Social Choice and Welfare

, Volume 36, Issue 1, pp 25–34

Arrow’s theorem and max-star transitivity

Authors

  • Conal Duddy
    • Government of Ireland Scholar, J. E. Cairnes School of Business and EconomicsNational University of Ireland Galway
  • Juan Perote-Peña
    • Departamento de Análisis EconómicoUniversidad de Zaragoza
    • J. E. Cairnes School of Business and EconomicsNational University of Ireland Galway
Original Paper

DOI: 10.1007/s00355-010-0461-x

Cite this article as:
Duddy, C., Perote-Peña, J. & Piggins, A. Soc Choice Welf (2011) 36: 25. doi:10.1007/s00355-010-0461-x

Abstract

In the literature on social choice with fuzzy preferences, a central question is how to represent the transitivity of a fuzzy binary relation. Arguably the most general way of doing this is to assume a form of transitivity called max-star transitivity. The star operator in this formulation is commonly taken to be a triangular norm. The familiar max- min transitivity condition is a member of this family, but there are infinitely many others. Restricting attention to fuzzy aggregation rules that satisfy counterparts of unanimity and independence of irrelevant alternatives, we characterise the set of triangular norms that permit preference aggregation to be non-dictatorial. This set contains all and only those norms that contain a zero divisor.

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© Springer-Verlag 2010