Social Choice and Welfare

, Volume 36, Issue 1, pp 25–34 | Cite as

Arrow’s theorem and max-star transitivity

Original Paper


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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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Conal Duddy
    • 1
  • Juan Perote-Peña
    • 3
  • Ashley Piggins
    • 2
  1. 1.Government of Ireland Scholar, J. E. Cairnes School of Business and EconomicsNational University of Ireland GalwayGalwayIreland
  2. 2.J. E. Cairnes School of Business and EconomicsNational University of Ireland GalwayGalwayIreland
  3. 3.Departamento de Análisis EconómicoUniversidad de ZaragozaZaragozaSpain

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