Arrow’s theorem and max-star transitivity Authors Conal Duddy Government of Ireland Scholar, J. E. Cairnes School of Business and Economics National University of Ireland Galway Juan Perote-Peña Departamento de Análisis Económico Universidad de Zaragoza Ashley Piggins J. E. Cairnes School of Business and Economics National University of Ireland Galway Original Paper

First Online: 20 May 2010 Received: 09 December 2009 Accepted: 04 May 2010 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.

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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