Min–max decision rules for choice under complete uncertainty: Axiomatic characterizations for preferences over utility intervals

• The framework of choice under complete uncertainty is generalized to imprecise ordinal utilities attaching to single outcomes.
• We define min–max decision rules and lexicographic refinements in this generalized framework.
• Complete axiomatic characterizations of these decision rules are presented.
• Further complete axiomatic characterizations of min–max decision rules in the standard framework are given.

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≽mnx in the classical framework of choice under complete uncertainty.