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

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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.

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References

  • B. Lemaire M. Le Menestrel (2006) Homothetic interval orders Discrete mathematics forthcoming

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  • M. Le Menestrel B. Lemaire (2004) ArticleTitleBiased extensive measurement: The homogeneous case Journal of Mathematical Psychology 48 9–14 Occurrence Handle10.1016/j.jmp.2003.11.001

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  • Le Menestrel, M. and Lemaire B. (2006), Biased extensive measurement: The general case, Journal of Mathematical Psychology, forthcoming.

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Authors and Affiliations

  1. Departament d’Economia i Empresa, Universitat Pompeu Fabra, Ramon Trias Fargas 25–27, 08005, Barcelona, Spain

    Marc Le Menestrel

  2. UMR 8628 du CNRS, Université de Paris-Sud, Mathématiques (bât. 425), 91405, Orsay cedex, France

    Bertrand Lemaire

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  1. Marc Le Menestrel
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  2. Bertrand Lemaire
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Correspondence to Marc Le Menestrel.

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Menestrel, M.L., Lemaire, B. Ratio-Scale Measurement with Intransitivity or Incompleteness: The Homogeneous Case. Theor Decis 60, 207–217 (2006). https://doi.org/10.1007/s11238-005-4592-y

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  • DOI: https://doi.org/10.1007/s11238-005-4592-y

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