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Roberts' Weak Welfarism Theorem: A Minor Correction

Peter Hammond ()

The Warwick Economics Research Paper Series (TWERPS) from University of Warwick, Department of Economics

Abstract: 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 (1980) claimed that the induced welfare ordering on social states has a one-way representation by a continuous, monotonic real-valued welfare function defined on the Euclidean space of interpersonal utility vectors that is, an increase in this welfare function is sufficient, but may not be necessary, for social strict preference. A counter-example shows that weak continuity is insufficient; a minor strengthening to pairwise continuity is proposed instead and its sufficiency demonstrated.

Keywords: social welfare functionals; weak welfarism JEL codes: D71 (search for similar items in EconPapers)
Date: 2020
New Economics Papers: this item is included in nep-hpe and nep-mic
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Working Paper: Roberts' Weak Welfarism Theorem: A Minor Correction (2020) Downloads
Working Paper: Roberts' Weak Welfarism Theorem: A Minor Correction (1999) Downloads
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Persistent link: https://EconPapers.repec.org/RePEc:wrk:warwec:1308

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