Totally convex preferences for gambles.
type: Item
instance of: scholarly article
title: Totally convex preferences for gambles.
zbMATH Open document ID: 1048.91037
DOI: 10.1016/S0165-4896(01)00074-9
author: Yutaka Nakamura
published in: Mathematical Social Sciences
publication date: 2003-04-02T00:00:00Z
review text: The author considers a set of gambles with a binary strict preference relation. Fishburn showed that there is a nontransitive convex representation if the relation has an open and totally convex structure. The author gives a necessary and sufficient condition that there is a transitive convex representation of the preference relation (Theorem 3.1). Relations to Dekel's implied representation are shown. A second theorem (Theorem 4.1) gives a necessary and sufficient condition for the existence of a separable SSB representation. A final theorem (Theorem 4.2) gives a necessary and sufficient condition for a nonnegative component of a separable SSB representation. Relations to Chew's weighted linear utility are shown.
reviewed by: Peter Kischka
Mathematics Subject Classification ID: 91B08
Mathematics Subject Classification ID: 91B16
zbMATH DE Number: 1891766
zbMATH Keywords: Totally convex preferences
zbMATH Keywords: SSB utility
zbMATH Keywords: transitivity
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1891766