Education and anomalies in decision making: Experimental evidence from Chinese adult twins

We estimate the effects of education on two dimensions of decision making behavior—risk and time—beyond those considered to be normal-ranged to encompass behavioral anomalies with respect to expected utility as well as time consistency. We conduct a number of incentivized choice experiments on Chinese adult twins to measure decision making behavior, and use a within-twin-pair fixed-effects estimator to deal with unobservable family-specific effects. The estimation results show that a higher education level tends to reduce the degree of risk aversion towards moderate prospects, moderate hazards, and longshot prospects. For anomalies under risk and uncertainty, college graduates exhibit significantly more Allais-type behavior compared to high school dropouts, while high school graduates exhibit more ambiguity aversion as well as a familiarity preference relative to high school dropouts. For decision making involving time, a higher education level tends to reduce the degree of impatience, and to reduce behavioral anomalies including hyperbolic discounting, dread, and hopefulness. The experimental observations suggest that people with a higher education level tend to exhibit more behavioral anomalies in risk attitudes but fewer behavioral anomalies involving time, hence implying that education has multi-functions in preference formation and human capability building. This study contributes to the understanding of the nature of these behavioral anomalies and the roles of education in human decision making.     

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.     

Stake effects on ambiguity attitudes for gains and losses

We test the effect of stake size on ambiguity attitudes. Compared to a baseline condition, we find subjects to be more ambiguity seeking for small-probability gains and large-probability losses under high stakes. They are also more ambiguity averse for large-probability gains and small-probability losses. We trace these effects back to stake effects on decisions under risk (known probabilities) and uncertainty (unknown probabilities). For risk, we replicate previous findings. For uncertainty, we find an increase in probabilistic insensitivity under high stakes that is driven by increased uncertainty aversion for large-probability gains and for small-probability losses.     

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.     

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.     

Recursive expected utility and the separation of attitudes towards risk and ambiguity: an experimental study

We use the multiple price list method and a recursive expected utility theory of smooth ambiguity to separate out attitude towards risk from that towards ambiguity. Based on this separation, we investigate if there are differences in agent behaviour under uncertainty over gain amounts vis-a-vis uncertainty over loss amounts. On an aggregate level, we find that (i) subjects are risk averse over gains and risk seeking over losses, displaying a “reflection effect” and (ii) they are ambiguity neutral over gains and are mildly ambiguity seeking over losses. Further analysis shows that on an individual level, and with respect to both risky and ambiguous prospects, there is limited incidence of a reflection effect where subjects are risk/ambiguity averse (seeking) in gains and seeking (averse) in losses, though this incidence is higher for ambiguous prospects. A very high proportion of such cases of reflection exhibit risk (ambiguity) aversion in gains and risk (ambiguity) seeking in losses, with the reverse effect being significantly present in the case of risk but almost absent in case of ambiguity. Our results suggest that reflection across gains and losses is not a stable individual characteristic, but depends upon whether the form of uncertainty is precise or ambiguous, since we rarely find an individual who exhibits reflection in both risky and ambiguous prospects. We also find that correlations between attitudes towards risk and ambiguity were domain dependent.      

Do ambiguity avoidance and the comparative ignorance hypothesis depend on people’s affective reactions?

Previous work has showed that people are averse to ambiguity and prefer to bet on known probabilities over unknown probabilities. There is also evidence that ambiguity aversion is stronger in comparative contexts rather than in non-comparative contexts. In the present paper we suggest that ambiguity aversion depends on people’s affective reactions and therefore the effect is more evident in comparative contexts because the comparison between the clear and ambiguous alternatives leads to more positive affective reactions toward the former rather than the latter. The present study extends the previous findings while, at the same time, supporting the “comparative ignorance hypothesis”.     

The Likelihood Method for Decision under Uncertainty

This paper introduces the likelihood method for decision under uncertainty. The method allows the quantitative determination of subjective beliefs or decision weights without invoking additional separability conditions, and generalizes the Savage–de Finetti betting method. It is applied to a number of popular models for decision under uncertainty. In each case, preference foundations result from the requirement that no inconsistencies are to be revealed by the version of the likelihood method appropriate for the model considered. A unified treatment of subjective decision weights results for most of the decision models popular today. Savage’s derivation of subjective expected utility can now be generalized and simplified. In addition to the intuitive and empirical contributions of the likelihood method, we provide a number of technical contributions: We generalize Savage’s nonatomiticy condition (“P6”) and his assumption of (sigma) algebras of events, while fully maintaining his flexibility regarding the outcome set. Derivations of Choquet expected utility and probabilistic sophistication are generalized and simplified similarly. The likelihood method also reveals a common intuition underlying many other conditions for uncertainty, such as definitions of ambiguity aversion and pessimism.     

Risk,ambiguity, and insurance

In a series of experiments, economically sophisticated subjects, including professional actuaries, priced insurance both as consumers and as firms under conditions of ambiguity. Findings support implications of the Einhorn-Hogarth ambiguity model: (1) For low probability-of-loss events, prices of both consumers and firms indicated aversion to ambiguity; (2) As probabilities of losses increased, aversion to ambiguity decreased, with consumers exhibiting ambiguity preference for high probability-of-loss events; and (3) Firms showed greater aversion to ambiguity than consumers. The results are shown to be incompatible with traditional economic analysis of insurance markets and are discussed with respect to the effects of ambiguity on the supply and demand for insurance.University of Chicago Graduate School of BusinessUniversity of Pennsylvania The Wharton School     

Uncertainty Aversion Vs. Competence: An Experimental Market Study

Heath and Tversky (1991, Journal of Risk and Uncertainty 4:5–28) posed that reaction to ambiguity is driven by perceived competence. Competence effects may be inconsistent with ambiguity aversion if betting on own judgement is preferred to betting on a chance event, because judgemental probabilities are more ambiguous than chance events. This laboratory experiment analyses whether ambiguity affects prices and volumes in a double auction market, and contrasts ambiguity aversion to competence effects. In order to test for the presence of competence effects, in the experiment uncertainty is tied to the realisation of events about which the decision maker is more or less knowledgeable. Two experiments are presented: in the first, knowledge is exogenous, whereas in the second the knowledge judgement is endogenous. Market prices provide evidence in favour of the competence hypothesis only when competence is self-assessed. Comparable volumes are observed in both experiments.      

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.     

The Aversion to the Sequential Resolution of Uncertainty

This paper sets forth and offers an explanation for preferences for the form of the timing of resolution of uncertainty; namely for uncertainty to be resolved all at one time rather than sequentially. The explanation is based on a weakening of the independence axiom, in particular on the notion of disappointment aversion developed in Gul's (1991) axiomatic model of preferences. Implications of this aversion are discussed for issues in finance, intertemporal decision making under uncertainty, high stakes risky situations and consumer self-regulation. The analysis encourages a formulation of preferences over all attributes of interest to the decision maker, including psychological satisfaction.     

How much ambiguity aversion?

Experimental results on the Ellsberg paradox typically reveal behavior that is commonly interpreted as ambiguity aversion. The experiments reported in the current paper find the objective probabilities for drawing a red ball that make subjects indifferent between various risky and uncertain Ellsberg bets. They allow us to examine the predictive power of alternative principles of choice under uncertainty, including the objective maximin and Hurwicz criteria, the sure-thing principle, and the principle of insufficient reason. Contrary to our expectations, the principle of insufficient reason performed substantially better than rival theories in our experiment, with ambiguity aversion appearing only as a secondary phenomenon.     

Subjectively weighted linear utility

An axiomatized theory of nonlinear utility and subjective probability is presented in which assessed probabilities are allowed to depend on the consequences associated with events. The representation includes the expected utility model as a special case, but can accommodate the Ellsberg paradox and other types of ambiguity sensitive behavior, while retaining familiar properties of subjective probability, such as additivity for disjoint events and multiplication of conditional probabilities. It is an extension, to the states model of decision making under uncertainty, of Chew's weighted linear utility representation for decision making under risk.     

Effects of Outcome and Probabilistic Ambiguity on Managerial Choices

Information ambiguity is prevalent in organizations and likely influences management decisions. This study examines, given imprecise probabilities and outcomes, how managers make choices when they are provided with single-figure benchmarks. Seventy-nine MBA students completed two experiments. We found that, in a decision framed as a decision under certainty involving an ambiguous outcome, the majority of the subjects were ambiguity prone in the loss condition and switched to ambiguity aversion in the gain condition. However, in the presence of probabilistic ambiguity in a decision under risk, this expected switching pattern was shown only when the difference in riskiness between the two choice options (in the loss condition) was perceived to be relatively small. In a companion study, we used a written protocol approach to identify factors that affect decision makers' investment choices when faced with ambiguous outcomes. Protocols frequently mentioned that the ambiguous outcome option was risky, even in the case which was framed as a decision under certainty in the problem statement. In a decision under risk with ambiguous outcomes, the combination of probabilistic risk and outcome ambiguity was seen as even more risky.     

The hot hand belief and the gambler’s fallacy in investment decisions under risk

We conduct experiments to analyze investment behavior in decisions under risk. Subjects can bet on the outcomes of a series of coin tosses themselves, rely on randomized ‘experts’, or choose a risk-free alternative. We observe that subjects who rely on the randomized experts pick those who were successful in the past, showing behavior consistent with the hot hand belief. Obviously the term ‘expert’ suffices to attract some subjects. For those who decide on their own, we find behavior consistent with the gambler’s fallacy, as the frequency of betting on heads (tails) decreases after streaks of heads (tails).     

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.     

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.     

Learning-by-doing in an ambiguous environment

How well do revealed ambiguity preferences predict how people choose to seek new information about uncertain events? In an economics experiment, we apply a new instrument to measure ambiguity preferences, and in a later session observe to what extent the measure predicts the choice to receive costly information in a learning-by-doing game. Ambiguity averse subjects are more willing to pay to receive information, while risk averse subjects are not. Holding ambiguity preferences constant, risk averse subjects tend to perform worse than risk loving subjects. The returns to experimentation, especially for ambiguity averse subjects, suggest a not-well studied but important role that ambiguity preferences play in decision-making under uncertainty.