Fair Interpersonal Comparisons : Characterizing Contour-Set Volume Measures of Well-Being

How can welfare be compared across individuals with heterogeneous preferences without imposing arbitrary interpersonal utility normalizations? Building on the resource-based approach to fairness and well-being measurement, the paper takes the indifference contour attained at the consumed bundle as the relevant information for comparison. The main question of the paper is then whether such contour-based wellbeing measures can be neutral with respect to commodity identities, as formalized by two invariance axioms: Symmetry and Rescaling Invariance. It is shown that these invariance requirements are incompatible with Pareto on unrestricted domains of continuous, convex, and monotone preferences. The positive analysis considers domains with common restrictions on the geometry of admissible preferences. On these domains, and conditional on a separability axiom of contour information, the invariance axioms characterize a family of volume-type well-being measures. These measures evaluate a situation by the weighted volume of the relevant lower or upper contour set, with a single exponent governing the weighting. They can therefore be interpreted as a continuous generalization of Borda-count ranking methods: they count the alternatives dominated by the individual's actual bundle or the alternatives that dominate it, with the latter counting against well-being. For CES preferences with a common elasticity of substitution different from one, the representation yields a geometrically normalized utility index.