Roberts' Weak Welfarism Theorem: A Minor Correction
Peter J. Hammond
September 1999 Roberts' "weak neutrality" or "weak welfarism" theorem concerns Sen social welfare functionals which are defined on an unrestricted domain of utility function profiles and satisfy independence of irrelevant alternatives, the Pareto condition, and a form of weak continuity. Roberts claimed that the induced welfare ordering on social states has a one-way representation by a continuous, monotonic real-valued function defined on the Euclidean space of interpersonal utility vectors. A counter-example shows that weak continuity is insufficient; a minor strengthening to pairwise continuity is proposed instead and its sufficiency demonstrated. Journal of Economic Literature classification: D71 Keywords: social welfare functionals, weak welfarism.
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