Abstract
A Sophisticated Social Welfare Function (SSWF) is a mapping from profiles of individual preferences into a sophisticated preference which is a pairwise weighted comparison of alternatives. We characterize Pareto optimal and pairwise independent SSWFs in terms of oligarchies that are induced by some power distribution in the society. This is a fairly large class ranging from dictatoriality to anonymous aggregation rules. Our results generalize the impossibility theorem of Arrow (Social choice and individual values. Wiley, New York, 1951) and the oligarchy theorem of Gibbard (Intransitive social indifference and the Arrow dilemma, University of Chicago, unpublished manuscript, 1969).
Highlights
It is possible to have a more general perspective of the preference aggregation problem by incorporating elements of ambiguity into individual and/or social preferences
Our characterization generalizes two major results of the literature: In case the ranges of Pareto optimal and pairwise independent Sophisticated Social Welfare Function (SSWF) are restricted to non-sophisticated preferences that are linear orders, the oligarchies must contain precisely one individual - which is the impossibility theorem of Arrow (1951, 1963)
In case the social outcome is restricted to non-sophisticated preferences that are complete and quasitransitive, Pareto optimal and pairwise independent SSWFs are oligarchical in the sense that the oligarchy has full decision power while all
Summary
It is possible to have a more general perspective of the preference aggregation problem by incorporating elements of ambiguity into individual and/or social preferences. An overall preference with possibly mixed feelings Given these interpretations, we require a certain consistency of the aggregated outcome, expressed by some transitivity condition imposed over sophisticated preferences: We qualify a sophisticated preference as transitive whenever given any three alternatives x; y and z, we have (x; y) = 1 =) (x; z) (y; z). Our characterization generalizes two major results of the literature: In case the ranges of Pareto optimal and pairwise independent SSWFs are restricted to non-sophisticated preferences that are linear orders, the oligarchies must contain precisely one individual ( a dictator) - which is the impossibility theorem of Arrow (1951, 1963). In case the social outcome is restricted to non-sophisticated preferences that are complete and quasitransitive, Pareto optimal and pairwise independent SSWFs are oligarchical in the sense that the oligarchy has full decision power while all.
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