Min–max Decision Rules for Choice Under Complete Uncertainty: Axiomatic Characterizations for Preferences Over Utility Intervals

Landes, Jürgen (2014): Min–max Decision Rules for Choice Under Complete Uncertainty: Axiomatic Characterizations for Preferences Over Utility Intervals. In: International Journal of Approximate Reasoning, Vol. 55, No. 5: 1301 - 1317

Abstract

Abstract We introduce two novel frameworks for choice under complete uncertainty. These frameworks employ intervals to represent uncertain utility attaching to outcomes. In the first framework, utility intervals arising from one act with multiple possible outcomes are aggregated via a set-based approach. In the second framework the aggregation of utility intervals employs multi-sets. On the aggregated utility intervals, we then introduce min–max decision rules and lexicographic refinements thereof. The main technical results are axiomatic characterizations of these min–max decision rules and these refinements. We also briefly touch on the independence of introduced axioms. Furthermore, we show that such characterizations give rise to novel axiomatic characterizations of the well-known min–max decision rule ≽ mnx in the classical framework of choice under complete uncertainty.

• Item Type: Journal article
• Form of publication: Postprint
• Keywords: Choice under complete uncertainty; Interval orders; Min–max decision rules; Nonprobabilistic decision rules; Interval utility
• Faculties: Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP); Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP) > Epistemology
• Subjects: 100 Philosophy and Psychology > 120 Epistemology
• ISSN: 0888-613X
• Language: English