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.     

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.      

Ambiguity and the value of information

The value of information is studied in a non-expected utility model of ambiguity with second-order probabilities. Information that reduces ambiguity has a positive value for ambiguity-averse decision makers, and the value of information that resolves ambiguity increases with greater ambiguity and with greater ambiguity aversion. Since information that resolves risk is valuable, and must also resolve ambiguity, the value of such information for ambiguity averters increases with greater ambiguity and with greater ambiguity aversion.     

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.     

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”.     

Regret theory and risk attitudes

We examine risk attitudes under regret theory and derive analytical expressions for two components—the resolution and regret premiums—of the risk premium under regret theory. We posit that regret-averse decision makers are risk seeking (resp., risk averse) for low (resp., high) probabilities of gains and that feedback concerning the foregone option reinforces risk attitudes. We test these hypotheses experimentally and estimate empirically both the resolution premium and the regret premium. Our results confirm the predominance of regret aversion but not the risk attitudes predicted by regret theory; they also clarify how feedback affects attitudes toward both risk and regret.     

The price for information about probabilities and its relation with risk and ambiguity

In this article, ambiguity attitude is measured through the maximum price a decision maker is willing to pay to know the probability of an event. Two problems are examined in which the decision maker faces an act: in one case, buying information implies playing a lottery, while, in the other case, buying information gives also the option to avoid playing the lottery. In both decision settings, relying on the Choquet expected utility model, we study how the decision maker??s risk and ambiguity attitudes affect the reservation price for ambiguity resolution. These effects are analyzed for different levels of ambiguity of the act. Operating instructions for the elicitation of the reservation price for ambiguity resolution in an experimental setting are provided at the end of the article.     

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.     

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.      

Expected utility with ambiguous probabilities and ‘irrational’ parameters

Savage's expected utility theory has been criticized for various reasons. Two of these are: (1) Subjective probabilities may be more or less ambiguous; this may affect the preference order. Savage's theory rules out any such effect. (2) Savage's theory rules out any influence of certain parameters of a probability distribution on the preference order. Such parameters are fractiles or pairs of fractiles, e.g., which have gained widespread attention as risk measures.This paper generalizes expected utility theory to include effects of ambiguity and those parameters on the preference order. Basic to this generalization is the classic paper by Herstein/Milnor.     

Ambiguity attitudes and social interactions: An experimental investigation

This paper reports the results of experiments testing prevalence of non-neutral ambiguity attitudes and how these attitudes change as a result of interpersonal interactions. To address the first question we conducted experiments involving individual choice between betting on ambiguous and unambiguous events of the subject’s choice. We found that a large majority of subjects display ambiguity neutral attitudes, many others display ambiguity incoherent attitudes, and few subjects display either ambiguity-averse attitudes or ambiguity-seeking attitudes. To address the second question we designed a new experiment with a built-in incentive to persuade. We found that interpersonal interactions without incentives to persuade have no effect on behavior. However, when incentives were introduced, the ambiguity neutral subjects were better able to persuade ambiguity seeking and ambiguity incoherent subjects to adopt ambiguity neutral choice behavior and, to a lesser extent, also ambiguity averse subjects.     

The influence of probabilities on the response mode bias in utility elicitation

The response mode bias, in which subjects exhibit different risk attitudes when assessing certainty equivalents versus indifference probabilities, is a well-known phenomenon in the assessment of utility functions. In this empirical study, we develop and apply a cardinal measure of risk attitudes to analyze not only the existence, but also the strength of this phenomenon. Since probability levels involved in decision problems are already known to have a strong impact on behavior, we use this approach to study the impact of probabilities on the extent of the response mode bias. We find that the direction in which probabilities influence measured risk aversion is the opposite in the certainty equivalence (CE) method versus in the probability equivalence (PE) method. Utilizing the CE elicitation approach leads to an increase of risk seeking for gambles involving high probabilities. For the PE method, subjects tend to behave risk averse with gambles of high probabilities. This behavior is reversed in the gain domain. This “tailwhip” effect is consistently replicated in several experiments, involving both loss and gain domains of lotteries.     

Ambiguity aversion under maximum-likelihood updating

Maximum-likelihood updating (MLU) is a well-known approach for extending static ambiguity sensitive preferences to dynamic set-ups. This paper develops an example in which MLU induces an ambiguity averse maxmin expected utility (MEU) decision-maker to (1) prefer a bet on an ambiguous over a risky urn and (2) be more willing to bet on the ambiguous urn compared to an (ambiguity neutral) subjective expected utility (SEU) decision-maker. This is challenging, since prior to observing (symmetric) draws from the urns, the MEU decision-maker (in line with the usual notion of ambiguity aversion) actually preferred the risky over the ambiguous bet and was less willing to bet on the ambiguous urn than the SEU decision-maker. The identified switch in betting preferences is not due to a violation of dynamic consistency or consequentialism. Rather, it results from MLU’s selection of extreme priors, causing a violation of the stability of set inclusion over the course of the updating process.     

Are the poor worse at dealing with ambiguity?

This paper studies the relationship between people’s ambiguity attitudes and income in the field using language as a natural source of ambiguity. It shows that the method of Baillon et al. (2017b) can be adapted for field studies, providing ambiguity measurement tasks that are more comprehensible for nonacademic subjects. Ambiguity attitudes were elicited in two groups of Chinese adolescents (poor rural and rich urban), among whom the income variation is big. In the rural group the poorer are both more ambiguity averse and more a-insensitive, whereas in the urban group the richer are more a-insensitivite. On average, the poor rural adolescents are worse at dealing with ambiguity than their urban counterparts. A-insensitivity, which measures people’s understanding of an ambiguous situation, is an important but sometimes neglected component of ambiguity attitude. Policies aiming to help people improve decisions may focus more on reducing a-insensitivity as this cognitive bias is more likely to be influenced by intervention than people’s intrinsic aversion towards ambiguity.     

The strength of sensitivity to ambiguity

We report an experiment where each subject’s ambiguity sensitivity is measured by an ambiguity premium, a concept analogous to and comparable with a risk premium. In our design, some tasks feature known objective risks and others uncertainty about which subjects have imperfect, heterogeneous, information (“ambiguous tasks”). We show how the smooth ambiguity model can be used to calculate ambiguity premia. A distinctive feature of our approach is estimation of each subject’s subjective beliefs about the uncertainty in ambiguous tasks. We find considerable heterogeneity among subjects in beliefs and ambiguity premia; and that, on average, ambiguity sensitivity is about as strong as risk sensitivity.     

Insurer ambiguity and market failure

A series of studies investigate the decision processes of actuaries, underwriters, and reinsurers in setting premiums for ambiguous and uncertain risks. Survey data on prices reveal that all three types of these insurance decision makers are risk averse and ambiguity averse. In addition, groups appear to be influenced in their premium-setting decisions by specific reference points such as expected loss and the concern with insolvency. This behavior is consistent with a growing analytical and empirical literature in economics and decision processes that investigates the role that uncertainty plays on managerial choices. Improved risk-assessment procedures and government involvement in providing protection against catastrophic losses may induce insurers to reduce premiums and broaden available coverage.This article is part of a larger effort supported by the National Science Foundation on The Role of Insurance, Compensation, Regulation, and Protective Behavior in Decision Making about Risk and Misfortune. We greatly appreciate the many helpful comments and suggestions by our colleagues on the project: Jon Baron, Colin Camerer, Neil Doherty, Jack Hershey, Eric Johnson, and Paul Kleindorfer. Support from NSF Grant #SES8809299 is gratefully acknowledged.     

Non-expected utility risk premiums: The cases of probability ambiguity and outcome uncertainty

This paper discusses two problems. (a) What happens to the conditional risk premium that a decision maker is willing to pay out of the middle prize in a lottery to avoid uncertainty concerning the middle prize outcome, when the probabilities of other prizes change? (b) What happens to the increase that a decision maker is willing to accept in the probability of an unpleasant outcome in order to avoid ambiguity concerning this probability, when this probability increases? We discuss both problems by using anticipated utility theory, and show that the same conditions on this functional predict behavioral patterns that are consistent both with a natural extension of the concept of diminishing risk aversion and with some experimental findings.