Theory and Decision

, Volume 60, Issue 2–3, pp 207–217 | Cite as

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

  • Marc Le MenestrelEmail author
  • Bertrand Lemaire


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.


intransitive preferences incomplete preferences irrational behavior emotional behavior procedural concerns ethical values biased measurement scale-invariance homotheticity 


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  1. Lemaire, B., Le Menestrel, M. 2006Homothetic interval ordersDiscrete mathematicsforthcomingGoogle Scholar
  2. Le Menestrel, M., Lemaire, B. 2004Biased extensive measurement: The homogeneous caseJournal of Mathematical Psychology48914CrossRefGoogle Scholar
  3. Le Menestrel, M. and Lemaire B. (2006), Biased extensive measurement: The general case, Journal of Mathematical Psychology, forthcoming.Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Departament d’Economia i EmpresaUniversitat Pompeu FabraBarcelonaSpain
  2. 2.UMR 8628 du CNRSUniversité de Paris-SudOrsay cedexFrance

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