Ambiguous choice problems which involve three or more outcome values can reveal aspects of ambiguity and ambiguity aversion which cannot be displayed in the classic two-outcome Ellsberg urn problems, and hence are not always captured by models designed to accommodate them. These aspects include Allais-type preferences over purely subjective acts, attitudes toward different sources involving different amounts of ambiguity, and attitudes toward ambiguity at different outcome levels. This paper presents a few such examples, and examines the standard models' predictions and performance in such cases.

Choice problems in the spirit of Ellsberg (1961) suggest that rank-dependent (“Choquet expected utility”) preferences over subjective gambles might be subject to the same difficulties that Ellsberg's earlier examples posed for subjective expected utility. These difficulties stem from event-separability properties that rank-dependent preferences partially retain from expected utility, and suggest that nonseparable models of preferences might be better at capturing features of behavior that lead to these paradoxes.

Although their goal is to separate a decision maker's underlying beliefs (their subjective probabilities of events) from their preferences (their attitudes toward risk), classic choice-theoretic derivations of subjective probability all rely upon some form of the Marschak-Samuelson "Independence Axiom" or the Savage "Sure-Thing Principle, " which is equivalent to requiring that the decision maker's preferences over lotteries conform to the expected utility hypothesis. This paper presents a choice-theoretic derivation of subjective probability which satisfies the axioms of classical probability theory, but which neither assumes nor implies that the decision maker's preferences over lotteries necessarily conform to the expected utility hypothesis.

This paper offers an interpretive comparison of the Arrow-Pratt and Ross characterizations of comparative risk aversion for expected utility maximizers. The tools used in this comparison are then applied to obtain a strengthening of the Ross cha racterization. This strengthened result is in turn extended to the ca se of general, smooth, nonexpected utility preferences over probabili ty distributions.