Manipulating an ordering

Conal Duddy, Juan Perote-Pena and Ashley Piggins ()

No 141, Working Papers from National University of Ireland Galway, Department of Economics

Abstract: 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.

Keywords: Ordinal fuzziness; social welfare function; manipulation Algorithmic Trading; MACD (search for similar items in EconPapers)
JEL-codes: D71 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2009, Revised 2009
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