, Volume 34, Issue 3, pp 411-428
Date: 01 Jul 2009

Manipulating an aggregation rule under ordinally fuzzy preferences

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It is well known that many aggregation rules are manipulable through strategic behaviour. Typically, the aggregation rules considered in the literature are social choice correspondences. In this paper the aggregation rules of interest are social welfare functions (SWFs). We investigate the problem of constructing a SWF that is non-manipulable. In this context, individuals attempt to manipulate a social ordering as opposed to a social choice. Using techniques from an ordinal version of fuzzy set theory, we introduce a class of ordinally fuzzy binary relations of which exact binary relations are a special case. Operating within this family enables us to prove an impossibility theorem. This theorem states that all non-manipulable SWFs are dictatorial, provided that they are not constant. This theorem uses a weaker transitivity condition than the one in Perote-Peña and Piggins (J Math Econ 43:564–580, 2007), and the ordinal framework we employ is more general than the cardinal setting used there. We conclude by considering several ways of circumventing this impossibility theorem.

We are grateful to seminar participants at NUI Galway, King’s College London, Universität Osnabrück, Queen’s University Belfast and PET 08 for comments and suggestions. In addition, we would like to thank Nick Baigent, James Jordan, Christian List, Andrew McLennan, Vincent Merlin, Maurice Salles and two anonymous referees for a number of helpful remarks. Financial support from the Spanish Ministry of Science and Innovation through Feder grant SEJ2007-67580-C02-02, the NUI Galway Millennium Fund and the Irish Research Council for the Humanities and Social Sciences is gratefully acknowledged.