How Affect Shapes Risky Choice: Distorted Probability Weighting Versus Probability Neglect

People's choices between prospects with relatively affect‐rich outcomes (e.g., medical side effects) can diverge markedly from their choices between prospects with relatively affect‐poor outcomes (e.g., monetary losses). We investigate the cognitive mechanisms underlying this “affect gap” in risky choice. One possibility is that affect‐rich prospects give rise to more distortion in probability weighting. Another is that they lead to the neglect of probabilities. To pit these two possibilities against each other, we fitted cumulative prospect theory (CPT) to the choices of individual participants, separately for choices between options with affect‐rich outcomes (adverse medical side effects) and options with affect‐poor outcomes (monetary losses); additionally, we tested a simple model of probability neglect, the minimax rule. The results indicated a qualitative difference in cognitive mechanisms between the affect‐rich and affect‐poor problems. Specifically, in affect‐poor problems, the large majority of participants were best described by CPT; in affect‐rich problems, the proportion of participants best described by the minimax rule was substantially higher. The affect gap persisted even when affect‐rich outcomes were supplemented by numerical information, thus providing no support for the thesis that choices in affect‐rich and affect‐poor problems diverge because the information provided in the former is nonnumerical. Our findings suggest that the traditional expectation‐based framework for modeling risky decision making may not readily generalize to affect‐rich choices. Copyright © 2015 John Wiley & Sons, Ltd.     

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)。     

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。     

Modeling the Impact of Control on the Attractiveness of Risk in a Prospect Theory Framework

Many decisions involve a degree of personal control over event outcomes, which is exerted through one's knowledge or skill. In three experiments we investigated differences in decision making between prospects based on a) the outcome of random events and b) the outcome of events characterized by control. In Experiment 1, participants estimated certainty equivalents (CEs) for bets based on either random events or the correctness of their answers to U.S. state population questions across the probability spectrum. In Experiment 2, participants estimated CEs for bets based on random events, answers to U.S. state population questions, or answers to questions about 2007 NCAA football game results. Experiment 3 extended the same procedure as Experiment 1 using a within-subjects design. We modeled data from all experiments in a prospect theory framework to establish psychological mechanisms underlying decision behavior. Participants weighted the probabilities associated with bets characterized by control so as to reflect greater risk attractiveness relative to bets based on random events, as evidenced by more elevated weighting functions under conditions of control. This research elucidates possible cognitive mechanisms behind increased risk taking for decisions characterized by control, and implications for various literatures are discussed.     

Money does not stink: Using unpleasant odors as stimulus material changes risky decision making

Odors are strong elicitors of affect, and they play an important role in guiding human behavior, such as avoiding fire or spoiled food. However, little is known about how risky decision making changes when stimuli are olfactory. We investigated this question in an experimental study of risky decision making with unpleasant odors and monetary losses in a fully incentivized task with real outcomes. Odor and monetary decisions were matched so that monetary losses corresponded to the amount of money participants were willing to pay to avoid smelling an odor. Hierarchical Bayesian analyses using prospect theory show that participants were less sensitive to probabilities when gambling with odors than when gambling with money. These results highlight the importance of taking the sensory modality into account when studying risky decision making.     

封面故事、选项框架和损益概率对风险偏好的影响

以股市投资为背景设计决策问题,考查了问题的封面故事类型、备择选项框架和风险项的概率水平对327名股民被试和465名大学生被试的风险偏好的影响。结果表明,股民被试的风险偏好不同于大学生被试,前者在所有实验处理上呈现出稳定的风险回避倾向。大学生被试在不同类型的封面故事下呈现出不同的风险偏好。在传统的坏封面故事下,风险偏好只受到备择选项框架的影响,不受损益概率的影响,即出现经典的框架效应现象。在好封面故事下,风险偏好受到备择选项框架、损益概率及两者交互作用的影响,即在高概率水平上出现框架效应现象,在低概率水平上出现框架效应反转现象     

Modeling the effect of reward amount on probability discounting

The present study with college students examined the effect of amount on the discounting of probabilistic monetary rewards. A hyperboloid function accurately described the discounting of hypothetical rewards ranging in amount from $20 to $10,000,000. The degree of discounting increased continuously with amount of probabilistic reward. This effect of amount was not due to changes in the rate parameter of the discounting function, but rather was due to increases in the exponent. These results stand in contrast to those observed with the discounting of delayed monetary rewards, in which the degree of discounting decreases with reward amount due to amount-dependent decreases in the rate parameter. Taken together, this pattern of results suggests that delay and probability discounting reflect different underlying mechanisms. That is, the fact that the exponent in the delay discounting function is independent of amount is consistent with a psychophysical scaling interpretation, whereas the finding that the exponent of the probability-discounting function is amount-dependent is inconsistent with such an interpretation. Instead, the present results are consistent with the idea that the probability-discounting function is itself the product of a value function and a weighting function. This idea was first suggested by Kahneman and Tversky (1979), although their prospect theory does not predict amount effects like those observed. The effect of amount on probability discounting was parsimoniously incorporated into our hyperboloid discounting function by assuming that the exponent was proportional to the amount raised to a power. The amount-dependent exponent of the probability-discounting function may be viewed as reflecting the effect of amount on the weighting of the probability with which the reward will be received.     

Choice Environment, Market Complexity, and Consumer Behavior: A Theoretical and Empirical Approach for Incorporating Decision Complexity into Models of Consumer Choice

Most empirical models of choice in economics and consumer research assume that the decision maker assesses all alternatives and information in a perfect information-processing sense. The complexity of the choice environment, the ability of the individual to make complex decisions, and the effect of choice context on the decision strategy are generally not considered in statistical model development. One of the reasons for this omission is that theoretical literature on choice complexity and imperfect ability to choose that has developed in psychology and behavioral decision theory (BDT) literatures has not been translated into empirical econometric analysis. Second, the data used in economics and consumer research studies tend to be somewhat different from the data structures used in psychology and BDT literatures. In this paper we outline a theoretical model that simultaneously considers task complexity, effort applied by the consumer, ability to choose, and choice. We then construct a measure of task complexity and incorporate this in an analysis of a number of data series based on the random utility framework. We also examine the performance of our measure of task complexity in a composite data set that allows for increased variability in factors affecting decision context. Our approach provides a mechanism to link research in BDT and econometric modeling of consumer choice. Our findings suggest that task complexity does affect inferences about choice model parameters and that context effects, such as complexity, have a systematic impact on the parameters of econometric models of choice. The modeling approach provides a mechanism for inclusion of results from psychology and BDT in traditional economic models of consumer choice.     

The Recovery of Correlation Between Latent Abilities Using Compensatory and Noncompensatory Multidimensional IRT Models

This research examined correlation estimates between latent abilities when using the two-dimensional and three-dimensional compensatory and noncompensatory item response theory models. Simulation study results showed that the recovery of the latent correlation was best when the test contained 100% of simple structure items for all models and conditions. When a test measured weakly discriminated dimensions, it became harder to recover the latent correlation. Results also showed that increasing the sample size, test length, or using simpler models (i.e., two-parameter logistic rather than three-parameter logistic, compensatory rather than noncompensatory) could improve the recovery of latent correlation.     

分类中相似性的理论与模型

相似性在分类的原型理论、样例理论、定义理论和理论解释观中都扮演着重要的角色。人们对相似性的研究由来已久,但是它在分类的领域中至今仍是一个相对模糊的概念,这部分地由于揭示相似性的真正机制将涉及到复杂的信息加工过程。本文以分类中的相似性为出发点介绍了近期相似性研究的一些理论与模型并在此基础上对概念和分类领域中的相似性研究进行了分析和总结。     

An eye‐tracking study on information processing in risky decisions: Evidence for compensatory strategies based on automatic processes

Many everyday decisions have to be made under risk and can be interpreted as choices between gambles with different outcomes that are realized with specific probabilities. The underlying cognitive processes were investigated by testing six sets of hypotheses concerning choices, decision times, and information search derived from cumulative prospect theory, decision field theory, priority heuristic and parallel constraint satisfaction models. Our participants completed 40 decision tasks of two gambles with two non‐negative outcomes each. Information search was recorded using eye‐tracking technology. Results for choices, decision time, the amount of information searched for, fixation durations, the direction of the information search, and the distribution of fixations conflict with the prediction of the non‐compensatory priority heuristic and indicate that individuals use compensatory strategies. Choice proportions are well in line with the predictions of cumulative prospect theory. Process measures indicate that individuals thereby do not rely on deliberate calculations of weighted sums. Information integration processes seem to be better explained by models that partially rely on automatic processes such as decision field theory or parallel constraint satisfaction models. Copyright © 2010 John Wiley & Sons, Ltd.     

Framing and Risky Choice as Influenced by Comparison of One's Achievements with Others: The Case of Investment in the Stock Exchange

Based on social comparison theory and equity theory, the first aim of this study was to examine the hypothesis that framing is affected not only by previous success or failure, but also by comparisons with relevant others' outcomes as well. The second aim of the study was to examine prospect theory propositions that people are risk aversive for gains and risk seeking for losses. A total of 220 students were administered scenarios that described outcomes of their stock investments (gains or losses). In addition, they were provided with information about their close friends' outcomes investing in similar stocks. Generally, the hypothesis regarding the influence of others' outcomes on framing was confirmed. However, results showed that, in contradiction to prospect theory, gain framing rather than loss framing was related to risk seeking behavior. Specifically, in the gain framing situation, the readiness to take risks was highest when the others' outcomes were equal to those of the participants. The limitations of prospect theory are discussed.     

Revealed Indifference and Models of Choice Behavior

This paper introduces an approach to the study of rational choice behavior which is based on the concept of subjective indifference, as well as its relationships with both the classical preference-based approach and the choice behavior approach. With regard to the first relationship (which has already been studied in Alcantud, 2001, as a purely topological and order-theoretical problem) new considerations are now put forward in the decision theory context. In short, if a decisionmaker has some indifference classes defined on a choice set, then we know the conditions under which his/her tastes can be modeled by a continuous preference yielding these indifference classes. The second problem is posed and tackled here and gives place to a theory of revealed indifference, where both the decisive, and indecisive cases will be considered.     

Extending Standard Models of ZFC to Models of Nonstandard Set Theories

We study those models of ZFCwhich are embeddable, as the class of all standard sets, in a model of internal set theory >ISTor models of some other nonstandard set theories. This revised version was published online in June 2006 with corrections to the Cover Date.     

Do Politicians Take Risks Like the Rest of Us? An Experimental Test of Prospect Theory Under MPs

Political psychologists have been quick to use prospect theory in their work, realizing its potential for explaining decisions under risk. Applying prospect theory to political decision‐making is not without problems, though, and here we address two of these: (1) Does prospect theory actually apply to political decision‐makers, or are politicians unlike the rest of us? (2) Which dimension do politicians use as their reference point when there are multiple dimensions (e.g., votes and policy)? We address both problems in an experiment with a unique sample of Dutch members of parliament as participants. We use well‐known (incentivized) decision situations and newly developed hypothetical political decision‐making scenarios. Our results indicate that politicians’ deviate from expected utility theory in the direction predicted by prospect theory but that these deviations are somewhat smaller than those of other people. Votes appear to be a more important determinant of politicians’ reference point than is policy.     

A Simple Axiomatization of Binary Rank-Dependent Utility of Gains (Losses)

For binary gambles composed only of gains (losses) relative to a status quo, the rank-dependent utility model with a representation that is dense in intervals is shown to be equivalent to ten elementary properties plus event commutativity and a gamble partition assumption. The proof reduces to a (difficult) functional equation that has been solved by Aczél, Maksa, and Páles (in press).     

表征动量的理论模型述评

表征动量是指由于诱导物理动量的作用, 人们对先前运动刺激最终位移的记忆将沿着运动的方向向前发生偏移的现象。诱导物理重力、摩擦力、万有引力同样影响运动刺激最终位移的定位, 扩展了表征动量的概念。相关的表征动量理论模型有：内化理论、朴素物理理论、预期理论、网络模型、眼动理论、双加工理论和计算理论。未来的研究应分别从普遍性和特殊性方面继续探讨表征动量的理论模型, 并加强神经机制的研究, 以便更好的解释日常生活中的内隐运动。