Abstract
The collective rationality requirement in Arrow's theorem is weakened to demanding a social quasi-ordering (a reflexive and transitive but not necessarily complete binary relation). This weakening leads to the existence of a group such that (a) whenever all members of the group strictly prefer one alternative to another then so does society and (b) whenever two members of the group have opposite strict preferences over a pair of alternatives then the pair is socially not ranked. This theorem is then used to provide an axiomatization of the strong Pareto rule. These results are compared and contrasted to Gibbard's oligarchy theorem and Sen's axiomatization of the Pareto extension rule.
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I would like to thank David Donaldson, Dieter Sondermann, and the referees for their comments. Thanks are also due to Peter Aranson for his editorial remarks. My work on this topic was initiated while I was a visitor to the Center for Operations Research and Econometrics. My stay at CORE was financed by the generous support of the Institut des Sciences Economiques of the Université Catholique de Louvain.
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Weymark, J.A. Arrow's theorem with social quasi-orderings. Public Choice 42, 235–246 (1984). https://doi.org/10.1007/BF00124943
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DOI: https://doi.org/10.1007/BF00124943