Consistent rationalizability

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CAHIER 12-2002

CONSISTENT RATIONALIZABILITY

Walter BOSSERT, Yves SPRUMONT and Kotaro SUZUMURA

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CAHIER 12-2002

CONSISTENT RATIONALIZABILITY

Walter BOSSERT1, Yves SPRUMONT1 and Kotaro SUZUMURA2

1 _{Centre de recherche et développement en économique (C.R.D.E.) / Centre interuniversitaire} de recherche en économie quantitative (CIREQ) and Département de sciences économiques, Université de Montréal

2 _{Institute of Economic Research, Hitotsubashi University}

May 2002

_______________________

Financial support through grants from the Social Sciences and Humanities Research Council of Canada, the Fonds pour la formation de chercheurs et l'aide à la recherche of Québec, and a Grant-in-Aid for Scientific Research for Priority Areas (B) Number 603 from the Ministry of

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RÉSUMÉ

Une relation de préférence est dite cohérente si les seuls cycles qu'elles contient sont des cycles d'indifférence. Nous étudions la "rationalisabilité" d'une fonction de choix par une relation de préférence cohérente.

Mots clés : choix rationnel, cohérence, domaines binaires

ABSTRACT

Consistency of a binary relation requires any preference cycle to involve indifference only. As shown by Suzumura (1976b), consistency is necessary and sufficient for the existence of an ordering extension of a relation. Because of this important role of consistency, it is of interest to examine the rationalizability of choice functions by means of consistent relations. We describe the logical relationships between the different notions of rationalizability obtained if reflexivity or completeness are added to consistency, both for greatest-element rationalizability and for maximal-element rationalizability. All but one notion of consistent rationalizability are characterized for general domains, and all of them are characterized for domains that contain all two-element subsets of the universal set.

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(10)

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(11)

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(12)

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(13)

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(14)

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(15)

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