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A Rubinesque theory of decision. (English) Zbl 1268.62009

Dasgupta, Anirban (ed.), A Festschrift for Herman Rubin. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 0-940600-61-7/pbk). Institute of Mathematical Statistics Lecture Notes - Monograph Series 45, 45-55 (2004).
Summary: We generalize a set of axioms introduced by Rubin (1987) to the case of partial preference. That is, we consider cases in which not all uncertain acts are comparable to each other. We demonstrate some relations between these axioms and a decision theory based on sets of probability/utility pairs. We illustrate by example how comparisons solely between pairs of acts is not sufficient to distinguish between decision makers who base their choices on distinct sets of probability/utility pairs.
For the entire collection see [Zbl 1066.62002].

MSC:

62C05 General considerations in statistical decision theory
62A01 Foundations and philosophical topics in statistics
91B06 Decision theory
91B14 Social choice
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