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Ratio-Scale Measurement with Intransitivity or Incompleteness: The Homogeneous Case

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  • Marc Menestrel
  • Bertrand Lemaire

Abstract

In the homogeneous case of one-dimensional objects, we show that any relation that is positive and homothetic can be represented by a ratio-scale and a unique and constant biasing factor. This factor may favor or disfavor the preference for an object over another. In the first case, preferences are complete but not transitive and an object may be preferred even when its value is lower. In the second case, preferences are asymmetric and transitive but not negatively transitive and it may not be sufficient for an object to have a greater value to be preferred. In this manner, the biasing factor reflects the extent to which preferences may depart from a maximization process. Copyright Springer 2006

Suggested Citation

  • Marc Menestrel & Bertrand Lemaire, 2006. "Ratio-Scale Measurement with Intransitivity or Incompleteness: The Homogeneous Case," Theory and Decision, Springer, vol. 60(2), pages 207-217, May.
    • Handle: RePEc:kap:theord:v:60:y:2006:i:2:p:207-217
    DOI: 10.1007/s11238-005-4592-y
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    References listed on IDEAS

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    1. Bertrand Lemaire & Marc Le Menestrel, 2004. "Homothetic interval orders," Economics Working Papers 793, Department of Economics and Business, Universitat Pompeu Fabra.
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    Cited by:

    1. Marc Le Menestrel, 2007. "The biased balance: Observation, formalism and interpretation of a dissymmetric measuring device," Economics Working Papers 1006, Department of Economics and Business, Universitat Pompeu Fabra.
    2. Sacha Bourgeois-Gironde & Raphaël Giraud, 2009. "Framing effects as violations of extensionality," Theory and Decision, Springer, vol. 67(4), pages 385-404, October.
    3. Marc Le Menestrel & Luk N. Wassenhove, 2016. "Subjectively biased objective functions," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 4(1), pages 73-83, June.

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