Manipulating an aggregation rule under ordinally fuzzy preferences
- 69 Downloads
It is well known that many aggregation rules are manipulable through strategic behaviour. Typically, the aggregation rules considered in the literature are social choice correspondences. In this paper the aggregation rules of interest are social welfare functions (SWFs). We investigate the problem of constructing a SWF that is non-manipulable. In this context, individuals attempt to manipulate a social ordering as opposed to a social choice. Using techniques from an ordinal version of fuzzy set theory, we introduce a class of ordinally fuzzy binary relations of which exact binary relations are a special case. Operating within this family enables us to prove an impossibility theorem. This theorem states that all non-manipulable SWFs are dictatorial, provided that they are not constant. This theorem uses a weaker transitivity condition than the one in Perote-Peña and Piggins (J Math Econ 43:564–580, 2007), and the ordinal framework we employ is more general than the cardinal setting used there. We conclude by considering several ways of circumventing this impossibility theorem.
Unable to display preview. Download preview PDF.
- Arrow KJ (1951) Social choice and individual values. Wiley, New YorkGoogle Scholar
- Billot A (1995) Economic theory of fuzzy equilibria. Springer, BerlinGoogle Scholar
- Broome J (1997) Is incommensurability vagueness. In: Chang R Incommensurability, incomparability, and practical reason. Harvard University Press, HarvardGoogle 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. Tilburg University Press, TilburgGoogle Scholar
- Gaertner W (2006) A primer in social choice theory. Oxford University Press, OxfordGoogle Scholar
- Leclerc B, Monjardet B (1995) Lattical theory of consensus. In: Barnett W, Moulin H, Salles M, Schofield N 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 Economics, rational choice and normative philosophy. Routledge, LondonGoogle Scholar
- Piggins A, Salles M (2007) Instances of indeterminacy. Anal Kritik 29: 311–328Google Scholar
- Salles M (1998) Fuzzy utility. In: Barbera S, Hammond PJ, Seidl C Handbook of utility theory, vol 1: principles. Kluwer, DordrechtGoogle Scholar
- Sen AK (1970b) Collective choice and social welfare. Holden-Day, San FranciscoGoogle Scholar
- Williamson T (1994) Vagueness. Routledge, LondonGoogle Scholar