Uncertainty aversion and aversion to increasing uncertainty

According to the original Ellsberg (1961) examples there is uncertainty version if the decision maker prefers to bet on an urn of known composition rather than on an urn of unknown composition. According to another definition (Schmeidler, 1989), there is uncertainty aversion if any convex combination of two acts is preferred to the least favorable of these acts. We show that these two definitions differ: while the first one truly refers to uncertainty aversion, the second one refers to aversion to increasing uncertainty. Besides, with reference to Choquet Expected Utility theory, uncertainty aversion means that there exists the core of a capacity, while aversion to increasing uncertainty means that the capacity is convex. Consequently, aversion to increasing uncertainty implies uncertainty aversion, but the opposite does not hold. We also show that a completely analogous situation holds for the case of risk and we define a set of risk and uncertainty premiums according to the previous analysis.     

An Experiment on Rational Insurance Decisions

We describe the results of an experiment on decision making in an insurance context. The experiment was designed to test for the underlying rationality of insurance consumers, where rationality is understood in usual economic terms. In particular, using expected utility as the preference function, we test for positive marginal utility, risk aversion, and decreasing absolute risk aversion, all of which are normal postulates for any microeconomic decision context under uncertainty or risk. We find that there the discrepancy from rational decision making increases with the sophistication of the rationality criteria, that irrationality concerning fair premium contracts is uncharacteristically high, and that the slope of absolute risk aversion seems to depend on the format of the insurance contract. This revised version was published online in June 2006 with corrections to the Cover Date.     

Dynamically Consistent Preferences with Quadratic Beliefs

This article characterizes a family of preference relations over uncertain prospects that (a) are dynamically consistent in the Machina sense and, moreover, for which the updated preferences are also members of this family and (b) can simultaneously accommodate Ellsberg- and Allais-type paradoxes.Replacing the "mixture independence" axiom by "mixture symmetry" proposed by Chew, Epstein, and Segal (1991) for decision making under objective risk, and requiring that for some partition of the state space the agent perceives ambiguity and so prefers a randomization over outcomes across that partition (proper uncertainty aversion), preferences can be represented by a (proper) quadratic functional. This representation may be further refined to allow a separation between the quantification of beliefs and risk preferences that is closed under dynamically consistent updating.     

Measuring ambiguity attitude: (Extended) multiplier preferences for the American and the Dutch population

Empirical studies of ambiguity aversion often use measures that are not grounded in theory. This paper shows how a theoretically-founded measure of ambiguity aversion can be derived from Hansen and Sargent’s theory of multiplier preferences. Multiplier preferences are used in macroeconomics to capture model uncertainty. At the micro level, they have not been applied yet, because they do not permit ambiguity seeking, which is usually observed for a substantial proportion of subjects. We give a preference foundation for (extended) multiplier preferences accommodating both ambiguity aversion and ambiguity seeking and we propose a simple method to measure them using matching probabilities. We illustrate our method in two large representative samples (Dutch and American) and obtain the first micro estimates of multiplier preferences.     

Ambiguity aversion and the propensities for self-insurance and self-protection

Two models of ambiguity preferences that permit comparative statics analysis of greater ambiguity aversion yield definite predictions concerning propensities for self-insurance and self-protection: The levels of both activities that are optimal for an ambiguity-averse decision maker are higher in the presence of ambiguity than in its absence, and demands for both activities increase with greater ambiguity aversion. The reason is that, at levels optimal for one decision maker, an increase in either activity results in a mean-preserving contraction in the distribution of expected utility in the presence of ambiguity, which is valuable to anyone with the same risk preferences who is more ambiguity averse.     

Risk Premiums and Benefit Measures for Generalized-Expected-Utility Theories

Standard tools for the analysis of economic problems involving uncertainty, including risk premiums, certainty equivalents and the notions of absolute and relative risk aversion, are developed without making specific assumptions on functional form beyond the basic requirements of monotonicity, transitivity, continuity, and the presumption that individuals prefer certainty to risk. Individuals are not required to display probabilistic sophistication. The approach relies on the distance and benefit functions to characterize preferences relative to a given state-contingent vector of outcomes. The distance and benefit functions are used to derive absolute and relative risk premiums and to characterize preferences exhibiting constant absolute risk aversion (CARA) and constant relative risk aversion (CRRA). A generalization of the notion of Schur-concavity is presented. If preferences are generalized Schur concave, the absolute and relative risk premiums are generalized Schur convex, and the certainty equivalents are generalized Schur concave.     

Ellsberg paradox: Ambiguity and complexity aversions compared

We present a simple model where preferences with complexity aversion, rather than ambiguity aversion, resolve the Ellsberg paradox. We test our theory using laboratory experiments where subjects choose among lotteries that “range” from a simple risky lottery, through risky but more complex lotteries, to one similar to Ellsberg’s ambiguity urn. Our model ranks lotteries according to their complexity and makes different—at times contrasting—predictions than most models of ambiguity in response to manipulations of prizes. The results support that complexity aversion preferences play an important and separate role from beliefs with ambiguity aversion in explaining behavior under uncertainty.     

Relative Risk Aversion: What Do We Know?

The relative risk aversion measure that represents the risk preferences of a decision maker depends on the outcome variable that is used as the argument of the utility function, and on the way that outcome variable is defined or measured. In addition, the relationship between any two such relative risk aversion measures is determined by the relationship between the corresponding outcome variables. These well-known facts are used to adjust several reported estimates of relative risk aversion so that those estimates can be directly compared with one another. After adjustment, the significant variation in the reported relative risk aversion measures for representative decision makers is substantially reduced. JEL Classification: D81     

Ambiguity aversion and familiarity bias: Evidence from behavioral and gene association studies

It is increasingly recognized that decision making under uncertainty depends not only on probabilities, but also on psychological factors such as ambiguity and familiarity. Using 325 Beijing subjects, we conduct a neurogenetic study of ambiguity aversion and familiarity bias in an incentivized laboratory setting. For ambiguity aversion, 49.4% of the subjects choose to bet on the 50–50 deck despite the unknown deck paying 20% more. For familiarity bias, 39.6% choose the bet on Beijing’s temperature rather than the corresponding bet with Tokyo even though the latter pays 20% more. We genotype subjects for anxiety-related candidate genes and find a serotonin transporter polymorphism being associated with familiarity bias, but not ambiguity aversion, while the dopamine D5 receptor gene and estrogen receptor beta gene are associated with ambiguity aversion only among female subjects. Our findings contribute to understanding of decision making under uncertainty beyond revealed preference.     

Conditioning Capacities and Choquet Integrals: The Role of Comonotony

Choquet integrals and capacities play a crucial role in modern decision theory. Comonotony is a central concept for these theories because the main property of a Choquet integral is its additivity for comonotone functions. We consider a Choquet integral representation of preferences showing uncertainty aversion (pessimism) and propose axioms on time consistency which yield a candidate for conditional Choquet integrals. An other axiom characterizes the role of comonotony in the use of information. We obtain two conditioning rules for capacities which amount to the well-known Bayes' and Dempster–Schafer's updating rules. We are allowed to interpret both of them as a lack of confidence in information in a dynamic extension of pessimism. This revised version was published online in June 2006 with corrections to the Cover Date.     

A variational model of preference under uncertainty

A familiar example devised by Daniel Ellsberg to highlight the effects of event ambiguity on preferences is transformed to separate aleatory uncertainty (chance) from epistemic uncertainty. The transformation leads to a lottery acts model whose states involve epistemic uncertainty; aleatory uncertainty enters into the statedependent lotteries. The model proposes von Neumann-Morgenstern utility for lotteries, additive subjective probability for states, and the use of across-states standard deviation weighted by a coefficient of aversion to variability to account for departures from Anscombe-Aumann subjective expected utility. Properties of the model are investigated and a partial axiomatization is provided.     

Take-up for genetic tests and ambiguity

Under the expected utility hypothesis a costless genetic test has, at worst, zero private value. This happens if it does not affect optimal decisions. If the genetic test facilitates better decision-making for at least one possible test outcome, then it has positive private value. This theoretical result seems to contradict the fact that empirically observed take-up rates for genetic tests are surprisingly low. We demonstrate that if individuals display ambiguity aversion, a costless genetic test that does not affect optimal decisions is never taken. Furthermore, there is a trade-off between aversion against uncertainty of test results and utility gains from better decision-making if optimal decisions depend on the level of information. The reason is that, from an ex-ante view, a genetic test introduces uncertainty of probabilities which diminishes the value of information to an ambiguity-averse decision-maker. Ambiguity aversion regarding test results thus provides an explanation for low take-up rates for genetic tests.     

Ambiguity Aversion in the Field of Insurance: Insurers’ Attitude to Imprecise and Conflicting Probability Estimates

This article presents the results of a survey designed to test, with economically sophisticated participants, Ellsberg’s ambiguity aversion hypothesis, and Smithson’s conflict aversion hypothesis. Based on an original sample of 78 professional actuaries (all members of the French Institute of Actuaries), this article provides empirical evidence that ambiguity (i.e. uncertainty about the probability) affect insurers’ decision on pricing insurance. It first reveals that premiums are significantly higher for risks when there is ambiguity regarding the probability of the loss. Second, it shows that insurers are sensitive to sources of ambiguity. The participants indeed, charged a higher premium when ambiguity came from conflict and disagreement regarding the probability of the loss than when ambiguity came from imprecision (imprecise forecast about the probability of the loss). This research thus documents the presence of both ambiguity aversion and conflict aversion in the field of insurance, and discuses economic and psychological rationales for the observed behaviours.     

The impact of risk attitude,uncertainty and disequilibria on optimal production and inventory

Summary The empirical facts seem to indicate that in real economies the effect of uncertainty tends to decrease production. The limitations of empirical investigations presented should be stressed: they were performed mainly on an aggregate level, they mainly refer to Austrian manufacturing, they rely heavily on questionnaires. Above all empirical investigation will never be able to decide normative questions or to explain the behavior in the general equilibrium. Nevertheless in the short run, given all the rigidities and disequilibria which exist, uncertainty tends to lower optimal production even in absence of risk aversion. Risk aversion becomes important for large, for once-for-all decisions, but it is not the only channel through which uncertainty changes decisions.Technological concavity created by concave marginal revenues or by convex marginal costs, marginal costs of uncertainty in disequilibria model or asymmetric costs of revisions of the preliminary decision are able to bias the decision downward in a real world economy without invokingPaper presented to the 2nd Conference on the Foundations of Risk and Utility (FUR), Venezia, 1984.     

Joint measurement of risk aversion,prudence, and temperance

Risk aversion—but also the higher-order risk preferences of prudence and temperance—are fundamental concepts in the study of economic decision making. We propose a method to jointly measure the intensity of risk aversion, prudence, and temperance. Our theoretical approach is to define risk compensations of different orders, and in an experiment we elicit these compensations with a price list technique. We find evidence for risk aversion, prudence, and temperance. These traits correlate within subjects. The compensations elicited for prudence are significantly larger than those for risk aversion and temperance. In contrast to commonly used utility functions, prospect theory can predict this behavioral pattern. In our experiment, risk-averse, risk-loving, and risk-neutral subjects are prudent. This supports a recent theoretical observation that prudence may be a more universal trait than previously realized.     

Judged knowledge and ambiguity aversion

Competence has recently been proposed as an explanation for the degree of ambiguity aversion. Using general knowledge questions we presented subjects with simple lotteries in which they could bet on an event and against the same event. We show that the sum of certainty equivalents for both bets depends on the judged knowledge of the class of events. We also elicited the decision weights for events and complementary events. We found a similar effect of knowledge on the sum of decision weights.     

Nontransitive preferences in decision theory

Intransitive preferences have been a topic of curiosity, study, and debate over the past 40 years. Many economists and decision theorists insist on transitivity as the cornerstone of rational choice, and even in behavioral decision theory intransitivities are often attributed to faulty experiments, random or sloppy choices, poor judgment, or unexamined biases. But others see intransitive preferences as potential truths of reasoned comparisons and propose representations of preferences that accommodate intransitivities. This article offers a partial survey of models for intransitive preferences in a variety of decisional contexts. These include economic consumer theory, multiattribute utility theory, game theory, preference between time streams, and decision making under risk and uncertainty. The survey is preceded by a discussion of issues that bear on the relevance and reasonableness of intransitivity.     

Regret aversion in reason-based choice

This research examines the moderating role of regret aversion in reason-based choice. Earlier research has shown that regret aversion and reason-based choice effects are linked through a common emphasis on decision justification, and that a simple manipulation of regret salience can eliminate the decoy effect, a well-known reason-based choice effect. We show here that the effect of regret salience varies in theory-relevant ways from one reason-based choice effect to another. For effects such as the select/reject and decoy effect, both of which were independently judged to be unreasonable bases for deciding, regret salience eliminated the effect. For the most-important attribute effect that is judged to be normatively acceptable, however, regret salience amplified the effect. Anticipated self-blame regret and perceived decision justifiability consistently predicted preferences and thus offer a parsimonious account of both attenuation and amplification of these reason-based choice effects.     

Economic consequences of Nth-degree risk increases and Nth-degree risk attitudes

We study comparative statics of Nth-degree risk increases within a large class of problems that involve bidimensional payoffs and additive or multiplicative risks. We establish necessary and sufficient conditions for unambiguous impact of Nth-degree risk increases on optimal decision making. We develop a simple and intuitive approach to interpret these conditions : novel notions of directional Nth-degree risk aversion that are characterized via preferences over lotteries.