Aggregation of binary evaluations with abstentions

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Abstract

A general model of aggregation of binary evaluations over interrelated issues, introduced by Wilson and further studied by Rubinstein and Fishburn and by the authors, is extended here to allow for abstentions on some of the issues. It is shown that the same structural conditions on the set of feasible evaluations that lead to dictatorship in the model without abstentions, lead to oligarchy in the presence of abstentions. Arrow's impossibility theorem for social welfare functions, Gibbard's oligarchy theorem for quasi-transitive social decision functions, as well as some apparently new theorems on preference aggregation, are obtained as corollaries.

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  • Cited by (46)

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    The first version of this paper was circulated in December 2006. Results that are essentially the same as the main result of this paper, but are phrased in a model of logical judgment aggregation, were independently obtained by Dietrich and List (2008) [10]. The overlap between the two works was discovered just before the Cowles Workshop on “Aggregation of Opinions,” September 2006, where both papers were presented. The comments of an associate editor and two referees are gratefully acknowledged.

    1

    Part of this author's work was done while he was a Fellow of the Institute for Advanced Studies at the Hebrew University of Jerusalem, in the academic year 2004–2005. Research supported by the Japan Technion Society Research Fund and by the Israel Science Foundation.

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