Stochastic dominance tests for ranking alternatives under ambiguity

Ambiguity in decision making is a condition associated with the existence of one-to-many, or more generally, many-to-many relations between outcomes and probabilities of outcomes. The current use of stochastic dominance tests to rank decision alternatives assumes that outcome probability distributions are unambiguous. This paper first establishes procedures to identify an envelope of the ambiguously-described probability-outcome mapping, then extends stochastic dominance theorems to provide tests that partition alternatives into dominated and non-dominated sets.