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"

Ellsberg Paradox and Second-order Preference Theories on Ambiguity: Some New Experimental Evidence

We study the two-color problem by Ellsberg (1961) with the modification that the decision maker draws twice with replacement and a different color wins in each draw. The 50-50 risky urn turns out to have the highest risk conceivable among all prospects including the ambiguous one, while all feasible color distributions are mean-preserving spreads to one another. We show that the well-known second-order sophisticated theories like MEU, CEU, and REU as well as Savage’s first-order theory of SEU share the same predictions in our design, for any first-order risk attitude. Yet, we observe that substantial numbers of subjects violate the theory predictions even in this simple design

The effect of elicitation methods on ambiguity aversion: an experimental investigation

In this paper we elicit preferences for the classical three-color Ellsberg Paradax employing three different methods, choices, minimal selling prices and maximal buying prices. The resulting data reveal a high frequency of preference reversals which have not been analyzed before in choice under uncertainty. Moreover, we analyze the effect of elicitation methods on the degree of ambiguity aversion. While there is no apparent difference in the attitude towards ambiguity between selling and buying prices we observe a rather distinct pattern of behavior for choices: Compared to choices, eliciting preferences by pricing tasks decreases the number of subjects being ambiguity averse in both tasks and increases the number of subjects being ambiguity neutral or prone. We argue that this difference between pricing and choice supports the hypothesis of comparative ignorance.Ellsberg Paradox, ambiguity aversion, preference reversal, comparative ignorance

Decision theory under uncertainty

We review recent advances in the field of decision making under uncertainty or ambiguity.Ambiguity ; ambiguity aversion ; uncertainty ; decision

Ambiguity aversion as a reason to choose tournaments

We test the implications of ambiguity aversion in a principal-agent problem with multiple agents. When output distributions are uncertain, models of ambiguity aversion suggest that tournaments may become more attractive than independent wage contracts, in contrast to the case where output distributions are known. We do so by presenting agents with a choice between tournaments and independent contracts, which are designed in a way that under uncertainty about output distribution (that is, under ambiguity), ambiguity averse agents should typically prefer tournaments, while ambiguity neutral agents prefer independent contracts, independent of their degree of risk aversion. This is the case, because the tournament removes all ambiguity about the equilibrium wages. We compare the share of participants who choose the tournament under ambiguity with the share of participants choosing the tournament in a control treatment, where output distributions are know. As the theory predicts, we find indeed that under ambiguity the share of agents who choose the tournaments is higher than in the case of known output distributions.Ambiguity aversion, tournaments, Ellsberg urn, contract design

A Quantum Cognition Analysis of the Ellsberg Paradox

The 'expected utility hypothesis' is one of the foundations of classical approaches to economics and decision theory and Savage's 'Sure-Thing Principle' is a fundamental element of it. It has been put forward that real-life situations exist, illustrated by the 'Allais' and 'Ellsberg paradoxes', in which the Sure-Thing Principle is violated, and where also the expected utility hypothesis does not hold. We have recently presented strong arguments for the presence of a double layer structure, a 'classical logical' and a 'quantum conceptual', in human thought and that the quantum conceptual mode is responsible of the above violation. We consider in this paper the Ellsberg paradox, perform an experiment with real test subjects on the situation considered by Ellsberg, and use the collected data to elaborate a model for the conceptual landscape surrounding the decision situation of the paradox. We show that it is the conceptual landscape which gives rise to a violation of the Sure-Thing Principle and leads to the paradoxical situation discovered by Ellsberg.Comment: 11 page

Ambiguity and uncertainty in Ellsberg and Shackle

This paper argues that Ellsberg’s and Shackle’s frameworks for discussing the limits of the (subjective) probabilistic approach to decision theory are not as different as they may appear. To stress the common elements in their theories Keynes’s Treatise on Probability provides an essential starting point. Keynes’s rejection of well-defined probability functions, and of maximisation as a guide to human conduct, is shown to imply a reconsideration of what probability theory can encompass, that is in the same vein of Ellsberg’s and Shackle’s concern in the years of the consolidation of Savage’s new probabilistic mainstream. The parallel between Keynes and the two decision theorists is drawn by means of a particular assessment of Shackle’s theory of decision, namely, it is interpreted in the light of Ellsberg’s doctoral dissertation. In this thesis, published only as late as 2001, Ellsberg developed the details and devised the philosophical background of his criticism of Savage as first put forward in the famed 1961 QJE article. The paper discusses the grounds on which the ambiguity surrounding the decision maker in Ellsberg’s urn experiment can be deemed analogous to the uncertainty faced by Shackle’s entrepreneur taking “unique decisions.” The paper argues also that the insights at the basis of the work of both Shackle and Ellsberg, as well as the criteria for decision under uncertainty they put forward, are relevant to understand the development of modern decision theory.uncertainty, weight of argument, non-additive probability

Shunning Uncertainty: The Neglect of Learning Opportunities

Financial, managerial, and medical decisions often involve alternatives whose possible outcomes have uncertain probabilities. In contrast to alternatives whose probabilities are known, these uncertain alternatives offer the benefits of learning. In repeat-choice situations, such learning brings value. If probabilities appear favorable (unfavorable), a choice can be repeated (avoided). In a series of experiments involving bets on the colors of poker chips drawn from bags, decision makers often prove to be blind to the learning opportunities offered by uncertain probabilities. Such decision makers violate rational decision making and forgo significant expected payoffs when they shun uncertain alternatives in favor of risky ones. Worse, when information is revealed, many make choices contrary to learning. A range of factors explain these violations. The results indicate that priming with optimal strategies offers little improvement.

Ambiguity

Ambiguity refers to a decision situation under uncertainty when there is incomplete information about the likelihood of events. Different formal models of this notion have been developed with differing implications about the representation of ambiguity and ambiguity aversion.uncertainty, ambiguity, ambiguity attitude