Arrow's theorem and max-star transitivity
AbstractIn the literature on social choice and 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 max-star transitive relations that permit preference aggregation to be non-dictatorial. This set contains all and only those triangular norms that contain a zero divisor.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by National University of Ireland Galway, Department of Economics in its series Working Papers with number 0140.
Length: 12 pages
Date of creation: 2009
Date of revision: 2009
Contact details of provider:
Postal: St. Anthony's College, Newcastle Road, Galway
Phone: +353-91 524411 ext. 2501
Fax: +353-91 524130
Web page: http://economics.nuigalway.ie
More information through EDIRC
Arrows theorem; triangular norm; fuzzy preference Algorithmic Trading; MACD;
Other versions of this item:
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Dietrich, Franz & List, Christian, 2008.
"The aggregation of propositional attitudes: towards a general theory,"
047, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Dietrich, Franz & List, Christian, 2008. "The aggregation of propositional attitudes: towards a general theory," Research Memorandum 047, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Barrett, C. & Pattanaik, P.K. & Salles, M., 1990.
"Rationality and Aggregation of Preferences in an Ordinally Fuzzy Framework,"
9006, Dijon - Institut des Mathematiques Economiques.
- Barrett, C.R. & Pattanaik, P.K. & Salles, M., 1990. "Rationality and Aggregation of Preferences in an Ordinally Fuzzy Framework," Institut des MathÃ©matiques Economiques â Document de travail de lâI.M.E. (1974-1993) 9006, Institut des Mathématiques Economiques. LATEC, Laboratoire d'Analyse et des Techniques EConomiques, CNRS, Université de Bourgogne.
- Basu, Kaushik, 1984. "Fuzzy revealed preference theory," Journal of Economic Theory, Elsevier, vol. 32(2), pages 212-227, April.
- Conal Duddy & Juan Perote-Peña & Ashley Piggins, 2010. "Manipulating an aggregation rule under ordinally fuzzy preferences," Social Choice and Welfare, Springer, vol. 34(3), pages 411-428, March.
- Dutta, Bhaskan, 1987. "Fuzzy preferences and social choice," Mathematical Social Sciences, Elsevier, vol. 13(3), pages 215-229, June.
- Sen, Amartya, 1970. "Interpersonal Aggregation and Partial Comparability," Econometrica, Econometric Society, vol. 38(3), pages 393-409, May.
- Juan Perote Pena & Ashley Piggins, 2005.
"Strategy-proof fuzzy aggregation rules,"
0098, National University of Ireland Galway, Department of Economics, revised 2005.
- Rajat Deb & Manabendra Dasgupta, 1996. "Transitivity and fuzzy preferences," Social Choice and Welfare, Springer, vol. 13(3), pages 305-318.
- Richard Barrett & Maurice Salles, 2006. "Social Choice With Fuzzy Preferences," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 200615, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
- Dutta, Bhaskar & Panda, Santosh C. & Pattanaik, Prasanta K., 1986. "Exact choice and fuzzy preferences," Mathematical Social Sciences, Elsevier, vol. 11(1), pages 53-68, February.
- Duddy, Conal & Piggins, Ashley, 2013. "Many-valued judgment aggregation: Characterizing the possibility/impossibility boundary," Journal of Economic Theory, Elsevier, vol. 148(2), pages 793-805.
- Conal Duddy & Ashley Piggins, 2012. "The proximity condition," Social Choice and Welfare, Springer, vol. 39(2), pages 353-369, July.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Srinivas Raghavendra).
If references are entirely missing, you can add them using this form.