Reference-dependent expected utility with incomplete preferences

An important reason why people deviate from expected utility is reference-dependence of preferences, implying loss aversion. Bleichrodt [Bleichrodt H. (2007). Reference-dependent utility with shifting reference points and incomplete preferences. Journal of Mathematical Psychology, 51, 266-276] argued that in the empirically realistic case where the reference point is always an element of the decision maker’s opportunity set, reference-dependent preferences have to be taken as incomplete. This incompleteness is a consequence of reference-dependence and is different in nature from the type of incompleteness usually considered in the literature. It cannot be handled by existing characterizations of reference-dependence, which all assume complete preferences. This paper presents new preference foundations that extend reference-dependent expected utility to cover this case of incompleteness caused by reference-dependence. The paper uses intuitive axioms that are easy to test. Two special cases of reference-dependent expected utility are also characterized: one model in which utility is decomposed into a normative and a psychological component and one model in which loss aversion is constant. The latter model has been frequently used in empirical research on reference-dependence.     

Prospects behind bars: Analyzing decisions under risk in a prison population

Criminal activity often involves considerable risks. It is therefore not surprising that criminals have been speculated to differ from noncriminals in risk attitude. Yet, few data exist to support this assumption. Moreover, the psychological underpinnings of differences in risk attitude are currently little understood. We presented prisoners and controls with sets of risky decision tasks and modeled their responses using cumulative prospect theory (CPT). The two groups showed several differences. Prisoners were more risk seeking than nonprisoners in lotteries involving losses, but they were less risk seeking in lotteries involving high-probability gains. Bestfitting CPT parameters indicated a reduced sensitivity to outcomes, for both gains and losses, and a stronger loss aversion among prisoners. In addition, prisoners showed a diminished sensitivity to the probability of gains. Our results contribute to a better understanding of prisoners’ risk attitudes and the underlying mechanisms that distinguish prisoners from nonprisoners and may thus help improve interventions designed to prevent crime.     

Loss aversion and perceptual risk aversion

We prove that, in cumulative prospect theory, the weak loss aversion for S-shaped value functions is equivalent to a notion of risk aversion that we define from the perceptual point of view. No additional assumption or condition on the probability distortion is needed. It is demonstrated that a power S-shaped value function does not satisfy weak loss aversion, i.e., a decision maker is risk seeking with respect to some mixed sign lotteries.     

睾酮对价值加工的影响——基于“累积前景”理论框架的决策行为研究

较多研究支持睾酮和决策中的风险寻求行为呈正相关,但是也有其他的研究未能发现这种关系。基于决策的累计前景理论,本研究使用动态估计参数估计任务(DEEP),结合计算模型的方法,对120名双盲给药、有安慰剂对照的被试进行睾酮对价值加工过程作用的探究。结果显示,睾酮减少了个体的概率扭曲以及增加了损失规避,但是没有引发明显的风险寻求行为,研究结果表明睾酮对个体的价值加工过程产生了影响,使个体对概率的感知更接近于客观值并且增加了对损失的敏感性。     

Hierarchical Bayesian parameter estimation for cumulative prospect theory

Cumulative prospect theory (CPT Tversky & Kahneman, 1992) has provided one of the most influential accounts of how people make decisions under risk. CPT is a formal model with parameters that quantify psychological processes such as loss aversion, subjective values of gains and losses, and subjective probabilities. In practical applications of CPT, the model’s parameters are usually estimated using a single-participant maximum likelihood approach. The present study shows the advantages of an alternative, hierarchical Bayesian parameter estimation procedure. Performance of the procedure is illustrated with a parameter recovery study and application to a real data set. The work reveals that without particular constraints on the parameter space, CPT can produce loss aversion without the parameter that has traditionally been associated with loss aversion. In general, the results illustrate that inferences about people’s decision processes can crucially depend on the method used to estimate model parameters.     

Cognitive models of risky choice: parameter stability and predictive accuracy of prospect theory

In the behavioral sciences, a popular approach to describe and predict behavior is cognitive modeling with adjustable parameters (i.e., which can be fitted to data). Modeling with adjustable parameters allows, among other things, measuring differences between people. At the same time, parameter estimation also bears the risk of overfitting. Are individual differences as measured by model parameters stable enough to improve the ability to predict behavior as compared to modeling without adjustable parameters? We examined this issue in cumulative prospect theory (CPT), arguably the most widely used framework to model decisions under risk. Specifically, we examined (a) the temporal stability of CPT’s parameters; and (b) how well different implementations of CPT, varying in the number of adjustable parameters, predict individual choice relative to models with no adjustable parameters (such as CPT with fixed parameters, expected value theory, and various heuristics). We presented participants with risky choice problems and fitted CPT to each individual’s choices in two separate sessions (which were 1 week apart). All parameters were correlated across time, in particular when using a simple implementation of CPT. CPT allowing for individual variability in parameter values predicted individual choice better than CPT with fixed parameters, expected value theory, and the heuristics. CPT’s parameters thus seem to pick up stable individual differences that need to be considered when predicting risky choice.     

Do people make decisions under risk based on ignorance? An empirical test of the priority heuristic against cumulative prospect theory

Brandstätter, Gigerenzer, and Hertwig [Brandstätter, E., Gigerenzer, G., & Hertwig, R. (2006). The Priority Heuristic: Making choices without trade-offs. Psychological Review, 113(2), 409–432] put forward the priority heuristic (PH) as a fast and frugal heuristic for decisions under risk. According to the PH, individuals do not make trade-offs between gains and probabilities, as proposed by expected utility models such as cumulative prospect theory (CPT), but use information in a non-compensatory manner and ignore information. We conducted three studies to test the PH empirically by analyzing individual choice patterns, decision times and information search parameters in diagnostic decision tasks. Results on all three dependent variables conflict with the predictions of the PH and can be better explained by the CPT. The predictive accuracy of the PH was high for decision tasks in which the predictions align with the predictions of the CPT but very low for decision tasks in which this was not the case. The findings indicate that earlier results supporting the PH might have been caused by the selection of decision tasks that were not diagnostic for the PH as compared to CPT.     

The priority heuristic: making choices without trade-offs

Bernoulli's framework of expected utility serves as a model for various psychological processes, including motivation, moral sense, attitudes, and decision making. To account for evidence at variance with expected utility, the authors generalize the framework of fast and frugal heuristics from inferences to preferences. The priority heuristic predicts (a) the Allais paradox, (b) risk aversion for gains if probabilities are high, (c) risk seeking for gains if probabilities are low (e.g., lottery tickets), (d) risk aversion for losses if probabilities are low (e.g., buying insurance), (e) risk seeking for losses if probabilities are high, (f) the certainty effect, (g) the possibility effect, and (h) intransitivities. The authors test how accurately the heuristic predicts people's choices, compared with previously proposed heuristics and 3 modifications of expected utility theory: security-potential/aspiration theory, transfer-of-attention-exchange model, and cumulative prospect theory.     

行为经济学中的损失规避

损失规避是指,人们总是强烈倾向于规避损失：一定数额的损失所引起的心理感受,其强烈程度约相当于两倍数额的获益感受。这种强烈的心理与行为倾向广泛存在于风险与非风险领域,在该两个领域中损失规避的研究范式也不同。损失规避常见于经济和消费等领域,可用于解释行为决策中有悖于规范化理论的诸多现象,如禀赋效应、现状偏差、股权溢价之迷和赢者的诅咒等。然而,损失规避的机制研究还存在许多尚未解决的问题,如损失规避的本质以及适用条件。今后的研究不仅要注重认知角度和情感依恋,还要结合认知过程来研究损失规避的性质和内在机制,以期帮助人们认识、预测及干预由损失规避造成的经济损失和非理性决策。     

Psychological determinants of decision attitude

Decision attitude — an analog of risk attitude — is the propensity to make (or avoid making) a decision: in decision aversion, a person finds it more desirable to receive through fiat the better of two options than to have a choice between them; in decision seeking, the choice is more desirable, even though it can lead to nothing better than the best option. Both decision aversion and decision seeking were found in hypothetical scenarios. Experimental manipulations and subjects' justifications point to anticipated regret, fear of blame for poor outcomes, and desire for equitable distributions as sources of decision aversion. One source of decision seeking (for self) and decision aversion (when deciding for others) appears to be the desire for the self-determination of the affected parties. We consider the implications of our results for personal choice and public policy decisions.     

The ability to process emotional information predicts loss aversion

On the basis of previous research it was hypothesized that alexithymia is associated with a higher tolerance for losses. This hypothesis is extended to explore whether the putative link between loss aversion and alexithymia remains once traits associated with risk taking (sensation seeking) and broad based personality traits (the Big 5) are controlled. Participants (N = 260) completed indices of alexithymia, sensation seeking and the Big 5 and both a riskless (endowment effect) and risky (lottery task) measure of loss aversion. It was found that the higher the alexithymia score the lower the loss aversion for both riskless and risky decisions even when sex, sensation seeking and the Big 5 are taken into account. The implications for this finding are discussed in the light of a neurological explanation of the relationship between alexithymia and loss aversion.     

How beliefs influence the relative magnitude of pleasure and pain

Loss aversion is an economic assumption about utility—people value giving up a good more than they value getting it. It also has hedonic meaning—the pain of a loss is greater in magnitude than the pleasure of a comparable gain. But value and pleasure are not necessarily identical. We test the hedonic interpretation of loss aversion in experimental markets. With hedonic forecasts, sellers imagine the pain of losing their endowment, and buyers imagine the pleasure of being endowed. With hedonic experiences, sellers rate the pleasure of having the endowment, and buyers rate the pain of being without it. Contrary to loss aversion, predicted pleasure is greater in magnitude than predicted pain, and experienced pleasure surpasses experienced pain. We show that the relative magnitude of pleasure and pain depends on beliefs about the likelihood of outcomes, as well as utilities. Surprise makes gains more pleasurable and losses more painful. With surprising gains and expected losses, pleasure can surpass pain. But when gains and losses are equally likely (or losses are surprising and gains are expected), the opposite pattern can occur. Finally, within‐group and between‐group prices are significantly correlated with hedonic experiences. Sellers who feel better with their endowments assign higher selling prices, and buyers who feel worse about the absence of endowment assign higher buying prices. Despite the fact that hedonic experiences deviate from loss aversion, these emotions predict the endowment effect. Copyright © 2009 John Wiley & Sons, Ltd.     

Additivity and expected utility in risky multiattribute preferences

This experiment analyzed human preferences among even chance gambles for commodity bundles. The purpose of the experiment was to test several independence assumptions that distinguish between models for risky multiattribute preferences. In particular, the additivity and the expected utility part of the additive expected utility model were tested symmetrically. The degree and form of model violations were established, and the effects of instructions and of response modes were examined. All independence assumptions were violated by a bias to prefer a gamble or a commodity bundle that was previously matched against a standard. Systematic and strong violations that superseded this bias questioned the validity of the additive expected utility model. In violation of the additivity part of that model subjects consistently preferred the gamble with more balanced outcomes when comparing gambles with identical marginal probability distributions. This trend, called multiattribute risk aversion, was independent of subjects' single attribute risk attitude. Instructions and response modes had no noticeable impacts on these response patterns.     

Risk aversion in information seeking

The information gain model argues that participants select alternatives with a larger expected value of information gain. The present study investigated risk aversion in information seeking to examine whether the expected value always determines information-seeking behaviour. For this investigation, we used a scale method selection task in which participants were required to select one of two scales for weighing coins in order to find an underweight coin. Two experiments showed that participants more frequently selected the alternative that provided information gain without risk, although its expected information gain was smaller. This finding indicates the presence of risk aversion in information seeking, suggesting that information-seeking behaviour is affected by risk associated with obtaining information gain.     

Framing Effects: Dynamics and Task Domains

The author examines the mechanisms and dynamics of framing effects in risky choices across three distinct task domains (i.e., life–death, public property, and personal money). The choice outcomes of the problems presented in each of the three task domains had a binary structure of a sure thing vs a gamble of equal expected value; the outcomes differed in their framing conditions and the expected values, raging from 6000, 600, 60, to 6, numerically. It was hypothesized that subjects would become more risk seeking, if the sure outcome was below their aspiration level (the minimum requirement). As predicted, more subjects preferred the gamble when facing the life–death choice problems than facing the counterpart problems presented in the other two task domains. Subjects’ risk preference varied categorically along the group size dimension in the life–death domain but changed more linearly over the expected value dimension in the monetary domain. Framing effects were observed in 7 of 13 pairs of problems, showing a positive frame–risk aversion and negative frame–risk seeking relationship. In addition, two types of framing effects were theoretically defined and empirically identified. Abidirectional framing effectinvolves a reversal in risk preference, and occurs when a decision maker's risk preference is ambiguous or weak. Four bidirectional effects were observed; in each case a majority of subjects preferred the sure outcome under a positive frame but the gamble under a negative frame. In contrast, aunidirectional framing effectrefers to a preference shift due to the framing of choice outcomes: A majority of subjects preferred one choice outcome (either the sure thing or the gamble) under both framing conditions, with positive frame augmented the preference for the sure thing and negative frame augmented the preference for the gamble. These findings revealed some dynamic regularities of framing effects and posed implications for developing predictive and testable models of human decision making.     

Dissociable effects of basolateral amygdala lesions on decision making biases in rats when loss or gain is emphasized

Individuals switch from risk seeking to risk aversion when mathematically identical options are described in terms of loss versus gains, as exemplified in the reflection and framing effects. Determining the neurobiology underlying such cognitive biases could inform our understanding of decision making in health and disease. Although reports vary, data using human subjects have implicated the amygdala in such biases. Animal models enable more detailed investigation of neurobiological mechanisms. We therefore tested whether basolateral amygdala (BLA) lesions would affect risk preference for gains or losses in rats. Choices in both paradigms were always between options of equal expected value—a guaranteed outcome, or the 50:50 chance of double or nothing. In the loss-chasing task, most rats exhibited strong risk seeking preferences, gambling at the risk of incurring double the penalty, regardless of the size of the guaranteed loss. In the betting task, the majority of animals were equivocal in their choice, irrespective of bet size; however, a wager-sensitive subgroup progressively shifted away from the uncertain option as the bet size increased, which is reminiscent of risk aversion. BLA lesions increased preference for the smaller guaranteed loss in the loss-chasing task, without affecting choice on the betting task, which is indicative of reduced risk seeking for losses, but intact risk aversion for gains. These data support the hypothesis that the amygdala plays a more prominent role in choice biases related to losses. Given the importance of the amygdala in representing negative affect, the aversive emotional reaction to loss, rather than aberrant estimations of probability or loss magnitude, may underlie risk seeking for losses.     

基于预期理论的风险决策的神经机制

预期理论基于对期望效用理论的批判与发展,提出了价值函数与权重函数,对以往风险决策研究中所发现的现象进行了很好的预测与解释。预期理论的核心概念包括参照依赖、损失规避与权重函数。基于预期理论的一些决策偏差包括框架效应、禀赋效应和默认偏差也部分揭示了与人们风险决策有关的脑区。近年来,通过采用功能性核磁共振等脑成像手段对预期理论的一些核心成分进行的研究表明,涉及到人们风险决策的脑区主要有前额叶、纹状体、脑岛与杏仁核。未来的研究可以从预期理论的产生根源、个体发展以及遗传基因等角度进行进一步的探讨。