Social Choice and Welfare

, Volume 34, Issue 3, pp 411–428

Manipulating an aggregation rule under ordinally fuzzy preferences

Original Paper

DOI: 10.1007/s00355-009-0405-5

Cite this article as:
Duddy, C., Perote-Peña, J. & Piggins, A. Soc Choice Welf (2010) 34: 411. doi:10.1007/s00355-009-0405-5


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.

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Conal Duddy
    • 1
  • Juan Perote-Peña
    • 2
  • Ashley Piggins
    • 1
  1. 1.J.E. Cairnes School of Business and EconomicsNational University of Ireland, GalwayGalwayIreland
  2. 2.Departamento de Análisis EconómicoUniversidad de ZaragozaZaragozaSpain