Pricing risk and ambiguity: The effect of perspective taking

In the valuation of uncertain prospects, a difference is often observed between selling and buying perspectives. This paper distinguishes between risk (known probabilities) and ambiguity (unknown probabilities) in decisions under uncertainty and shows that the valuation disparity increases under ambiguity compared to risk. It is found that both the comparative versus noncomparative evaluation of risky and ambiguous prospects and the uniqueness of the valuation perspective (either seller or buyer) moderate this increase in the disparity under ambiguity. The finding is consistent with recent theoretical accounts of pricing under uncertainty. We discuss implications for market behaviour and for the ambiguity paradigm as a research tool.     

The Effect of Temporal Distance on Attitudes toward Imprecise Probabilities and Imprecise Outcomes

Many personal, managerial, and societal decisions involve uncertain or ambiguous consequences that will occur in the future. Yet, previous empirical research on ambiguity preferences has focused mainly on decisions with immediate outcomes. To close this gap in the literature, this paper examines ambiguity attitudes toward future prospects, particularly how they may differ from the attitudes toward comparable prospects in the present. On the basis of a recent paradigm, we first distinguish between two types of ambiguity: imprecise probabilities and imprecise outcomes. Then, in accordance with construal level theory, which shows that temporal distance increases the relative importance of outcomes over probabilities in evaluating prospects, we conjecture that temporal distance would moderate attitudes toward imprecise probabilities but amplify attitudes toward imprecise outcomes. Through a series of experiments, we demonstrate that when the prospects are in the future, individuals are less averse toward imprecise probabilities and more seeking toward imprecise outcomes. However, the effect is most prominent for prospects where both the probability and outcome dimensions are concurrently imprecise. The paper ends with a discussion on how dimension salience may have contributed to this result. Copyright © 2012 John Wiley & Sons, Ltd.     

Neurobiological studies of risk assessment: A comparison of expected utility and mean-variance approaches

When modeling valuation under uncertainty, economists generally prefer expected utility because it has an axiomatic foundation, meaning that the resulting choices will satisfy a number of rationality requirements. In expected utility theory, values are computed by multiplying probabilities of each possible state of nature by the payoff in that state and summing the results. The drawback of this approach is that all state probabilities need to be dealt with separately, which becomes extremely cumbersome when it comes to learning. Finance academics and professionals, however, prefer to value risky prospects in terms of a trade-off between expected reward and risk, where the latter is usually measured in terms of reward variance. This mean-variance approach is fast and simple and greatly facilitates learning, but it impedes assigning values to new gambles on the basis of those of known ones. To date, it is unclear whether the human brain computes values in accordance with expected utility theory or with mean-variance analysis. In this article, we discuss the theoretical and empirical arguments that favor one or the other theory. We also propose a new experimental paradigm that could determine whether the human brain follows the expected utility or the mean-variance approach. Behavioral results of implementation of the paradigm are discussed.     

Valuing information and options: an experimental study

Participants in four studies were faced with everyday‐life decision scenarios involving risk, such as purchasing an airline ticket whose price may change. They were asked to state their maximum willingness to pay (WTP) for resolving the uncertainty with either perfect information or an option. The two are strategically equivalent, therefore, should be valued in the same way. Across all experiments, individuals tend to value the option more than the information. In addition, the distributions of responses reveal frequent and gross violations of normative bounds. Contrary to normative predictions, no relationship is found between individuals' valuation of the gamble and their reported WTP for information or option. Furthermore, although participants pay attention to the probabilities of outcomes in valuing the gambles, they ignore the probabilities in valuing uncertainty resolution. Several reasoning heuristics that participants use to come up with a value of information are identified, and it appears that the Information and Option contexts tend to trigger different heuristics. Shift in reference point and regret are consistent with the Information–Option valuation discrepancy. Copyright © 2007 John Wiley & Sons, Ltd.     

成就动机和性别对风险倾向的预测作用

研究通过对等同绝对值(CE)的比较将冒险倾向转换为可以量化比较的变量,旨在探讨成就动机和性别在经济获益和损失的各种概率情景下对冒险倾向的预测作用。结果发现,高低成就动机组并没有表现出冒险倾向的显著差异。进一步的相关分析发现,成就动机中的回避失败维度与获益情景下的冒险倾向相关显著,而追求成功维度与各个情景下的相关都不显著。以回避失败维度聚类得到的高低回避失败组,体现出来的冒险倾向趋势显示高回避失败组的被试在获益低概率、获益中等概率、获益高概率、损失低概率、损失中等概率和损失高概率6种情景下都更加回避冒险,而且两组等同绝对值中位数的差异在获益中等概率和获益高概率两种情况下达到显著。另外,冒险倾向的性别差异只在损失中等概率和损失高概率两种情景中达到显著,这两种情况下都是女性更冒险,这与传统的女性更保守的刻板印象不同。     

Strength of evidence, judged probability, and choice under uncertainty

This paper traces, within subjects, the relationship between assessed strength of evidence, judgments of probability, and decisions under uncertainty. The investigation relies on the theoretical framework provided by support theory (Tversky & Koehler, 1994; Rottenstreich & Tversky, 1997), a nonextensional model of judgment under uncertainty. Fans of professional basketball (N = 50) judged the probability that each of eight teams, four divisions, and two conferences would win the National Basketball Association championship. Additionally, participants rated the relative strength of each team, judged the probability that a given team would win the championship assuming a particular pairing in the finals, priced prospects contingent on the winner of the championship, and made choices between chance prospects. The data conformed to the major tenets of support theory, and the predicted relationships between assessed strength of evidence, hypothetical support, judged probabilities, and choices under uncertainty also held quite well.     

Beyond risk and ambiguity: Deciding under ignorance

In this study, we examined the neural basis of decision making under different types of uncertainty that involve missing information: ambiguity (vague probabilities) and sample space ignorance (SSI; unknown outcomes). fMRI revealed that these two different types of uncertainty recruit distinct neural substrates: Ambiguity recruits the left insula, whereas SSI recruits the anterior cingulate cortex, bilateral inferior parietal cortex, and the lateral orbitofrontal cortex. The finding of unique activations for different types of uncertainty may not necessarily be predicted within the reductive approach of modern theories of decision making under uncertainty, because these theories purport that humans reduce more complicated uncertain environments to subjectively formed less complicated ones (i.e., SSI to ambiguity). The predictions of the reductive view held only for ambiguityaverse individuals and not for ambiguity-tolerant individuals. Consequently, theories of decision making under uncertainty should include individual tolerance for missing information and how these individual differences modulate the neural systems engaged during decision making. Supplemental materials for this article may be downloaded from http://cabn.psychonomic-journals.org/content/supplemental.     

Ambiguity Attitudes over Time

Previous research demonstrates that individuals exhibit a stronger level of ambiguity aversion for high probabilities than for low probabilities. Given that risky and ambiguous prospects are often unresolved until a future date (e.g., investment decisions, new product launches, and medical interventions), this study examines the impact of time on ambiguity preferences at different probability levels. Our experimental results indicate that although ambiguity preferences for low‐probability events remain constant, a robust effect of time occurs for high‐probability events. More specifically, temporal distance mitigates ambiguity aversion. This effect is consistent for different elicitation methods (preference rating and probability–ambiguity trade‐off tasks). We propose a dual‐process model (affective versus cognitive processing styles) to explain our results. Affective processing for high‐probability lotteries resolved in the current period increases ambiguity aversion, while cognitive processing leads to less ambiguity‐averse choices for future lotteries. Copyright © 2015 John Wiley & Sons, Ltd.     

从对框架效应的分析看风险决策的神经基础

对风险决策的研究近年来一直是微观经济学和心理学的热门,但是从传统的决策理论到主张有限理性的预期理论大多是对决策行为的研究,决策的心理机制一直是无法解释的黑箱子。令人兴奋的是近几年来神经科学家及其他领域的学者开始用先进的神经心理学的方法来研究风险决策,试图理解神经过程调节风险决策行为的方式。文章从分析违背“不变性”原则的框架效应入手,从正反框架、确定选择和风险选择、风险规避和风险寻求、高估小概率事件几个方面,全面分析风险决策可能的神经基础。在总结已有研究的基础上提出了把风险决策研究扩展到不确定决策,把风险决策中的一次决策研究扩展到多次决策的研究思路     

Robust Tolerance for Ambiguity

We argue first that "ambiguous prospects" should be defined in a way that is compatible with dictionary definitions and other technical uses of ambiguity. We then define an ambiguous prospect as a disjunction of risky prospects. Then to harmonize some findings in the literature we test the hypothesis that people are ambiguity indifferent up to moderate amounts of ambiguity and are ambiguity averse only for large amounts of ambiguity. To test the hypothesis we found probability equivalents to risk for prospects of varying degrees of ambiguity. Up to an ambiguity range of .7 the equivalents were near that of a normatively equivalent risky prospect while the equivalents of highly ambiguous prospects differed. We interpret the data in terms of competing desires for minimum effort and maximum accuracy.     

概率水平与模糊性对短视损失规避的影响

短视损失规避是指如果投资者频繁地评估其投资回报,那么他就会经常改变其投资决策,进而减少对风险资产的投入。本文采用实验法探讨了任务概率水平以及模糊性对短视损失规避的影响。结果发现短视损失规避只存在于中等损失概率任务中,说明该现象并非普遍存在;当概率模糊时,高损失概率任务中出现短视损失规避,而低损失概率任务中则出现反向的短视损失规避,说明模糊性能扩展“短视”起作用的概率范围。     

Common and distinct factors in decision making under ambiguity and risk: A psychometric study of individual differences

The relation between decision making under ambiguity and risky decision making was examined. In Studies 1 and 2, choices under ambiguity were measured for a large sample receiving an Ellsberg-type Ambiguity-Probability Tradeoff Task. Participants with extreme scores were recruited for Part 2 of each study which consisted of a risky decision making task (Study 1) or a series of decisions under ambiguity in “real life” scenarios (Study 2). Despite a time gap of up to 2 months, individual differences in scores on Part 1 predicted scores on Part 2. In Study 3 participants received in a single session several risky decision making tasks, several measures of decision making under ambiguity, and several personality scales related to uncertainty and decision making style. Taken together, the findings support the existence of a stable dispositional trait to reduce uncertainty in decision making but also task-specific differences related to gains and losses.     

From the casino to the jungle

Clear-cut cases of decision-making under risk (known probabilities) are unusual in real life. The gambler’s decisions at the roulette table are as close as we can get to this type of decision-making. In contrast, decision-making under uncertainty (unknown probabilities) can be exemplified by a decision whether to enter a jungle that may contain unknown dangers. Life is usually more like an expedition into an unknown jungle than a visit to the casino. Nevertheless, it is common in decision-supporting disciplines to proceed as if reasonably reliable probability estimates were available for all possible outcomes, i.e. as if the prevailing epistemic conditions were analogous to those of gambling at the roulette table. This mistake can be called the tuxedo fallacy. It is argued that traditional engineering practices such as safety factors and multiple safety barriers avoid this fallacy and that they therefore manage uncertainty better than probabilistic risk analysis (PRA). PRA is a useful tool, but it must be supplemented with other methods in order not to limit the analysis to dangers that can be assigned meaningful probability estimates.     

Attributions for ambiguity in a treatment-decision context can create ambiguity aversion or seeking

The phenomenon of ambiguity aversion suggests that people prefer options that offer precisely rather than imprecisely known chances of success. However, past work on people's responses to ambiguity in health treatment contexts found ambiguity seeking rather than aversion. The present work addressed whether such findings reflected a broad tendency for ambiguity seeking in health treatment contexts or whether specific attributions for ambiguity play a substantial role. In three studies, people choose between two treatment options that involved similar underlying probabilities, except that the probabilities for one option involved ambiguity. The attributions offered for the ambiguity played an important role in the results. For example, when the range of probabilities associated with an ambiguous treatment was attributed to the fact that different studies yield different results, participants tended to show ambiguity aversion or indifference. However, when the range was attributed to something that participants could control (e.g., regular application of a cream) or something about which they were overoptimistic (e.g., their immune system function), participants tended to show ambiguity seeking. Health professionals should be mindful of how people will interpret and use information about ambiguity when choosing among treatments.     

模糊规避的形成机制：基于可评价性假设的视角

模糊规避是指在相同奖赏的情况下,决策者会力图规避从主观上判断具有模糊概率的事件而偏好具有相同精确概率的事件。本研究使用同时评价、单独评价的研究范式从随机事件和自然事件两个领域来探讨模糊规避的形成机制。研究结果表明,当风险事件和模糊事件同时评价时,个体倾向于模糊规避;当风险事件和模糊事件单独评价时,模糊规避会消失。     

When do peers influence adolescent males' risk taking? Examining decision making under conditions of risk and ambiguity

Risk taking is highly prevalent among adolescent males, and a range of studies have shown that decisions become riskier if a peer is present. However, previous studies have typically provided participants with explicit probabilities of risk in each situation. This does not accurately reflect adolescents' real‐world risk taking, where decisions are made in ambiguous situations alongside their peers. Aiming for a more ecologically valid design, the present experiment manipulated situational ambiguity and examined its interplay with group decision making and developmental factors. Adolescent males (N = 202) aged 12–15 completed a “Wheel of Fortune” task and then self‐reported their score, presenting an opportunity to cheat as a measure of antisocial risk taking. As predicted, adolescents were more likely to take risks when probabilities were ambiguous rather than explicit. Further, higher levels of gambling choices were made by groups in ambiguous, but not risk situations. Age significantly predicted gambling in ambiguous conditions, whereas developmental dispositions (risk perception, reward sensitivity, and inhibitory control) did not play a role. Findings provide an insight into the social and situational conditions under which adolescent males engage in reckless behavior.     

概率大小、损益结果和认知闭合需要对模糊规避的影响

模糊规避是指在相同奖赏的情况下,决策者会力图规避从主观上判断具有模糊概率的事件而偏好具有相同精确概率的事件。本研究探讨了概率大小、损益结果和认知闭合需要对模糊规避的影响。研究发现,在小概率受益的情况下,个体倾向于模糊寻求;在中概率受益的情况下,个体倾向于模糊规避;在高概率受益的情况下,个体倾向于模糊规避;在小概率损失的情况下,个体倾向于模糊规避;在中概率损失的情况下,个体倾向于模糊规避;在高概率损失的情况下,个体倾向于模糊寻求。但是,研究并未发现认知闭合需要对模糊规避有预测作用。     

不确定性容忍度对风险偏好的影响及其情景依赖性

研究以经营店面为背景设计决策材料,采用2(不确定性容忍度:高/低)×2(损益背景:损失/获益)×2(选项描述框架:积极/消极)×3(损益概率:高/中/低)混合实验设计,探讨不同任务情景下个体不确定性容忍度对风险偏好的影响。结果发现,不确定性容忍度主效应显著,高容忍度者比低容忍度者更冒险。不确定性容忍度与损益背景交互作用显著：在损失背景下,高容忍度者比低容忍度者更冒险,在获益背景下无此效应。不确定性容忍度与选项描述框架交互作用显著：在积极框架下,高容忍度者比低容忍度者更冒险,在消极框架下无此效应。这表明,不确定性容忍度对风险偏好产生影响,但这种影响会受到损益背景和选项描述框架的调节,具有情景依赖性。     

The combined effects of risk and time on choice: Does uncertainty eliminate the immediacy effect? Does delay eliminate the certainty effect?

Researchers have noted parallels between decisions under uncertainty and over time. Three experiments evaluated the theory that uncertainty and time affect choice via a common underlying dimension, such that delaying an outcome is equivalent to making it uncertain. To test this account we asked whether adding uncertainty to outcomes would eliminate the immediacy effect bias. We also asked whether adding time delay to outcomes would eliminate the certainty effect bias. The answer to both questions was yes, provided the prospects were presented singly rather than jointly. In single evaluation uncertainly eliminated the immediacy effect and delay eliminated one form of the certainty effect, while in joint evaluation, these effects did not occur. These findings suggest that at least in some contexts decision makers may equate risk and delay. Other explanations are possible, however, demonstrating that the interaction between risk and delay is complex and not easily understood.