NDLI: On Elements of Chance

Content Provider	Springer Nature Link
Author	Duncan Luce, R. Marley, A.A.J.
Copyright Year	2000
Abstract	One aspect of the utility of gambling may evidence itself in failures of idempotence, i.e., when all chance outcomes give rise to the same consequence the `gamble' may not be indifferent to its common consequence. Under the assumption of segregation, such gambles can be expressed as the joint receipt of the common consequence and what we call `an element of chance', namely, the same gamble with the common consequence replaced by the status quo. Generalizing, any gamble is indifferent to the joint receipt of its element of chance and a certain consequence, which is called the `kernel equivalent' of the gamble. Under idempotence, the kernel equivalent equals the certainty equivalent. Conditions are reported (Theorem 4) that are sufficient for the kernel equivalents to have the kind of utility representation first discussed by Luce and Fishburn (1991), including being idempotent. This utility representation of the kernel equivalents together with the derived form of utility over joint receipts yields a utility representation of the original structure. Possible forms for the utility of an element of chance are developed.
Starting Page	97
Ending Page	126
Page Count	30
File Format	PDF
ISSN	00405833
Journal	Theory and Decision
Volume Number	49
Issue Number	2
e-ISSN	15737187
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2000-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Economics/Management Science Operation Research/Decision Theory Methodology of the Social Sciences
Content Type	Text
Resource Type	Article
Subject	Arts and Humanities Economics, Econometrics and Finance Developmental and Educational Psychology Social Sciences Decision Sciences Applied Psychology Computer Science Applications

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