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Manipulating an ordering


  • Conal Duddy
  • Juan Perote-Pena
  • Asjley Piggins

    (Department of Economics, National University of Ireland, Galway)


It is well known that many social decision procedures are manipulable through strategic behaviour. Typically, the decision procedures considered in the literature are social choice correspondences. In this paper we investigate the problem of constructing a social welfare function 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 social welfare functions are dictatorial, provided that they are not constant. This theorem generalizes the one in Perote-Pena and Piggins (Perote-Pena, J., Piggins, A., 2007. Strategy-proof fuzzy aggregation rules. J. Math. Econ., vol. 43, p. 564 - p. 580). We conclude by considering several ways of circumventing this impossibility theorem.

Suggested Citation

  • Conal Duddy & Juan Perote-Pena & Asjley Piggins, 2009. "Manipulating an ordering," Working Papers 0141, National University of Ireland Galway, Department of Economics, revised 2009.
  • Handle: RePEc:nig:wpaper:0141

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    Cited by:

    1. Ján Palguta, 2011. "Voting Experiments: Measuring Vulnerability of Voting Procedures to Manipulation," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 5(3), pages 324-345, November.

    More about this item


    Ordinal fuzziness; social welfare function; manipulation Algorithmic Trading; MACD;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations


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