Abstract
Arrow's independence of irrelevant alternatives (IIA) condition makes social choice depend only on personal rather than interpersonal comparisons of relevant social states, and so leads to dictatorship. Instead, a new “independence of irrelevant interpersonal comparisons” (IIIC) condition allows anonymous Paretian social welfare functionals such as maximin and Sen's “leximin,” even with an unrestricted preference domain. But when probability mixtures of social states are considered, even IIIC may not allow escape from Arrow's impossibility theorem for individuals' (ex-ante) expected utilities. Modifying IIIC to permit dependence on interpersonal comparisons of relevant probability mixtures allows Vickrey-Harsanyi utilitarianism.
Thus, if we wish to go beyong the comparisons that are possible using only the [pareto] principle of the new welfare economics, the issue is not whether we can do so without making interpersonal comparisons of satisfactions. It is rather, what sorts of interpersonal comparisons are we willing to make. Unless the comparisons allowed by Arrow's Condition 3 [independence of irrelevant alternatives] could be shown to have some ethical priority, there seems to be no reason for confining consideration to this group.
Hildreth (1953, p 91)
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Hammond, P.J. Independence of irrelevant interpersonal comparisons. Soc Choice Welfare 8, 1–19 (1991). https://doi.org/10.1007/BF00182445
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DOI: https://doi.org/10.1007/BF00182445