Biased extensive measurement: The general case |
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Authors: | Marc Le Menestrel Bertrand Lemaire |
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Affiliation: | a Universitat Pompeu Fabra, Departament d’Economia i Empresa, Ramon Trias Fargas 25-27, 08005 Barcelona, Spain b UMR 8628 du CNRS, Université de Paris-Sud, Mathématiques (bât. 425), 91405 Orsay cedex, France |
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Abstract: | We develop a theory of biased extensive measurement which allows us to prove the existence of a ratio-scale without transitivity of indifference and with a property of homothetic invariance weaker than independence. These representations, which cover the cases of interval orders and of semiorders, reveal a unique biasing function smaller or equal to 1 that distorts extensive measurement and explains departures from its standard axioms. We interpret this biasing function as characterizing the qualitative influence of the underlying measurement process and we show that it induces a proportional indifference threshold. |
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Keywords: | Semiorder Interval order Intransitive indifference Independence Homotheticity Scale-invariance Weber's law Foundations of measurement Measurement process Measurement error |
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