Modeling certainty equivalents for imprecise gambles

We present results from two experiments on the relative importance of, and subjects' differential sensitivity to, vagueness on both probabilities and outcomes. Subjects in these studies made certainty equivalent (CE) judgments for precise and vague gambles. In the first study subjects responded to gain gambles only; in the second they judged both gain and loss gambles. Model-free analyses of the results indicate (a) a higher concern for the precision of the outcomes than that of the probabilities, (b) vagueness seeking for positive outcomes and (c) vagueness avoidance for negative outcomes and (d) no strong modal attitude toward vagueness on the probability dimension. The greater salience of the outcomes can be explained by the nature of the response mode (CEs). The reflection of attitudes towards outcome vagueness in the two domains can be explained by the distinct goals of the DMs in the two cases, which cause them to focus on the highest (most desirable) possible gain or the largest (most dreaded) conceivable loss. We propose and fit a new model of decision making with vaguely specified attributes that generalize the Prospect Theory model for the precise case. The new generalized model combines the two submodels (preference among precise lotteries and effects of vagueness) and allows estimation of the vagueness parameters. These estimated parameters are consistent with, and confirm, the patterns uncovered by the qualitative analysis.     

Boundary effects of vague risk information on taxpayer decisions

In compliance decisions, the decision maker usually has only vague or ambiguous knowledge of the probability of being caught and the outcome (amount of penalty). An experiment is reported which extends work on effects of probability ambiguity by manipulating outcome ambiguity as well. When outcomes were limited to a bounded range and probabilities ranged between their natural boundaries [0, 1] in experimental tax decisions, symmetrical boundary effects were found in which vague estimates for both the probability and outcome dimensions caused vagueness aversion (and higher compliance) when the vague estimate was near the more favorable lower boundary of either dimension and vagueness seeking (and lower compliance) when the vague estimate was near the less favorable upper boundary. Probability and outcome vagueness effects were found to be independent of the vagueness of the other dimension, and vagueness effects were not systematically related to the level of the other dimension.The results suggest that a common cognitive process mediates the impact of vagueness on both dimensions. This may be a vagueness-adjustment process in which vague estimates are adjusted toward the middle of the bounded range, or a vagueness-preference process in which vague outcomes, and vague probabilities as well, are evaluated based on utility considerations, as though probability were a tangible commodity. For increasing compliance, the results suggest that risk information should be disseminated only when risks of punishment are relatively high. When risks are low, random enforcement techniques that enhance vagueness become more effective.     

Effects of religious denomination on sex differences in occupational expectations

The degree of difference between men and women in occupational expectations and attitude toward careers for married women are related to the degree of discrimination against women in religious denominations. Occupational expectations are scored along the dimension of masculinity. Discrimination against women is indicated by extent and timing of the ordination of women within the denominations for which subjects indicated a preference. Data are a subselection of 12,018 cases from a national sample of 189,733 first-time full-time entering college freshmen. The difference between women and men in masculinity of occupational choice and agreement with the attitude “Activities of married women are best confined to the home and family” are positively related to denominational discrimination against women.     

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.     

Stochastic transitivity and the unidimensional control of choice

A concurrent-chains paradigm was used to test three models of preference for schedules of reinforcement. Each model assumes choice to be a monotonic function of values on a single dimension (“simple scalability”). For choices involving variable-interval and fixed-interval schedules, this dimension is assumed to be an harmonic average of the interreinforcement intervals; for choices involving fixedinterval and fixed-ratio schedules, the dimension is the time to reinforcement irrespective of response rate; for choices involving different combinations of rate and duration of reinforcement, the dimension is the rate of “reinforcement-time”, or the product of the two parameters. Each model implies a strong form of transitivity (“functional equivalence”), which held for half the subjects (that half exclusively sensitive to the reinforcement variable specified by the model). An alternative unidimensional model which implies a weaker form of transitivity (“weak binary utility model”) was consistent with the preferences of all subjects. This model states that a single factor controls the direction of preferences but not necessarily the exact choice probability, as simple scalability assumes.     

Social comparison on two dimensions

In this experiment social comparison on two task dimensions has been studied. The subjects received bogus feedback on their performance on two tests, one allegedly measuring creativity, the other alertness. By means of this feedback four relative position conditions were induced: scoring high on both tests, scoring low on both tests, scoring high on creativity and low on alertness, and vice versa. Anticipating either a co-operative or a competitive game, the subjects indicated their preference for one or the other task dimension and also expressed their preference for a comparison person. It was found that, as predicted, the subjects preferred and valued comparison dimensions on which they occupied a favourable position. With respect to preference for a comparison person, compensatory choices were obtained: on the dimension on which the subject performed well, they preferred an inferior other. On the dimension on which they performed poorly, they preferred a superior other. This pattern of choices was found in co-operation as well as in competition. Finally, upward preference was stronger in co-operative than in competitive conditions, particularly on the dimension on which the subject's own score was low. These and other results were discussed in relation to theoretical social comparison notions.     

Optional processes in similarity judgments

This research investigates the nature of similarity relations among three pairs of interacting dimensions: (1) the integral dimensions of auditory pitch and loudness, (2) the configurai dimensions of paired parentheses, and (3) the cross-modally corresponding dimensions of visual position and auditory pitch. We evaluated the rules by which information from each dimension combines in similarity judgments. Our claim is that, when judging similarity, processes that are obligatory, or what we call mandatory processes, can commingle with processes of choice, or what we call optional processes. By varying instructions, we found strong evidence of optional processing. Instructions to rate overall similarity encouraged subjects to attend to stimuli as wholes and led to a Euclidean rule in similarity scaling. Instructions to focus on dimensions encouraged subjects to consider each stimulus dimension separately and led to a city-block rule. We argue that optional processes may obscure mandatory ones, and so need to be identifled-beforernandatory processes can be understood.     

Optional processes in similarity judgments.

This research investigates the nature of similarity relations among three pairs of interacting dimensions: (1) the integral dimensions of auditory pitch and loudness, (2) the configural dimensions of paired parentheses, and (3) the cross-modally corresponding dimensions of visual position and auditory pitch. We evaluated the rules by which information from each dimension combines in similarity judgments. Our claim is that, when judging similarity, processes that are obligatory, or what we call mandatory processes, can commingle with processes of choice, or what we call optional processes. By varying instructions, we found strong evidence of optional processing. Instructions to rate overall similarity encouraged subjects to attend to stimuli as wholes and led to a Euclidean rule in similarity scaling. Instructions to focus on dimensions encouraged subjects to consider each stimulus dimension separately and led to a city-block rule. We argue that optional processes may obscure mandatory ones, and so need to be identified before mandatory processes can be understood.     

An hypothesis generation model for judgment in nonmetric multiple-cue probability learning

The purpose of this paper is to present a two-phase hypothesis generation model to describe behavior in multiple-cue probability learning tasks with nonmetric cues. The model assumes that on each trial the subject generates two sets of hypotheses: (a) a hypothesis concerning which cue dimension (or pattern) will lead to a correct prediction on that trial and (b) a hypothesis concerning which response will be correct given the cue dimension attended to on that trial.Five-hundred-twelve subjects were assigned to 20 groups in a binary choice task involving two binary cue dimensions. Each group observed cues which differed in validity. Analysis of the data indicated that subjects attend to both cue dimensions in making judgments even when one cue has zero validity. A test of the fit of the observed data to the asymptotic response proportions predicted by the model indicated a reasonable fit.     

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.     

Testing the bi‐dimensional effects of attitudes on behavioural intentions and subsequent behaviour

Attitudes are typically treated as unidimensional predictors of both behavioural intentions and subsequent behaviour. On the basis of previous research showing that attitudes comprise two independent, positive and negative dimensions, we hypothesized that attitudes would be bi‐dimensional predictors of both behavioural intentions and subsequent behaviour. We focused on health‐risk behaviours. We therefore also hypothesized that the positive dimension of attitude (evaluations of positive behavioural outcomes) would better predict both behavioural intentions and subsequent behaviour than would the negative dimension, consistent with the positivity bias/offset principle. In Study 1 (cross sectional design), N = 109 university students completed questionnaire measures of their intentions to binge‐drink and the positive and negative dimensions of attitude. Consistent with the hypotheses, both attitude dimensions independently predicted behavioural intentions and the positive dimension was a significantly better predictor than was the negative dimension. The same pattern of findings emerged in Study 2 (cross sectional design; N = 186 university students) when we predicted intentions to binge‐drink, smoke and consume a high‐fat diet. Similarly, in Study 3 (prospective design; N = 1,232 speed limit offenders), both the positive and negative dimensions of attitude predicted subsequent (6‐month post‐baseline) speeding behaviour on two different road types and the positive dimension was the better predictor. The implications for understanding the motivation of behaviour and the development of behaviour‐change interventions are discussed.     

The Common Ratio Effect in Choice,Pricing, and Happiness Tasks

The Allais common ratio effect is one of the most robust violations of rational decision making under risk. In this paper, we conduct a novel test of the common ratio effect in which we elicit preferences for the common ratio choice alternatives in choice, pricing, and happiness rating tasks. We find large shifts in preference patterns across tasks, both within and between subjects. In particular, we find that both the consistency and distribution of responses differ systematically across tasks, with modal choices replicating the Allais preference pattern, modal happiness ratings exhibiting consistent risk aversion, and modal prices maximizing expected value. We discuss the predictions of various cognitive explanations of the common ratio effect in the context of our experiment. We find that a dual process framework provides the most complete account of our results. Surprisingly, we also find that although the Allais pattern was the modal behavior in the choice task, none of the 158 respondents in our experiment exhibited the Allais pattern simultaneously in choice, happiness, and pricing tasks. Our results constitute a new paradox for the leading theories of choice under risk. Copyright © 2017 John Wiley & Sons, Ltd.     

Bi-dimensional attitudes,attitude accessibility and speeding behaviour

Positive and negative attitude dimensions (i.e., bi-dimensional attitudes) asymmetrically predict behaviour, with the positive dimension being the better predictor than the negative dimension. These findings have been demonstrated using self-reported behaviour measures. In this study, we aimed to test the bi-dimensional attitude-behaviour relationship using objectively measured speeding behaviour derived from a driving simulator and test if the asymmetrical prediction of behaviour from the positive and negative attitude dimensions could be explained by attitude accessibility (how available an attitude is in memory and therefore how readily it is able to guide behaviour). One hundred and six drivers completed online measures of the positive and negative dimensions of their attitudes towards exceeding the speed limit. Response latency measures of the accessibilities of both dimensions were also taken. A driving simulator was used to measure speeding behaviour. Both attitude dimensions independently predicted speeding, with the positive dimension being the stronger predictor. The positive attitude dimension was also more accessible than was the negative dimension. The difference in the accessibilities of the positive and negative attitude dimensions significantly mediated the difference in their predictive validities. The results demonstrate that the positive attitude dimension is the principle predictor of speeding and a reason for this is that it is more accessible in memory than is the negative attitude dimension. Road safety interventions (e.g., education) that aim to reduce speeding and associated traffic crashes might usefully decrease the valence or accessibility of the positive attitude dimension. There would also appear to be scope to reduce speeding by increasing the valence or accessibility of the negative attitude dimension.     

Consumer information processing strategies in middle and late adulthood

The purpose of the present study was to investigate the extent to which performance of a complex cognitive task of a type resembling that encountered in everyday life is maintained through adulthood. A total of 80 subjects participated; 20 in their thirties, 20 in their fifties, 20 in their sixties, and 20 in their seventies. Subjects were asked to make preference judgments with respect to 32 pocket-size notebooks of a sort they might encounter as consumers in a stationery or variety store. Independently, they were also asked to express their preferences with respect to each of the four dimensions on which the notebooks varied. With only minor differences across age groups, most subjects demonstrated the ability to integrate their individual dimension preferences into a complex preference judgment of an object embodying those dimensions, in a logically consistent manner.     

艾勒悖论(Allais Paradox)另释

艾勒悖论违背了期望效用(Expected Utility)理论的独立性(independence)原则,成为欲推翻期望效用理论的杠杆。“齐当别”抉择模型不将风险决策行为看成是追求某种“最大期望值”的抉择反应,而将其看成是“最好可能结果之间的取舍”或者“最坏可能结果之间的取舍”。此项研究设计了一“判断”技术,并用此对艾勒设计的选择问题加以检验。实验表明,判断结果所示的“齐当别”策略能满意地对艾勒选择题作出解释。     

Perceived control,nature of risk information and risk taking. An experimental test of a simple taxonomy of uncertainty

Uncertainty may be categorized along two dimensions: (1) the nature of probabilistic information (i.e. frequency information, about the outcomes of similar situations in the past, versus process information, about the way(s) in which a future loss might occur), and (2) the degree of personal control (i.e. the extent to which an activity's outcomes depend on internal factors (e.g. knowledge, skills) versus external (e.g. chance) factors). The effects of variations in both dimensions on people's risk-taking tendency were experimentally studied. In a computerized task, subjects had to stop a fast-moving symbol before it passed a target line. Success yielded a financial gain, failure led them into a ‘penalty task’ with the possibility of a considerable loss. On each trial subjects chose among 10 risk levels (varying symbol speeds): low levels resulted in small but almost sure gains, high levels yielded larger but less probable gains. Across subgroups of subjects, three penalty task characteristics were varied: (1) the actual loss probability, (2) the external versus internal determination of outcomes, and (3) the available risk information. Major findings were: (a) subjects did not set a lower risk level, but they did appear to be more attentive (i.e. they failed fewer trials) when the actual loss probability was lower; (b) internal outcome determination resulted in more failed trials (lesser caution); (c) subjects ignored frequency information, but were sensitive to process information. Results are discussed in terms of effort allocation for controlling risk during task performance.     

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。     

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.     

Reinforcement uncertainty enhances preference for choice in humans

Under concurrent‐chains schedules of reinforcement, participants often prefer situations that allow selection among alternatives (free choice) to situations that do not (forced choice). The present experiment examined the effects of reinforcement probability on choice preferences. Preferences for free versus forced choice were measured under a condition in which participants' choices were always reinforced (reinforcement probability of 1.0) and a condition in which outcomes were uncertain (reinforcement probability of 0.5). Forty‐four college students participated and preferences were examined under a concurrent‐chains schedule of reinforcement. Participants preferred free choice under uncertain reinforcement, but a bias toward free choice was not observed when reinforcement was certain. These results align with previous findings of preference for free choice under conditions of uncertainty, but suggest that preference may be dependent upon probabilistic reinforcement contingencies in the terminal links of the concurrent‐chains arrangement. Thus, reinforcement probability is an important variable to consider when conducting similar studies on the value of choice.     

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.