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Journal of Logic and Computation Advance Access originally published online on June 26, 2008
Journal of Logic and Computation 2009 19(3):503-515; doi:10.1093/logcom/exn010
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© The Author, 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

This article appears in the following Journal of Logic and Computation issue: Special Issue: Connections between Belief Revision, Belief Merging and Social Choice [View the issue table of contents]

Original Articles

Non-manipulable Social Welfare Functions when Preferences are Fuzzy

Juan Perote-Peña

Departamento de Análisis Económico, Fac. de CC.EE. y EE., Universidad de Zaragoza, Gran Vía 2, 50005 Zaragoza, Spain
E-mail: jperote{at}unizar.es

Ashley Piggins

Department of Economics, National University of Ireland, Galway, Ireland
E-mail: ashley.piggins{at}nuigalway.ie

Received 16 February 2007.


  Abstract

It is well known that many social decision procedures are manipulable through strategic behaviour. Typically, the decision procedures considered in the literature have been social choice correspondences. In this article, 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 fuzzy set theory, we introduce a class of 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. A proof of this theorem first appeared in Perote-Peña and Piggins (2007, J. Math. Econ., 43, 564–580). This article contains a new proof of this theorem which is considerably simpler than the original. Moreover, we also consider a possibility result which this earlier article neglects.

Keywords: Manipulation; social welfare functions; fuzzy preferences


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