Preference intensity representation and revelation
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This paper introduces preference intensity functions -an extension of (neo)classical cardinal utility functions- and characterizes by means of three simple standard axioms the class of basic preference intensity orderings over a finite set of general alternatives that can be represented numerically by such a function in an essentially ordinal way. Unlike utility-difference representations on finite sets, the one proposed here imposes neither behaviourally uninterpretable nor precision-demanding axioms on the preference intensity relation, while its novel uniqueness properties are pinned down in a simple way. The observable implications of this model are then analyzed. Considering general datasets that comprise (i) menus of feasible alternatives, (ii) the alternatives chosen at these menus, and (iii) the amounts of a measurable resource (e.g. money, time) that the individual has foregone in order to make these choices, it is first shown that two new testable consistency requirements on such datasets are necessary and sufficient for the latter to be preference-intensity rationalizable. In addition to encompassing standard rationalizability, this notion disciplines the directions that the observed differences in foregone resources can take, and at the same time allows for the decision maker's resource allocation on the same alternative to potentially vary with the menu where it was chosen. The novel concept of cardinal-utility rationalizability emerges as the special case where such resource allocation is menu-invariant.
Gerasimou , G 2018 ' Preference intensity representation and revelation ' School of Economics and Finance Discussion Paper , no. 1716 , University of St Andrews , St Andrews .
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