Seminar Abstract

【Lexicographic Expected Utility for Rational-Valued Lotteries】

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Speaker: 池田 潔

Affiliation: 北陸先端科学技術大学院大学 情報科学研究科

Date and Time: 2002.12. 5 (Thu), 4:30 - 6:00 p.m.

Place: 3F1223

Chair: 金子 守

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Abstract: 

The well known expected utility theory for decision making 
under risk, as developed by von Neumann and Morgenstern 
(1944), is based on the assumptions that the preference 
relation over the lotteries is a complete preorder satisfying 
an independence condition and a continuity property. 
The role of the continuity property in single person decision 
theory is merely technical, namely, to ensure the existence 
of a real-valued utility function. As Hausner (1954) pointed 
out, dropping this assumption modifies the classical expected 
utility theory by allowing lexicographic utility functions.

The aim of this article is to show that a similar form of 
the lexicographic expected utility representation considered 
by Hausner (1954) is also valid even if we omit the existence 
of irrational-valued lotteries. That is to say, Hausner's 
lexicographic utility theory can be founded on the domain 
of rational-valued probability distributions on an outcome set.

Reference

 Hausner, M. (1954). Multidimensional Utilities. In Thrall,
   R.C.C. and Davis, R., eds, ``Decision Processes,'' 
   pages 167-180. Wiley, New York.