An experimental test of the Anscombe-Aumann Monotonicity axiom

Most models of ambiguity aversion satisfy Anscombe-Aumann’s Monotonicity axiom. Monotonicity imposes separability of preferences across events that occur with unknown probability. We construct a test of Monotonicity by modifying the Allais paradox to a setting with both subjective and objective uncertainty. Two experimental studies are conducted: while study 1 uses U.S. online workers and a natural source of ambiguity, study 2 employs European students and an Ellsberg urn. In both studies, modal behavior violates Monotonicity in a specific, intuitive way. Overall, our data suggest that violations of Monotonicity are as prevalent as violations of von Neumann-Morgenstern’s Independence axiom

A Class of Incomplete and Ambiguity Averse Preferences

This paper characterizes ambiguity averse preferences in the absence of the completeness axiom. We axiomatize multiple selves versions of some of the most important examples of complete and ambiguity averse preferences, and characterize when those incomplete preferences are ambiguity averse.

A subjective spin on roulette wheels.

We provide a behavioral foundation to the notion of ‘mixture’ of acts, which is used to great advantage in he decision setting introduced by Anscombe and Aumann. Our construction allows one to formulate mixture-space axioms even in a fully sub-jective setting, without assuming the existence of randomizing devices. This simplifies the task of developing axiomatic models which only use behavioral data. Moreover, it is immune from the difficulty that agents may ‘distort’ the probabilities associated with randomizing devices. For illustration, we present simple subjective axiomatizations of some models of choice under uncertainty, including the maxmin expected utility model of Gilboa and Schmeidler, and Bewley’s model of choice with incomplete preferences.

Ambiguous correlation

Many decisions are made in environments where outcomes are determined by the realization of multiple random events. A decision maker may be uncertain how these events are related. We identify and experimentally substantiate behavior that intuitively reflects a lack of confidence in their joint distribution. Our findings suggest a dimension of ambiguity which is different from that in the classical distinction between risk and "Knightian uncertainty"

Testing axiomatizations of ambiguity aversion

The study of the normative and positive theory of choice under uncertainty has made major advances through thought experiments often referred to as paradoxes: the St. Petersburg paradox, the Allais paradox, the Ellsberg paradox, and the Rabin paradox. Machina proposes a new thought experiment which posits a choice between two acts that have three outcomes. As in the Ellsberg paradox there are three events, but while the Ellsberg paradox has two (monetary) outcomes in Machina there are three. Machina shows that four prominent theories of ambiguity aversion predict indifference between the acts. Introspection, however, suggests that many people might very well strictly prefer one act over the other. This paper makes four contributions: first, to our knowledge, it is the first to experimentally implement the Machina thought experiment. Second, we employ a novel method to simultaneously elicit the certainty equivalent of an embedded lottery. Third, our results—across three experiments—indicate non-indifference, which rejects earlier theories of ambiguity aversion, but is consistent with a newer one, which we apply to explain our results. Fourth, we show that independence is a sufficient condition for indifference in the Machina paradox, and thereby explains why so many models predict indifference

Making the Anscombe-Aumann approach to ambiguity suitable for descriptive applications

The Anscombe-Aumann (AA) model, originally introduced to give a normative basis to expected utility, is nowadays mostly used for another purpose: to analyze deviations from expected utility due to ambiguity (unknown probabilities). The AA model makes two ancillary assumptions that do not refer to ambiguity: expected utility for risk and backward induction. These assumptions, even if normatively appropriate, fail descriptively. This paper relaxes these ancillary assumptions to avoid the descriptive violations, while maintaining AA’s convenient mixture operation. Thus, it becomes possible to test and apply all AA-based ambiguity theories descriptively while avoiding confounds due to violated ancillary assumptions. The resulting tests use only simple stimuli, avoiding noise due to complexity. We demonstrate the latter in a simple experiment where we find that three assumptions about ambiguity, commonly made in AA theories, are violated: reference independence, universal ambiguity aversion, and weak certainty independence. The second, theoretical, part of the paper accommodates the violations found for the first ambiguity theory in the AA model—Schmeidler’s CEU theory—by introducing and axiomatizing a reference dependent generalization. That is, we extend the AA ambiguity model to prospect theory