This paper constructs continuous Paretian social welfare functions for which one agent is a homotopic dictator but another is, in a precise sense, almost all powerful. The significance of this arises from the widely differing views1 that have been expressed about a theorem in Chichilnisky (1982) showing that, for all continuous Paretian social welfare functions there must be a homotopic dictator. What the analysis in this paper therefore shows is that Chichilnisky’s theorem is not a genuine Arrow-type impossibility theorem in the sense that desirable properties are not shown to entail some undesirable concentration of power.
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Baigent, N. (2008). Harmless Homotopic Dictators. In: Pattanaik, P.K., Tadenuma, K., Xu, Y., Yoshihara, N. (eds) Rational Choice and Social Welfare. Studies in Choice and Welfare. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79832-3_2
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DOI: https://doi.org/10.1007/978-3-540-79832-3_2
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