Minimal Books of Rationales

18 Pages Posted: 23 Mar 2005

See all articles by Jose Apesteguia

Jose Apesteguia

Universitat Pompeu Fabra - Department of Economics and Business (DEB)

Miguel A. Ballester

University of Navarra - School of Economics

Date Written: July 2005

Abstract

Kalai, Rubinstein, and Spiegler (2002) propose the rationalization of choice functions that violate the "independence of irrelevant alternatives" axiom through a collection (book) of linear orders (rationales). In this paper we show that the problem of finding a minimal book is equivalent to a particular problem in graph theory. This allows us to render the behavioral information given by the choice function c and the book of rationales to be completely equivalent, as in the classical setup. That is, in principle, for any c we will be able to give: (1) the minimal composition of rationales that rationalizes c, and (2) information on how choice problems are associated to rationales. Further, the above mentioned equivalence will also allow us to show that the problem of finding a minimal book is NP-complete. Hence, we will develop on the complexity of finding minimal books of rationales.

Keywords: Rationalization, independence of irrelevant alternatives, order partition, computational effort

JEL Classification: D01

Suggested Citation

Apesteguia, Jose and Ballester, Miguel A., Minimal Books of Rationales (July 2005). Available at SSRN: https://ssrn.com/abstract=677902 or http://dx.doi.org/10.2139/ssrn.677902

Jose Apesteguia (Contact Author)

Universitat Pompeu Fabra - Department of Economics and Business (DEB) ( email )

Barcelona, 08005
Spain

HOME PAGE: http://www.econ.upf.es/~apesteguia/

Miguel A. Ballester

University of Navarra - School of Economics ( email )

Universidad de Navarra
Campus Universitario
Pamplona, 31009
Spain