Order indifference and rank-dependent probabilities
type: Item
instance of: scholarly article
title: Order indifference and rank-dependent probabilities
zbMATH Open document ID: 0801.90014
DOI: 10.1016/0304-4068(93)90024-F
author: Uzi Segal
published in: Journal of Mathematical Economics
publication date: 1993-12-02T00:00:00Z
review text: The paper presents a new axiomatization of the anticipated utility model in a two-stage lotteries framework. It is a common assumption in decision theory that a multi-stage lottery is equally attractive as the simple lottery yielding the same prizes with the compound probabilities (reduction of compound lotteries). This paper adopts a different point of view. Only a weakening of the reduction axiom which is called order indifference is assumed. Let \(L_ 1\) be the set of all finite lotteries with non-negative outcomes, and \(L_ 2\) the set of all two-stage lotteries over \(L_ 1\), i.e., the set of all lotteries whose outcomes are tickets for lotteries in \(L_ 1\). For lotteries in \(L_ 1\) the following notation is used: \((x_ 1,p_ 1;\dots;x_ n,p_ n)\) denotes the lottery giving \(x_ i\) with probability \(p_ i\), \(i= 1,\dots,n\). Analogously, lotteries in \(L_ 2\) are denoted by \((X_ 1,p_ 1;\dots;X_ n, p_ n)\), where \(X_ 1,\dots,X_ n\) are lotteries in \(L_ 1\). Lotteries in \(L_ 1\) can be embedded in \(L_ 2\) in two different ways. The lottery \((x_ 1,p_ 1;\dots; x_ n,p_ n)\) can either be represented by the two-stage lottery \(((x_ 1,p_ 1;\dots; x_ n,p_ n),1)\) or by the lottery \((x_ 1,1),p_ 1;\dots; (x_ n, 1),p_ n)\). The time neutrality axiom states that the decision maker is indifferent between these two lotteries. The key axiom in the axiomatization is called order indifference. It assumes that for every one-stage lottery \((x_ 1,q_ 1;\dots; x_ n,q_ n)\) and every \(p\in [0,1]\) the decision maker is indifferent between the two-stage lotteries \(((0,1),1- p;(x_ 1,q_ 1;\dots;x_ n,q_ n),p)\) and \(((0,1-p; x_ 1,p),q_ 1);\dots; (0,1-p;x_ n,p),q_ n)\). This means that the decision maker does not care on which stage he is informed that he will gain nothing. Under time neutrality, order indifference, and four other technical axioms (continuity, first- order stochastic dominance, irrelevance, Archimedean) the preference relation over one-stage lotteries can be …
Mathematics Subject Classification ID: 91B16
Mathematics Subject Classification ID: 91B06
zbMATH DE Number: 429102
zbMATH Keywords: anticipated utility
zbMATH Keywords: two-stage lotteries
zbMATH Keywords: order indifference
zbMATH Keywords: time neutrality axiom
MaRDI profile type: Publication
cites work: Q5514010
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description: scientific article; zbMATH DE number 429102