The Shape of Incomplete Preferences

The Shape of Incomplete Preferences

Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple axiomatization of incomplete preferences and characterizes the shape o...

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Veröffentlicht in:The Annals of Statistics. - Institute of Mathematical Statistics. - 34(2006), 5, Seite 2430-2448
1. Verfasser: Nau, Robert (VerfasserIn)
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2006
Zugriff auf das übergeordnete Werk:The Annals of Statistics
Schlagworte:Axioms of decision theory Bayesian robustness State-dependent utility Coherence Partial order Imprecise probabilities and utilities Economics Mathematics Behavioral sciences Philosophy
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520 |a Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple axiomatization of incomplete preferences and characterizes the shape of their representing sets of probabilities and utilities. Deletion of the completeness assumption from the axiom system of Anscombe and Aumann yields preferences represented by a convex set of state-dependent expected utilities, of which at least one must be a probability/utility pair. A strengthening of the state-independence axiom is needed to obtain a representation purely in terms of a set of probability/utility pairs. 
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