The predictive accuracy of intertemporal‐choice models

How do people choose between a smaller reward available sooner and a larger reward available later? Past research has evaluated models of intertemporal choice by measuring goodness of fit or identifying which decision‐making anomalies they can accommodate. An alternative criterion for model quality, which is partly antithetical to these standard criteria, is predictive accuracy. We used cross‐validation to examine how well 10 models of intertemporal choice could predict behaviour in a 100‐trial binary‐decision task. Many models achieved the apparent ceiling of 85% accuracy, even with smaller training sets. When noise was added to the training set, however, a simple logistic‐regression model we call the difference model performed particularly well. In many situations, between‐model differences in predictive accuracy may be small, contrary to long‐standing controversy over the modelling question in research on intertemporal choice, but the simplicity and robustness of the difference model recommend it to future use.     

Cognitive models of choice: comparing decision field theory to the proportional difference model

People often face preferential decisions under risk. To further our understanding of the cognitive processes underlying these preferential choices, two prominent cognitive models, decision field theory (DFT; Busemeyer & Townsend, 1993 ) and the proportional difference model (PD; González-Vallejo, 2002 ), were rigorously tested against each other. In two consecutive experiments, the participants repeatedly had to choose between monetary gambles. The first experiment provided the reference to estimate the models' free parameters. From these estimations, new gamble pairs were generated for the second experiment such that the two models made maximally divergent predictions. In the first experiment, both models explained the data equally well. However, in the second generalization experiment, the participants' choices were much closer to the predictions of DFT. The results indicate that the stochastic process assumed by DFT, in which evidence in favor of or against each option accumulates over time, described people's choice behavior better than the trade-offs between proportional differences assumed by PD.     

睡眠剥夺影响风险决策的双系统模型探讨

睡眠剥夺是指由于环境或自身原因无法满足正常睡眠时间的情况。大量实证研究发现, 睡眠剥夺会导致个体在风险决策中更倾向于风险寻求, 同时也有研究表明睡眠剥夺会导致个体风险规避, 而目前尚无统一结论。睡眠剥夺从风险感知、风险容忍、风险决策策略三个方面影响了风险决策, 其心理机制可由认知和情绪双路径模型进行解释, 且脑神经生理学研究也提供了相关证据。未来的研究应该进一步关注：(1)现实工作生活中的睡眠不足对风险决策的影响; (2)睡眠剥夺影响风险决策的理论模型建构。     

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.     

Causal report accuracy: Retrospect and prospect

The paper by M. Sprangers, W. van den Brink, J. van Heerden, and J. Hoogstraten (1987, Journal of Experimental Social Psychology, 23, 302–310) shows that my experiment (P. White, 1980, Psychological Review, 87, 105–112) cannot be interpreted as evidence against the proposal by R. Nisbett and T. Wilson (1977, Psychological Review, 84, 231–259) that accuracy of causal reports cannot be improved by information about internal events. However, the state of all existing literature on this topic is inconclusive because of the failure so far to run an internally valid test. It is suggested that further progress on this topic may depend upon theoretical innovation concentrating on social and practical factors in verbal report generation.     

Self‐framing of risky choice

Previous research on framing effects has largely focused on how choice information framed by external sources influences the response of a decision maker. This research examined how decision makers framed choice options and how the hedonic tone of self‐framing influenced their risk preference. By using pie charts and a complementary sentence‐completion task in Experiment 1, participants were able to interpret and frame the expected choice outcomes themselves before making a choice between a sure option and a gamble in either a life–death or a monetary problem. Each of these self‐frames (phrases) was then rated by a group of independent judges in terms of its hedonic tone. The hedonic tone of self‐frames was mostly positive and was more positive in the life–death than the monetary context, suggesting a motivational function of self‐framing. However, positive outcomes were still more likely to be framed positively than negative outcomes. In Experiment 2, choice outcomes were depicted with a whole‐pie chart instead of a pie slice in order to emphasize positive and negative outcomes equally. The results showed that the hedonic tone of self‐framing was still largely positive and more positive in the life domain than the monetary domain. However, compared to Experiment 1, the risk preference in the life–death domain was reversed, showing an outcome salience effect: when the pie‐slice chart emphasized only survival outcomes, participants were more risk taking under positive hedonic frames whereas when the whole‐pie chart depicted both survival and mortality outcomes, they became risk averse under positive frames. In sum, self‐framing reflected a positive bias in encoding risk information and affected the risk preference of the decision maker. Like the tone of voice used in communication, the hedonic tone of self‐framing, either positive or negative, can affect risk perception of a choice problem. Copyright © 2003 John Wiley & Sons, Ltd.     

风险敏感理论:需要驱动风险决策

风险敏感理论由研究动物觅食行为发展而来,提出有机体在有需要的状况下会出现从风险规避到风险寻求的行为,是风险决策领域内的一种生物学理论。目前风险敏感理论所做出的预测在动物和人类身上都获得了大量实证研究的支持,表明该理论可以解释很多领域中的风险决策。因此有必要对这一理论做一个系统的论述,包括对其理论来源和数学模型的发展演变进行梳理;从参照点等不同的角度分析该理论与其他决策理论的区别;并且,风险敏感理论也为经济不平等和权力等外部因素下的风险转移提供了解释,对已有研究做出了独特的贡献。     

Social cues and verbal framing in risky choice

We examined how people use social and verbal cues of differing priorities in making social decisions. In Experiment 1, formally identical life – death choice problems were presented in different hypothetical group contexts and were phrased in either a positive or negative frame. The risk‐seeking choice became more dominant as the number of kin in an endangered group increased. Framing effects occurred only in a heterogeneous group context where the lives at risk were a mixture of kin and strangers. No framing effect was found when the same problem was presented in the context of a homogeneous group consisting of either all kin or all strangers. We viewed the framing effects to be a sign of indecisive risk preference due to the differential effects of a kinship cue and a stranger cue on choice. In Experiment 2, we presented the life – death problem in two artificial group contexts involving either 6 billion human lives or 6 billion extraterrestrial lives. A framing effect was found only in the human context. Two pre‐conditions of framing effects appear to be social unfamiliarity of a decision problem and aspiration level of a decision maker. In Experiment 3, we analyzed the direction of the framing effect by balancing the framing. The direction of the framing effect depended on the baseline level of risk preference determined by a specific decision context. Copyright © 2001 John Wiley & Sons, Ltd.     

Forward inference in risky choice: Mapping gaze and decision processes

The study of cognitive processes is built on a close mapping between three components: overt gaze behavior, overt choice, and covert processes. To validate this overt–covert mapping in the domain of decision‐making, we collected eye‐movement data during decisions between risky gamble problems. Applying a forward inference paradigm, participants were instructed to use specific decision strategies to solve those gamble problems (maximizing expected values or applying different choice heuristics) during which gaze behavior was recorded. We revealed differences between overt behavior, as indicated by eye movements, and covert decision processes, instructed by the experimenter. However, our results show that the overt–covert mapping is for some eye‐movement measures not as close as expected by current decision theory, and hence question reverse inference as being prone to fallacies due to a violation of its prerequisite, that is, a close overt–covert mapping. We propose a framework to rehabilitate reverse inference.     

Risk perception and risky choice: Situational, informational and dispositional effects

We investigated how situational (gain–loss), informational (opportunity–threat framing) and dispositional (achievement motive and avoidance motive) variables affected opportunity–threat perception and risky choice in managerial decision-making contexts. In Study 1, the risk preference of the participants showed a reflection effect due to situational differences (gain or loss) and a partial framing effect caused by presenting the same choice information in terms of either opportunities or threats. However, both effects were in the opposite direction of predictions from prospect theory. Gains and positive framing enhanced risk-seeking preference whereas losses and negative framing augmented risk-averse preference. Risk-seeking choices were mediated by opportunity perception whereas risk-averse choices were mediated by threat perception. In Study 2, the participants high in achievement motive perceived greater opportunities in a negative situation, and the participants high in avoidance motive perceived greater threats in a positive situation, suggesting that ambition (achievement motive) operates more significantly in the face of adversities whereas cautiousness (avoidance motive) functions more significantly in prosperity.     

风险决策和跨期决策的过程比较：以确定效应和即刻效应为例

风险决策和跨期决策与人类生存发展密切相关, 且两类决策在理论发展、行为效应及神经基础等方面具有相似性。为检验二者是否具有共同过程机制, 本研究以风险决策中的确定效应和跨期决策中的即刻效应为例, 采用眼动追踪技术比较了它们的局部、整体过程及模型拟合。辅以贝叶斯因子分析实验数据表明：二者的主要过程特征均相似, 且更符合非折扣模型假设; 二者在加工复杂程度等少数特征上有所不同; 确定和即刻信息在加工方向等特征上存在特异性。这表明二者可能具有共同的核心决策规则：两类决策更可能遵循非折扣模型预期的简捷、启发式规则, 而不是折扣模型所假设的补偿性、基于选项规则。本研究为建立两类决策的共同解释框架做出了有益尝试, 并为决策比较研究方法提供新的方向。     

Sample size planning for longitudinal models: accuracy in parameter estimation for polynomial change parameters

Longitudinal studies are necessary to examine individual change over time, with group status often being an important variable in explaining some individual differences in change. Although sample size planning for longitudinal studies has focused on statistical power, recent calls for effect sizes and their corresponding confidence intervals underscore the importance of obtaining sufficiently accurate estimates of group differences in change. We derived expressions that allow researchers to plan sample size to achieve the desired confidence interval width for group differences in change for orthogonal polynomial change parameters. The approaches developed provide the expected confidence interval width to be sufficiently narrow, with an extension that allows some specified degree of assurance (e.g., 99%) that the confidence interval will be sufficiently narrow. We make computer routines freely available, so that the methods developed can be used by researchers immediately.     

Probability matching in risky choice: The interplay of feedback and strategy availability

Probability matching in sequential decision making is a striking violation of rational choice that has been observed in hundreds of experiments. Recent studies have demonstrated that matching persists even in described tasks in which all the information required for identifying a superior alternative strategy—maximizing—is present before the first choice is made. These studies have also indicated that maximizing increases when (1)?the asymmetry in the availability of matching and maximizing strategies is reduced and (2)?normatively irrelevant outcome feedback is provided. In the two experiments reported here, we examined the joint influences of these factors, revealing that strategy availability and outcome feedback operate on different time courses. Both behavioral and modeling results showed that while availability of the maximizing strategy increases the choice of maximizing early during the task, feedback appears to act more slowly to erode misconceptions about the task and to reinforce optimal responding. The results illuminate the interplay between “top-down” identification of choice strategies and “bottom-up” discovery of those strategies via feedback.     

Human risky choice under temporal constraints: tests of an energy-budget model

Risk-sensitive foraging models predict that choice between fixed and variable food delays should be influenced by an organism's energy budget. To investigate whether the predictions of these models could be extended to choice in humans, risk sensitivity in 4 adults was investigated under laboratory conditions designed to model positive and negative energy budgets. Subjects chose between fixed and variable trial durations with the same mean value. An energy requirement was modeled by requiring that five trials be completed within a limited time period for points delivered at the end of the period (block of trials) to be exchanged later for money. Manipulating the duration of this time period generated positive and negative earnings budgets (or, alternatively, "time budgets"). Choices were consistent with the predictions of energy-budget models: The fixed-delay option was strongly preferred under positive earnings-budget conditions and the variable-delay option was strongly preferred under negative earnings-budget conditions. Within-block (or trial-by-trial) choices were also frequently consistent with the predictions of a dynamic optimization model, indicating that choice was simultaneously sensitive to the temporal requirements, delays associated with fixed and variable choices on the upcoming trial, cumulative delays within the block of trials, and trial position within a block.