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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This article was first presented at the conference “New Developments in Social Choice and Welfare Theories: A Tribute to Maurice Salles”, which was held at the Université Caen in June 2009. It was later presented at the PET 09 conference in NUI Galway.
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Duddy, C., Perote-Peña, J. & Piggins, A. Arrow’s theorem and max-star transitivity. Soc Choice Welf 36, 25–34 (2011). https://doi.org/10.1007/s00355-010-0461-x
- Social Choice
- Social Welfare Function
- Transitivity Condition
- Zero Divisor
- Judgment Aggregation