Nontransitive multidimensional preferences: Theoretical analysis of a model

✍ Scribed by Oswald Huber

• Book ID: 104631979
• Publisher: Springer US
• Year: 1979
• Tongue: English
• Weight: 767 KB
• Volume: 10
• Category: Article
• ISSN: 0040-5833
• DOI: 10.1007/bf00126336

✦ Synopsis

A descriptive multidimensional preference-model (WM) is developed which amalgamates dimension-wise preference-relations (preferences in respect to different decision.criteria) into an overall-preference, according to the weights of the dimensions. Apart from the common preference-axioms, WM is based on an axiomatic system C for the weighing of the dimensions. Proofs of consistency and of independence of the axioms are presented. The overall-preference-relation is shown to be nontransitive. The likewise nontransitive overall-indifference is divided into two other overall-indifference-relations, one of them is transitive, the other nontransitive. Thus WM is able to explain 'intransitivities' even if perfect diseriminability is assumed. System C is further interpreted as system of Qualitative Probability and its relations to the standard system of Qualitative Probability are analyzed. In the last section WM is compared with some other decisionmodels (Dominance-rule, Lexicographic-ordering, Majority-rule, Additive-differencemodel), some possible interpretations of WM and the limits of WM are discussed.