We study preference relations on conditional gambles of a decision maker acting under ambiguity. Dutch book rationality conditions are provided under a linear utility scale, encoding either an optimistic or a pessimistic attitude towards uncertainty. These conditions characterize possibly incomplete preferences representable by totally alternating or monotone conditional functionals. In general, the uniqueness of the representation is not guaranteed, but it can be obtained by adding the hypothesis of existence of a conditional fair price for every conditional gamble. The given rationality conditions have a betting scheme interpretation relying on “penalty fees” for betting on strict preference comparisons.

Dutch book rationality conditions for conditional preferences under ambiguity / Coletti, G.; Petturiti, D.; Vantaggi, B.. - In: ANNALS OF OPERATIONS RESEARCH. - ISSN 0254-5330. - 279:1-2(2019), pp. 115-150. [10.1007/s10479-019-03299-8]

Dutch book rationality conditions for conditional preferences under ambiguity

Vantaggi B.
2019

Abstract

We study preference relations on conditional gambles of a decision maker acting under ambiguity. Dutch book rationality conditions are provided under a linear utility scale, encoding either an optimistic or a pessimistic attitude towards uncertainty. These conditions characterize possibly incomplete preferences representable by totally alternating or monotone conditional functionals. In general, the uniqueness of the representation is not guaranteed, but it can be obtained by adding the hypothesis of existence of a conditional fair price for every conditional gamble. The given rationality conditions have a betting scheme interpretation relying on “penalty fees” for betting on strict preference comparisons.
2019
Ambiguity; Choquet expected value; Conditional gambles; Conditional totally alternating capacity; Conditional totally monotone capacity; Dutch book; Preferences
01 Pubblicazione su rivista::01a Articolo in rivista
Dutch book rationality conditions for conditional preferences under ambiguity / Coletti, G.; Petturiti, D.; Vantaggi, B.. - In: ANNALS OF OPERATIONS RESEARCH. - ISSN 0254-5330. - 279:1-2(2019), pp. 115-150. [10.1007/s10479-019-03299-8]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1355406
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