Numeracy as a Predictor of Adaptive Risky Decision Making

Numeracy or one's ability to appropriately process and use numerical information has been shown to be an important individual difference factor in decision making. The current study utilized a risky decision‐making task (called the “cups task”) in which choices are made to both earn and avoid losing hypothetical money. Critically, this design allowed investigators to examine numeracy‐related differences in adaptive decision‐making as measured by sensitivity to expected value (EV) differences over 54 paired‐choice trials—some in which it was advantageous to take a risk and some in which it was not. Results showed that in an undergraduate sample of 114 individuals, the less numerate took more risks and were less sensitive to varying EV levels than the more numerate, especially when it was disadvantageous to take a risk and when the choice involved a potential loss (rather than a gain). These results are consistent with a dual processing account in which the more numerate are much better than the less numerate at extracting the precise affective “gist” of the numerical information, which is then used to determine the goodness or badness of a particular choice. Copyright © 2012 John Wiley & Sons, Ltd.     

整合模型还是占优启发式模型? 从齐当别模型视角进行的检验

实验从齐当别模型的视角,通过对决策过程反应时的考察分别对以累积预期理论(cumulative prospect theory)为代表的整合模型和启发式模型家族的重要成员--占优启发式模型(priority heuristic)--进行检验。结果表明,决策过程反应时并未随着占优启发式模型所假定的决策步骤的增加而变慢;也未随着选项之间整体值差值的变大而变快;模糊决策过程的反应时反而快于风险决策过程的反应时。无论是以累积预期理论为代表的整合模型还是占优启发式模型均不能满意地描述和解释人们的实际决策过程,而齐当别模型则能解释大部分实验结果。文章建议多角度、多指标探讨人们的决策过程,检验、修改、完善,以及建立新的启发式模型或决策过程模型(process model),以增进对人们如何进行风险决策的理解。     

A signal detection analysis of gist-based discrimination of genetic breast cancer risk

Pervasive biases in probability judgment render the probability scale a poor response mode for assessing risk judgments. By applying fuzzy trace theory, we used ordinal gist categories as a response mode, coupled with a signal detection model to assess risk judgments. The signal detection model is an extension of the familiar model used in binary choice paradigms. It provides three measures of discriminability—low versus medium risk, medium versus high risk, and low versus high risk—and two measures of response bias. We used the model to assess the effectiveness of BRCA Gist, an intelligent tutoring system designed to improve women’s judgments and understanding of genetic risk for breast cancer. Participants were randomly assigned to the BRCA Gist intelligent tutoring system, the National Cancer Institute (NCI) Web pages, or a control group, and then they rated cases that had been developed using the Pedigree Assessment Tool and also vetted by medical experts. BRCA Gist participants demonstrated increased discriminability for all three risk categories, relative to the control group; the NCI group showed increased discriminability for two of the three levels. This result suggests that BRCA Gist best improved discriminability among genetic risk categories, and both BRCA Gist and the NCI website improved participants’ ability to discriminate, rather than simply shifting their decision criterion. A spreadsheet that fits the model and compares parameters across the conditions can be downloaded from the Behavior Research Methods website and used in any research involving categorical responses.     

A Model of Financial Incentive Effects in Decision Making

This paper proposes a model of the mediating processes whereby performance-contingent financial incentives influence decision quality and provides empirical evidence relevant to assessing the model. We hypothesize that performance-contingent incentives impact both cognitions and emotions, and that these cognitive and affective changes mediate the relationship between incentives and decision quality. To test these hypotheses, 84 undergraduate students were randomly assigned to conditions in which financial incentives were either performance contingent or randomly distributed. Participants used software that collected data on their information processing behavior to make choices from multiattribute choice information displays. After completing their choices, participants′ level of negative affect was assessed. Consistent with the predictions of the model, participants offered performance-contingent incentives took longer to choose, examined more information, had higher levels of negative affect, and used decision strategies that led to more accurate choices than participants offered randomly distributed incentives. Path analyses using structural equations modeling indicated that the changes in information processing behavior induced by financial incentives increased decision quality, while the increased levels of negative affect associated with incentives decreased decision quality. The paper concludes that identifying and measuring mediating variables is an important component of a research agenda designed to generate predictive theory of the relationship between financial incentives and decision quality.     

The effect of imperfect memory recall on risk preferences

People often take on different levels of risk when deciding on future actions compared with when they take actions with immediate consequences. The presently reported research investigated how imperfect recall of previously chosen options influences temporal fluctuations in risk preferences. In two incentivized studies with a waiting time before decision resolution (a 4-week waiting period from an initial decision), we observed that errors in the recall of previous choices played a substantial role in constructing risk preferences for choices that are usually resolved after a delay. More specifically, in a first study, we found that after a waiting period (i.e., after participants waited for their risky choices to be resolved), participants perceived that they took less risk during their initial choices than they actually did. Importantly, when asked about whether they would change their initial choices, participants declared that they would take riskier choices. In a second study, we tested directly whether such a shift in initial choices could also be demonstrated behaviorally. Results revealed that after beliefs about past choices were induced, participants changed their risk preferences in line with the information presented during belief induction.     

Down the Garden Path: The Role of Conditional Inference Processes in Self‐Persuasion

In a controlled experiment, information format and prior knowledge of risk‐related decision attributes altered the response to decision conflict produced by negatively correlated attributes (NCA) in choice under uncertainty. When dominated choice alternatives were presented in a format in which the displayed attributes were not negatively correlated, decision makers used a simple choice process based on the displayed information. This allowed them to detect the dominated alternatives, regardless of their prior knowledge. However, when the same alternatives were presented in a format in which the displayed attributes were negatively correlated, the more‐knowledgeable decision makers used a compensatory choice process based on the displayed attributes and, consequently, missed the dominated alternatives. The less‐knowledgeable participants, who were unable to use the displayed attributes because of their lack of expertise, calculated the nondisplayed attributes and detected the dominated alternatives. With NCA, the more‐knowledgeable participants followed a conflict‐resolution strategy using the displayed NCAs, whereas the less‐knowledgeable individuals followed a conflict‐avoidance strategy using the uncorrelated, nondisplayed attributes that inadvertently revealed the dominance structure of the decision. The implications of person factors for the effects of NCA and in other types of decisions with NCA are discussed.     

对整合模型和占优启发式模型的检验：基于信息加工过程的眼动研究证据

基于信息加工过程视角, 本研究采用眼动技术检验风险决策整合模型和占优启发式模型。结果表明, 自主决策任务条件下决策过程反应时及信息搜索模式均不同于期望价值(EV)迫选任务条件下的决策过程反应时及信息搜索模式; 自主决策任务条件下决策过程反应时并未随着选项间整体值(CPT值)差值的变大而变快, 且基于特征(attribute-based)的信息搜索多于基于选项(option-based)的信息搜索, 不符合整合模型预期。此外, 决策者亦未按照占优启发式模型所假定的决策步骤进行决策。基于信息加工过程的检验结果既不利于以累积预期理论为代表的整合模型, 亦不利于占优启发式模型。文章建议从决策过程视角检验已有决策模型及建立新的启发式决策过程模型(process model)。     

Sex Differences in Risk Taking: Repeated Sessions on a Computer-Simulated Task

Two experiments were conducted to investigate sex differences in risktaking behavior on a computer-generated and controlled task. Male and female subjects faced a video display of simulated mine fields with varying numbers and patterns of dots representing mines in the fields. In Experiment 1, they estimated the probability that a tank might successfully cross 100 mine fields when starting from an unknown point below each field. This was followed by the risk-taking task in which they decided whether to send a tank across each of the fields. The participants were tested on the risk-taking task once in Experiment 1 and over four separate sessions in Experiment 2. Scores, based on decision outcomes, and decision latencies were recorded. No significant sex differences were found in the participants' ability to estimate probabilities or in their total scores for decisions made on the risk-taking task. In low probability-of-success situations, women initially took greater risks than men but took longer to make their decisions; in all subsequent sessions, this pattern was reversed, with men taking greater risks and a longer time to make decisions. The findings support the growing body of evidence that men are more inclined to take risks than women in a variety of situations, indicate the importance of obtaining data over repeated sessions when investigating sex differences in risk taking, and demonstrate that computer-simulated tasks can provide a valid means for laboratory studies of sex differences in risk taking.     

Developmental patterns of change in the influence of safe and risky peer choices on risky decision‐making

Adolescents take more risks when peers monitor their behavior. However, it is largely unknown how different types of peer influence affect adolescent decision‐making. In this study, we investigate how information about previous choices of peers differentially influences decision‐making in adolescence and young adulthood. Participants (N = 99, age range 12–22) completed an economic choice task in which choice options were systematically varied on levels of risk and ambiguity. On each trial, participants selected between a safer choice (low variability in outcome) and a riskier choice (high variability in outcome). Participants made choices in three conditions: a solo condition in which they made choices with no additional information, a social condition in which they saw choices of supposed peers, and a computer condition in which they saw choices of a computer. Results showed that participants’ choices conform to the choices made by the peers, but not a computer. Furthermore, when peers chose the safe option, late adolescents were especially likely to make a safe choice. Conversely, when the peer made a risky choice, late adolescents were least likely to follow choices made by the peer. We did not find evidence for differential influence of social information on decisions depending on their level of risk and ambiguity. These results show that information about previous decisions of peers are a powerful modifier for behavior and that the effect of peers on adolescents’ decisions is less ubiquitous and more specific than previously assumed.     

不确定性容忍度、损益概率及延迟风险对延迟选择的影响

研究通过两个实验考查了不确定性容忍度及相关变量对延迟选择的影响,其中实验1采用2（不确定性容忍度：高/低）×2（概率水平：高/中）被试间实验设计;研究2将实验任务设定在有延迟风险情景下中等概率水平,采用单因素（不确定性容忍度：高/低）被试间实验设计.实验1结果表明：不确定性容忍度与概率水平存在交互作用：中等概率时,低容忍度个体比高容忍度个体更偏好延迟选择,高概率时,两者的延迟选择无显著差异,都偏好于选择决策.实验2结果表明：在有延迟风险中等概率时,高、低容忍度个体的决策偏好无显著差异,都偏好选择决策.结论：不确定性容忍度对延迟选择存在影响且受概率水平和延迟风险的调节.     

Understanding variability in binary and continuous choice

Excessive variability in binary choice (categorical judgment) can take the form of probability matching rather than the normatively correct behavior of deterministically choosing the more likely alternative. Excessive variability in continuous choice (judgment rating) can take the form of underconfidence, understating the probability of highly likely events and overstating the probability of very unlikely events. We investigated the origins of choice variability in terms of noise prior to decision (at the evidence stage) and at the decision stage. A version of the well-known medical diagnosis task was conducted with binary and continuous choice on each trial. Noise at evidence stage was reduced by allowing the subjects to view historical summaries of prior relevant trials, and noise at the decision stage was reduced by giving the subjects a numerical score on the basis of their continuous choice and the actual outcome. Both treatments greatly reduced variability. Cash payments based on the numerical score had a less reliable incremental effect in our experiment. The overall results are more consistent with a Logit model of decision than with a simple criterion (or maximization) rule or a simple probabilitymatching rule.     

Consumer affects when making undesirable purchases to meet the minimum purchase requirement: Decision‐related variables as moderators

One common type of sales promotion involves a minimum purchase requirement (MinPR), where customers must purchase at least a minimum number of products to enjoy a discount. In the process of making purchases to qualify for the discount, consumers may find their first‐choice product options or have to settle for products that they did not originally prefer. Three between‐subjects experiments examines whether, in various decision situations, counterfactual thinking (CFT) might bias individuals' emotions in response to desirable versus undesirable purchases. Study 1 demonstrates that participants who made undesirable purchases to meet the MinPR felt less satisfied with the purchase outcome precipitated by upward CFT, whereas downward CFT led to feelings of pleasure in participants who could find their first‐choice product options. Studies 2 and 3 find that counterfactual emotions of undesirable purchases were more pronounced when participants experienced a difficult decision process because of a narrow promotion scope or when time pressure, manipulated in terms of explicit deadlines, is heavy rather than light, respectively. On the contrary, participants' responses to desirable purchases did not vary as a function of decision difficulty or time pressure.     

越老越风险规避吗？——年龄对冲动性预测决策行为的调节效应

年老化伴随着风险承担倾向的改变,而决策行为受冲动性的影响是否受到年龄的调节尚不清楚。研究采用两种不同类型的决策任务以及Barratt冲动性量表,考察老年人风险承担在自我报告和决策行为上的改变。结果显示老年人在剑桥博弈任务中更加风险寻求而在模拟充气球任务中更加风险规避。同时冲动性可以显著预测模拟充气球的行为,且该预测受到年龄的调节。研究结果提示,老年人并不是单一的更加风险规避或者风险寻求,而是与任务特异性相关。同时,冲动性可以较好的预测年轻人的决策行为,而对老年人的决策行为没有预测作用。     

Strategy Selection in Risky Choice: The Impact of Numeracy,Affect, and Cross‐Cultural Differences

Real‐world decisions often involve options with outcomes that are uncertain and trigger strong affect (e.g., side effects of a drug). Previous work suggests that when choosing among affect‐rich risky prospects, people are rather insensitive to probability information, potentially compromising decision quality. We modeled the strategies of less and more numerate participants in the United States and in Germany when choosing between affect‐rich prospects and between monetarily equivalent affect‐poor prospects. Using large probabilistic national samples (n = 1047 from the United States and Germany), Study 1 showed that compared with more numerate participants, less numerate participants chose the normatively better option (i.e., the one with the higher expected value) less often, guessed more often, and relied more on a simple risk‐minimizing strategy. U.S. participants—although less numerate—selected the normatively better option more frequently and were more consistent across affect‐rich and affect‐poor problems than the German participants. Using a targeted quota sample (n = 118 from Germany), Study 2 indicated that although both more and less numerate participants paid less attention to probability information in affect‐rich than in affect‐poor problems, the two numeracy groups relied on different outcome‐based heuristics: More numerate participants often followed the minimax heuristic, and less numerate participants the affect heuristic. The observed strategy differences suggest that attempts to improve decision‐making need to take into account individual differences in numeracy as well as cultural‐specific experiences in making trade‐offs. Copyright © 2012 John Wiley & Sons, Ltd.     

Decision making under time pressure, modeled in a prospect theory framework

The current research examines the effects of time pressure on decision behavior based on a prospect theory framework. In Experiments 1 and 2, participants estimated certainty equivalents for binary gains-only bets in the presence or absence of time pressure. In Experiment 3, participants assessed comparable bets that were framed as losses. Data were modeled to establish psychological mechanisms underlying decision behavior. In Experiments 1 and 2, time pressure led to increased risk attractiveness, but no significant differences emerged in either probability discriminability or outcome utility. In Experiment 3, time pressure reduced probability discriminability, which was coupled with severe risk-seeking behavior for both conditions in the domain of losses. No significant effects of control over outcomes were observed. Results provide qualified support for theories that suggest increased risk-seeking for gains under time pressure.     

资源困境中共同收益延迟的影响：时间折扣的调节效应

通过测量83名大学生的时间折扣率和不同共同收益延迟时距上的金币拿取量,以探讨资源困境中共同收益延迟对个体决策的影响及时间折扣的调节效应。结果表明：（1）金币拿取量随共同收益延迟时距的增长而增加,增加趋势和初始时间点的金币拿取量均存在显著的个体差异;（2）时间折扣率反向调节初始延迟时间点的金币拿取量,正向调节金币拿取量随延迟时距增长而增加的速率。这表明资源困境与跨期选择两个不同研究领域具有紧密联系,对当前资源保护制度的制定与实施具有一定的启发意义。     

Learning to allocate limited time to decisions with different expected outcomes

The goal of this article is to investigate how human participants allocate their limited time to decisions with different properties. We report the results of two behavioral experiments. In each trial of the experiments, the participant must accumulate noisy information to make a decision. The participants received positive and negative rewards for their correct and incorrect decisions, respectively. The stimulus was designed such that decisions based on more accumulated information were more accurate but took longer. Therefore, the total outcome that a participant could achieve during the limited experiments’ time depended on her “decision threshold”, the amount of information she needed to make a decision. In the first experiment, two types of trials were intermixed randomly: hard and easy. Crucially, the hard trials were associated with smaller positive and negative rewards than the easy trials. A cue presented at the beginning of each trial would indicate the type of the upcoming trial. The optimal strategy was to adopt a small decision threshold for hard trials. The results showed that several of the participants did not learn this simple strategy. We then investigated how the participants adjusted their decision threshold based on the feedback they received in each trial. To this end, we developed and compared 10 computational models for adjusting the decision threshold. The models differ in their assumptions on the shape of the decision thresholds and the way the feedback is used to adjust the decision thresholds. The results of Bayesian model comparison showed that a model with time-varying thresholds whose parameters are updated by a reinforcement learning algorithm is the most likely model. In the second experiment, the cues were not presented. We showed that the optimal strategy is to use a single time-decreasing decision threshold for all trials. The results of the computational modeling showed that the participants did not use this optimal strategy. Instead, they attempted to detect the difficulty of the trial first and then set their decision threshold accordingly.     

How race affects evidence accumulation during the decision to shoot

The biasing role of stereotypes is a central theme in social cognition research. For example, to understand the role of race in police officers’ decisions to shoot, participants have been shown images of Black and White males and instructed to shoot only if the target is holding a gun. Findings show that Black targets are shot more frequently and more quickly than Whites. The decision to shoot has typically been modeled and understood as a signal detection process in which a sample of information is compared against a criterion, with the criterion set for Black targets being lower. We take a different approach, modeling the decision to shoot as a dynamic process in which evidence is accumulated over time until a threshold is reached. The model accounts for both the choice and response time data for both correct and incorrect decisions using a single set of parameters. Across four studies, this dynamic perspective revealed that the target’s race did not create an initial bias to shoot Black targets. Instead, race impacted the rate of evidence accumulation with evidence accumulating faster to shoot for Black targets. Some participants also tended to be more cautious with Black targets, setting higher decision thresholds. Besides providing a more cohesive and richer account of the decision to shoot or not, the dynamic model suggests interventions that may address the use of race information in decisions to shoot and a means to measure their effectiveness.     

Decision making in a dynamic situation: The effect of false alarms and time pressure

An experiment was conducted to investigate the effect of a priori probability of false alarms and time pressure on decision-making behaviour in a dynamic task environment. In order to assess whether strategy selection in a dynamic task environment would be adaptive, we modelled the task mathematically, and compared actual decision strategies to the optimal ones. In addition to the selected strategy, we also studied decision-making behaviour at a lower operational level, reflecting the amount of effort subjects are willing to spend on the decision process. Subjects were required to monitor the fitness level of a simulated athlete, who was running a race, and had to provide treatments whenever the athlete's fitness level suggested a real physiological problem. When a decline of the athlete's fitness was caused by a false alarm, a spontaneous recovery would occur after some time, without any need for intervention. Time pressure was manipulated by the rate at which the athlete's fitness level declined. Overall, subjects did not select the most efficient strategy: they dominantly selected information before applying an action, even though it would have been more profitable, and less effortful, just to apply actions. At the operational level, subjects appeared to invest less effort when the probability of false alarms increased and to invest more effort when time pressure increased. However, in contrast to the outcomes of our mathematical model, subjects adjusted the amount of intervention to the a priori probability of false alarms and not to time pressure. Together, the results indicate that the selection of a decision strategy in a dynamic task is less adaptive then is generally concluded from studies with static tasks.     

Which Is Better: Simultaneous or Sequential Choice?

The term "diversification bias" refers to the tendency for people to take more variety when choosing several items simultaneously than when choosing them sequentially. In this article, we investigate whether this really is a bias by measuring evaluations of sets chosen simultaneously or sequentially. In Experiment 1 participants made two choices between audio tracks for consecutive consumption. Participants liked low-variety sets most and were more likely to choose high-variety sets in simultaneous choice. In Experiment 2 participants chose between three gambles which varied in the probability of winning and their expected value. Again, simultaneous choices seemed worse than sequential ones: The simultaneous-choice groups took far more low expected value gambles than did sequential-choice subjects and rated their enjoyment as lower. We conclude that simultaneous choice often leads to outcomes that are worse than sequential choice and discuss the circumstances when this is likely to be true.