans explanation, supposedly an ordinal theory, relies on utilities in the cardinal measurement class. In social choice theory, a concavity compromise between ordinality and cardinality is also possible and rationalizes the core utilitarian policies. (JEL D01)

Suggested Citation

  • Michael Mandler, 2006. "Cardinality versus Ordinality: A Suggested Compromise," American Economic Review, American Economic Association, vol. 96(4), pages 1114-1136, September.
    • Handle: RePEc:aea:aecrev:v:96:y:2006:i:4:p:1114-1136
    Note: DOI: 10.1257/aer.96.4.1114
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    Citations

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    Cited by:

    1. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
    2. Milan Zafirovski, 2024. "Contradictions of the Marginal Utility Theory of Value? Identifying Some Logical Errors," HISTORY OF ECONOMIC THOUGHT AND POLICY, FrancoAngeli Editore, vol. 2024(1), pages 53-98.
    3. Pivato, Marcus, 2013. "Multiutility representations for incomplete difference preorders," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 196-220.
    4. Paolo Giovanni Piacquadio, 2017. "A Fairness Justification of Utilitarianism," Econometrica, Econometric Society, vol. 85, pages 1261-1276, July.
    5. Pivato, Marcus, 2010. "Aggregation of incomplete ordinal preferences with approximate interpersonal comparisons," MPRA Paper 25271, University Library of Munich, Germany.
    6. Dupoux, Marion & Martinet, Vincent, 2022. "Could the environment be a normal good for you and an inferior good for me? A theory of context-dependent substitutability and needs," Resource and Energy Economics, Elsevier, vol. 69(C).
    7. 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.
    8. Giarlotta, Alfio & Greco, Salvatore, 2013. "Necessary and possible preference structures," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 163-172.
    9. Pivato, Marcus, 2010. "Approximate interpersonal comparisons of well-being," MPRA Paper 25224, University Library of Munich, Germany.
    10. Michael Mandler, 2021. "The lexicographic method in preference theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 553-577, March.
    11. Rojas, Mariano, 2009. "Economía de la felicidad. Hallazgos relevantes respecto al ingreso y el bienestar," El Trimestre Económico, Fondo de Cultura Económica, vol. 0(303), pages 537-573, julio-sep.
    12. Pivato, Marcus, 2009. "Social choice with approximate interpersonal comparisons of well-being," MPRA Paper 17060, University Library of Munich, Germany.
    13. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.

    More about this item

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles

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