Arrow’s theorem and max-star transitivity
- 97 Downloads
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.
Unable to display preview. Download preview PDF.
- Arrow KJ (1951) Social choice and individual values. Wiley, New YorkGoogle Scholar
- Barrett CR, Salles M (2006) Social choice with fuzzy preferences, Working paper, Centre for Research in Economics and Management, UMR CNRS 6211, University of CaenGoogle Scholar
- Billot A (1995) Economic theory of fuzzy equilibria. Springer, BerlinGoogle Scholar
- Dasgupta M, Deb R (1999) An impossibility theorem with fuzzy preferences. In: de Swart H (ed) Logic, game theory and social choice: proceedings of the international conference, LGS ’99, May 13–16, 1999, Tilburg University PressGoogle Scholar
- Dietrich F, List C (2009) The aggregation of propositional attitudes: towards a general theory, forthcoming in Oxford Studies in EpistemologyGoogle Scholar
- Duddy C, Piggins A (2009) Many-valued judgment aggregation: characterizing the possibility/impossibility boundary for an important class of agendas, Working paper, Department of Economics, National University of Ireland, GalwayGoogle Scholar
- Klement EP, Mesiar R, Pap E (2000) Triangular norms. Kluwer Academic Publishers, DordrechtGoogle Scholar
- Leclerc B, Monjardet B (1995) Lattical theory of consensus. In: Barnett W, Moulin H, Salles M, Schofield N (eds) Social choice, welfare and ethics. Cambridge University Press, CambridgeGoogle Scholar
- Perote-Peña J, Piggins A (2009b) Social choice, fuzzy preferences and manipulation. In: Boylan T, Gekker R (eds) Economics, rational choice and normative philosophy. Routledge, LondonGoogle Scholar
- Piggins A, Salles M (2007) Instances of indeterminacy. Analyse und Kritik 29: 311–328Google Scholar
- Salles M (1998) Fuzzy utility. In: Barbera S, Hammond PJ, Seidl C (eds) Handbook of utility theory, vol 1: principles. Kluwer, DordrechtGoogle Scholar