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Comonotonic proper scoring rules to measure ambiguity and subjective beliefs
Author(s) -
Kothiyal Amit,
Spinu Vitalie,
Wakker Peter P.
Publication year - 2010
Publication title -
journal of multi‐criteria decision analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.462
H-Index - 47
eISSN - 1099-1360
pISSN - 1057-9214
DOI - 10.1002/mcda.454
Subject(s) - ambiguity , scoring rule , subjective expected utility , measure (data warehouse) , expected utility hypothesis , maximization , value (mathematics) , bounded function , computer science , domain (mathematical analysis) , quadratic equation , artificial intelligence , mathematics , econometrics , mathematical economics , machine learning , mathematical optimization , data mining , mathematical analysis , geometry , programming language
Proper scoring rules serve to measure subjective degrees of belief. Traditional proper scoring rules are based on the assumption of expected value maximization. There are, however, many deviations from expected value, primarily due to risk aversion. Correcting techniques have been proposed in the literature for deviations due to nonlinear utility. These techniques still assumed expected utility maximization. More recently, corrections for deviations from expected utility have been proposed. The latter concerned, however, only the quadratic scoring rule, and could handle only half of the domain of subjective beliefs. Further, beliefs close to 0.5 could not be discriminated. This paper generalizes the correcting techniques to all bounded binary proper scoring rules, covers the whole domain of beliefs and, in particular, can discriminate between all degrees of belief. Thus, we fully extend the properness requirement (in the sense of identifying all degrees of subjective beliefs) to virtually all models that deviate from expected value. Copyright © 2011 John Wiley & Sons, Ltd.