Ambiguous Lotteries Research Articles

Delayed risk in individual and social decisions

This paper studies temporal-distance effects on individual and social risks, testing Construal Level Theory. We elicit WTPs for risky and ambiguous lotteries and vary the timing (immediately vs. in two weeks) when the uncertainty is resolved. Subjects have lower WTPs for longshots than for safer lotteries. Under ambiguity, this gap decreases with temporal distance. Subjects are ambiguity averse, which becomes less pronounced when low-probability lotteries are processed in the future. In a trust game, we study temporal-distance effects on social risks. Time distance lowers trust as trustors correctly anticipate that reciprocity is lower when trustees decide in the future.

Body in the face of uncertainty: The role of autonomic arousal and interoception in decision-making under risk and ambiguity.

Influential theories posit that bodily responses are important for decision-making under uncertainty. However, the evidence of the role of our ability to perceive subtle bodily changes (interoception) in decision-making under uncertainty is mixed. These differences may arise from the fact that uncertainty, a part of daily decision-making, can be fractionated into risk (known probabilities) and ambiguity (unknown probabilities). Here we examine the role of arousal and interoception in shaping risky and ambiguous decisions. We measured skin conductance responses and heart rate changes while participants (N=40) made gambling decisions in the context of risky and ambiguous lotteries. Results reveal that the anticipation phase produced the largest arousal responses, suggesting that the anticipation is a major contributor to arousal during gambling behavior, regardless of the uncertainty type. Moreover, physiological responses were higher following positive outcomes than negative outcomes. We did not find any direct relation between interoceptive dimensions and the attitudes toward risk and ambiguity. However, in those with higher interoceptive accuracy, skin conductance responses differentiated between risk and ambiguity as well as between the gamble phases (decision, anticipation, and outcome). Together, our findings demonstrate that decision-making under uncertainty is to some extent associated with individual differences in the ability both to generate and to perceive accurately subtle changes in bodily arousal during the decision-making process. However, these changes seem to be moderately related to the type of uncertainty (risk or ambiguity).

Non-human primates use combined rules when deciding under ambiguity.

Decision outcomes in unpredictable environments may not have exact known probabilities. Yet the predictability level of outcomes matters in decisions, and animals, including humans, generally avoid ambiguous options. Managing ambiguity may be more challenging and requires stronger cognitive skills than decision-making under risk, where decisions involve known probabilities. Here we compare decision-making in capuchins, macaques, orangutans, gorillas, chimpanzees and bonobos in risky and ambiguous contexts. Subjects were shown lotteries (a tray of potential rewards, some large, some small) and could gamble a medium-sized food item to obtain one of the displayed rewards. The odds of winning and losing varied and were accessible in the risky context (all rewards were visible) or partially available in the ambiguous context (some rewards were covered). In the latter case, the level of information varied from fully ambiguous (individuals could not guess what was under the covers) to predictable (individuals could guess). None of the species avoided gambling in ambiguous lotteries and gambling rates were high if at least two large rewards were visible. Capuchins and bonobos ignored the covered items and gorillas and macaques took the presence of potential rewards into account, but only chimpanzees and orangutans could consistently build correct expectations about the size of the covered rewards. Chimpanzees and orangutans combined decision rules according to the number of large visible rewards and the level of predictability, a process resembling conditional probabilities assessment in humans. Despite a low sample size, this is the first evidence in non-human primates that a combination of several rules can underlie choices made in an unpredictable environment. Our finding that non-human primates can deal with the uncertainty of an outcome when exchanging one food item for another is a key element to the understanding of the evolutionary origins of economic behaviour. This article is part of the theme issue 'Existence and prevalence of economic behaviours among non-human primates'.

Learning about the Ellsberg Paradox reduces, but does not abolish, ambiguity aversion.

Ambiguity aversion-the tendency to avoid options whose outcome probabilities are unknown-is a ubiquitous phenomenon. While in some cases ambiguity aversion is an adaptive strategy, in many situations it leads to suboptimal decisions, as illustrated by the famous Ellsberg Paradox. Behavioral interventions for reducing ambiguity aversion should therefore be of substantial practical value. Here we test a simple intervention, aimed at reducing ambiguity aversion in an experimental design, where aversion to ambiguity leads to reduced earnings. Participants made a series of choices between a reference lottery with a 50% chance of winning $5, and another lottery, which offered more money, but whose outcome probability was either lower than 50% (risky lottery) or not fully known (ambiguous lottery). Similar to previous studies, participants exhibited both risk and ambiguity aversion in their choices. They then went through one of three interventions. Two groups of participants learned about the Ellsberg Paradox and their own suboptimal choices, either by actively calculating the objective winning probability of the ambiguous lotteries, or by observing these calculations. A control group learned about base-rate neglect, which was irrelevant to the task. Following the intervention, participants again made a series of choices under risk and ambiguity. Participants who learned about the Ellsberg Paradox were more tolerant of ambiguity, yet ambiguity aversion was not completely abolished. At the same time, these participants also exhibited reduced aversion to risk, suggesting inappropriate generalization of learning to an irrelevant decision domain. Our results highlight the challenge for behavioral interventions: generating a strong, yet specific, behavioral change.

\u201cBetting on nature\u201d or \u201cbetting on others\u201d: anti-coordination induces uniquely high levels of entropy

Uncertainty in the form of risk or ambiguity can arise from the interaction with nature and other players, while strategic uncertainty arises only in interactions with others. Here, we systematically compare binary decisions between a safe option and a potentially higher paying but uncertain option in four experimental conditions with the same potential monetary outcomes: coordination vs. anti coordination games, as well as risky and ambiguous lotteries. In each condition, we progressively increase the value of the safe option and measure subjects’ certainty equivalents (i.e., the specific safe payoff-threshold that makes a subject indifferent between the two options). We find that anti-coordination games and ambiguous lotteries elicit equally high aversion to uncertainty, relative to the other domains. In spite of this similarity, we find that subjects alternate between the safe and uncertain options much more frequently, thus displaying higher entropy, under anti-coordination relative to any of the other environments. These differences are predicted by theories of recursive reasoning in strategic games (e.g., thinking what others think we think etc.). Indeed, this can occur when interacting with intentional counterparts, but not with nature.

Does exposure to unawareness affect risk preferences? A preliminary result

One fundamental assumption often made in the literature on unawareness is that risk preferences are invariant to changes of awareness. We study how exposure to unawareness affects choices under risk. Participants in our experiment choose repeatedly between varying sure outcomes and a lottery in three phases. All treatments are exactly identical in phase 1 and phase 3, but differ in phase 2. There are five different treatments pertaining to the lottery faced in phase 2: The control treatment (i.e., a standard lottery), the treatment with awareness of unawareness of lottery outcomes but known number of outcomes, the treatment with awareness of unawareness of outcomes but with unknown number of outcomes, the treatment with unawareness of unawareness of some outcomes, and the treatment with an ambiguous lottery. We study both whether behavior differs in phase 3 across treatments (between subjects effect) and whether differences of subjects’ behavior between phases 1 and phase 3 differ across treatments (within subject effects). We observe no significant treatment effects.

Does Exposure to Unawareness Affect Risk Preferences? A Preliminary Result

One fundamental assumption often made in the literature on unawareness is that risk preferences are invariant to changes of awareness. We study how exposure to unawareness affects choices under risk. Participants in our experiment choose repeatedly between varying sure outcomes and a lottery in 3 phases. All treatments are exactly identical in phase 1 and phase 3, but differ in phase 2. There are five different treatments pertaining to the lottery faced in phase 2: The control treatment (i.e., a standard lottery), the treatment with awareness of unawareness of lottery outcomes but known number of outcomes, the treatment with awareness of unawareness of outcomes but with unknown number of outcomes, the treatment with unawareness of unawareness of some outcomes, and the treatment with an ambiguous lottery. We study both whether behavior differs in phase 3 across treatments (between subjects effect) and whether differences of subjects' behavior between phases 1 and phase 3 differs across treatments (within subject effects). We observe no significant treatment effects.

Impact of Non Professional Physicians' Characteristics on Medical Decision Making in Older Patients with Acute Myeloid Leukemia

Frontline therapy for newly diagnosed AML in older adults can be classified as "more" or "less" intensive. Assignment of patients (pts) to intensive chemotherapy (ICT) or low-intensity therapy (LIT) such as hypomethylating agents (HMA), low-dose aracytine (LDAC) or best supportive care (BSC), should be based on patient- and disease-related prognosis factors. Although scoring systems have been proposed to rationalize this clinical decision-making, there is a strong heterogeneity in clinical practice. Cancer management study mainly focused on patients' determinants of care but very few have assessed the influence of physicians' characteristics and none in AML. In behavioral sciences, attitudes towards risk and ambiguity are psychological traits that may explain medical choices. These traits are connected with theoretical models of decision under uncertainty that can be divided in Expected Utility (EU) and Non-Expected Utility (Non-EU) models where the former is often considered as a benchmark of "economic rationality". Choice patterns in decision task known as Allais paradox allow classifying individuals in these two classes of models. In addition, behavioral consequences when the probabilities of uncertain events are unknown are defined as ambiguity attitudes.Our study investigated the impact of physician's characteristics on their medical decisions regarding 6 clinical vignettes of older AML pts that highlight distinct and difficult situations derived from clinical practice.Physicians’ demographical and occupational characteristics were collected through a national cross-sectional web survey among French hematologists. We categorized physicians as EU or non-EU using their responses to the binary lottery choice questions of the Allais paradox (Kahneman & Tversky, 1979). A last question elicited a certainty equivalent (sure gain between 0 and 500 euros) of an ambiguous lottery (Abdellaoui & al, 2011) as a proxy of physicians’ ambiguity tolerance.Physicians were asked to decide how to treat (ICT, LIT or BSC) elderly AML pts presented in 6 vignettes (table1). Assessable respondents included those who answered all cases. We used k-means clustering method in order to define clinician's groups with homogeneous pattern of responses to the clinical cases.Among the 230 physicians with assessable answers, the median age was 42 years [standard deviation (SD)± 11.2], 123 were male (54%), 160 were consultant or professor (70%), 166 worked in an academic center (72%), 197 were specialized in hematology (86%), and the mean number of older AML pts treated a year per physician was 20.7 (SD ± 17.1). Regarding the Allais paradox, EU, non-EU and undefined represented respectively 101 (43.9%), 109 (47.3%) and 20 (8.7%) respondents. Regarding ambiguity tolerance, the mean of the certainty equivalent was 241 euros (SD ±136).From the pattern of responses to the vignettes, the K-means clustering yielded two distinct groups identified as (1) clinicians who were more prone to prescribe "more" intensive therapy (ICT), and (2) clinicians who were more prone to prescribe "less" intensive therapy (LIT or BSC).We studied the factors associated with the probability of belonging to the "more intensive" category of physicians. A multivariate model (n=210) on variables identified from the bivariate analyses systematically adjusted for age and gender highlighted the following effects and trend:ambiguity tolerant physicians prescribe significantly less ICT (OR 0.87 [for each 50 euros-increase]; 95%CI, 0.77-0.99, p=0.039), physicians not conforming to expected utility ("economically irrational") recommend more ICT (OR 1.85; 95%CI, 0.92-3.73, p=0.084) and female physicians tend to prescribe less ICT (OR 0.58; 95%CI, 0.28-1.20, p=0.14).Physicians' age, hierarchical status, hospital facility or volume of older AML pts treated a year were not associated with the clusters.Final results of national cross-sectional study performed on French hematologists, show that physicians' attitudes towards risk and ambiguity, i.e. physicians' nonprofessional characteristics, may influence their medical decision making process between "more" and "less" intensive therapy for older AML patients. The extension of this study in different countries is planned to test the cross-cultural robustness of our results and increase our knowledge on psychological traits that could influence physicians' practice. [Display omitted] [Display omitted] DisclosuresMalak:Novartis: Membership on an entity's Board of Directors or advisory committees. Recher:Celgene, Sunesis, Amgen, Novartis, Chugai: Research Funding; Celgene, Sunesis, Amgen, Novartis: Membership on an entity's Board of Directors or advisory committees.

Alcohol reduces aversion to ambiguity.

Several years ago, Cohen et al. (1958) demonstrated that under the influence of alcohol drivers became more risk prone, although their risk perception remained unchanged. Research shows that ambiguity aversion is to some extent positively correlated with risk aversion, though not very highly (Camerer and Weber, 1992). The question addressed by the present research is whether alcohol reduces ambiguity aversion. Our research was conducted in a natural setting (a restaurant bar), where customers with differing levels of alcohol intoxication were offered a choice between a risky and an ambiguous lottery. We found that alcohol reduced ambiguity aversion and that the effect occurred in men but not women. We interpret these findings in terms of the risk-as-value hypothesis, according to which, people in Western culture tend to value risk, and suggest that alcohol consumption triggers adherence to socially and culturally valued patterns of conduct different for men and women.

Testing for Fictive Learning in Decision-Making Under Uncertainty

We conduct two experiments where subjects make a sequence of binary choices between risky and ambiguous binary lotteries. Risky lotteries are defined as lotteries where the relative frequencies of outcomes are known. Ambiguous lotteries are lotteries where the relative frequencies of outcomes are not known or may not exist. The trials in each experiment are divided into three phases: pre-treatment, treatment and post-treatment. The trials in the pre-treatment and post-treatment phases are the same. As such, the trials before and after the treatment phase are dependent, clustered matched-pairs, that we analyze with the alternating logistic regression (ALR) package in SAS. In both experiments, we reveal to each subject the outcomes of her actual and counterfactual choices in the treatment phase. The treatments differ in the complexity of the random process used to generate the relative frequencies of the payoffs of the ambiguous lotteries. In the first experiment, the probabilities can be inferred from the converging sample averages of the observed actual and counterfactual outcomes of the ambiguous lotteries. In the second experiment the sample averages do not converge. If we define fictive learning in an experiment as statistically significant changes in the responses of subjects before and after the treatment phase of an experiment, then we expect fictive learning in the first experiment, but no fictive learning in the second experiment. The surprising finding in this paper is the presence of fictive learning in the second experiment. We attribute this counterintuitive result to apophenia: seeing meaningful patterns in meaningless or random data. A refinement of this result is the inference from a subsequent Chi-squared test, that the effects of fictive learning in the first experiment are significantly different from the effects of fictive learning in the second experiment.

Shadow Probability Theory for Asset Pricing under Ambiguity

Assuming that probabilities (capacities) of events are random, this paper introduces a novel model of decision making under ambiguity, called Shadow probability theory, a generalization of the Choquet expected utility. In this model, probabilities of observable events in a subordinated outcome-space are dominated by second-order unobservable events in a directing probability space. The level of ambiguity, and the decision maker’s attitude toward it, are measured with respect to the directing space. Risk and risk attitude, on the other hand, apply to the subordinated space, as in classical expected utility theory. The desired distinction between preferences and beliefs and between risk and ambiguity is then obtained. A measure of ambiguity is naturally carried over on these settings. The present paper proves that in most cases ambiguity cannot be diversified. Counterintuitively, adding an ambiguous lottery to a portfolio of lotteries usually increases its ambiguity. This result, which implies that full diversification is not always optimal, challenges the common notion in the financial literature that investors should hold a fully diversified portfolio. Using this model of choice, the current paper generalizes the classical asset pricing theory by incorporating ambiguous probabilities. It proposes a well defined ambiguity premium that can be measured empirically.

Revealed Preferences for Risk and Ambiguity

We replicate the essentials of the Huettel et al. (2006) experiment on choice under uncertainty with 30 Yale undergraduates, where subjects make 200 pair-wise choices between risky and ambiguous lotteries. Inferences about the independence of economic preferences for risk and ambiguity are derived from estimation of a mixed logit model, where the choice probabilities are functions of two random effects: the proxies for risk-aversion and ambiguity-aversion.Our principal empirical finding is that we cannot reject the null hypothesis that risk and ambiguity are independent in economic choice under uncertainty. This finding is consistent with the hypothesized independence of the neural mechanisms governing economic choices under risk and ambiguity, suggested by the double dissociation-fMRI study reported in Huettel et al.

Self-serving interpretations of ambiguity in other-regarding behavior

We demonstrate that people can adopt a favorable view of ambiguous risks relative to ones with known probabilities, contrary to the usual attitude of ambiguity aversion, when doing so permits justification for unfair behavior. We use binary dictator games involving a choice between a relatively equitable allocation and an “unfair” allocation that is both less generous and makes the recipient's payment dependent on a p = 0.5 lottery. Dictators choose the unfair option more frequently when the recipient's allocation depends on an ambiguous lottery than on a lottery with a known probability — even though the objective distributions of outcomes are identical under the two kinds of lotteries. Dictators' estimates of the expected value of the recipients' allocations are inflated under ambiguity, indicating that dictators form self-serving beliefs about ambiguity. Finally, increased unfair behavior under ambiguity is extinguished when dictators are constrained by their own initial unmotivated, and negative, attitudes towards ambiguity.

A brain imaging study of the choice procedure

We study the behavior of subjects facing choices between certain, risky, and ambiguous lotteries. Subjects' choices are consistent with the economic theories modeling ambiguity aversion. Our results support the conjecture that subjects face choice tasks as an estimation of the value of the lotteries, and that the difficulty of the choice is an important explanatory variable (in addition to risk and ambiguity aversion). The brain imaging data suggest that such estimation is of an approximate nature when the choices involve ambiguous and risky lotteries, as the regions in the brain that are activated are typically located in parietal lobes. Thus such choices require mental faculties that are shared by all mammals, and in particular are independent of language. In contrast, choices involving partial ambiguous lotteries additionally produce an activation of the frontal region, which indicates a different, more sophisticated cognitive process.

Favorable Interpretations of Ambiguity and Unstable Preferences for Fairness

We show that people manipulate their attitudes towards ambiguity when doing so allows them to behave more self-interestedly. In a decision subject chose between a fair and an choice. By choosing the latter, dictators increase their own allocation by decreasing the allocation to the recipient and making the recipient's allocation dependent on a p=0.5 lottery. More unfair allocations were made when the lottery was ambiguous than when it involved simple risk. Overestimation of the expected value of allocations to recipients was higher in ambiguity, indicating that dictators believe the ambiguous lottery to be more attractive. These results are extinguished if dictators are constrained from adopting a favorable attitude towards ambiguity. These findings suggest that the relationship between ambiguity and unfairness results from a self-serving bias involving the adoption of a favorable view of ambiguity, counter to the typical unfavorable view (ambiguity aversion). We also conducted a contextualized dictator game experiment involving hypothetical managerial decisions. In line with the above findings, participants made more unfair decisions when the consequences of their decisions were ambiguous compared to when they involved simple risk, even though they prefer simple risk over ambiguity when there is no conflict between self-interest and social concerns.

Willingness-to-pay and willingness-to-accept for risky and ambiguous lotteries

Willingness-to-pay and willingness-to-accept for risky and ambiguous lotteries

Willingness-to-pay and willingness-to-accept for risky and ambiguous lotteries : 074065 (E12) Eisenberger R., Weber M., Universität Mannheim, Germany, Journal of Risk and Uncertainty, Vol. 10, nr. 3, 1995, pp. 223–233

Willingness-to-pay and willingness-to-accept for risky and ambiguous lotteries : 074065 (E12) Eisenberger R., Weber M., Universität Mannheim, Germany, Journal of Risk and Uncertainty, Vol. 10, nr. 3, 1995, pp. 223–233

Willingness-to-pay and willingness-to-accept for risky and ambiguous lotteries

Former studies have shown that people tend to give buying prices that are lower than selling prices. In our study, we investigate if this willingness-to-accept and willingness-to-pay disparity is affected by ambiguity. Using a Becker, DeGroot, and Marschak procedure, we elicit buying, selling, short-selling, and short-buying prices. The results indicate that subjects clearly distinguish between risky and ambiguous lotteries and the different ways in which lotteries are framed. However, the average WTA/WTP ratios are remarkably close for all lotteries considered, as well as for negative and positive framing.

The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach

The paper describes a decision process under which it is rational to prefer a lottery with known probabilities to a similar ambiguous lottery where the decision maker does not know the exact values of the probabilities (the Ellsberg paradox). This is done by modeling ambiguous lotteries as two-stage lotteries, by assuming the independence axiom without the reduction of compound lotteries axiom, and by using the anticipated utility functional. This paper also gives conditions under which less ambiguity is preferred and presents some comparative statics analysis as well as some inter-personal comparisons. Finally, it proves that within the anticipated utility framework, risk and ambiguity are almost identical. Copyright 1987 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.