The Negative Effect of Probability Assessments on Decision Quality

It is commonly assumed that uncertain information can be reduced to numerical probabilities without biasing preferences. It is also implicitly assumed in much research and many applications that people can express these probabilities. In contradiction to these assumptions Experiment 1 shows that the production of probability assessments biases decisions in an n-person game. Experiment 2 shows that the explicit assessment of numerical probabilities renders choices between gambles concerning future basketball events less optimal. These findings seem to be a result of overweighting the probability dimension relative to the payoff dimension given numerical judgments. Experiment 2 also suggests that without explicit numerical probability judgments subjects are less likely to violate the dominance principle. The theoretical and practical implications of the results are discussed.     

The Directionality of Verbal Probability Expressions: Effects on Decisions,Predictions, and Probabilistic Reasoning

Verbal phrases denoting uncertainty are of two kinds: positive, suggesting the occurrence of a target outcome, and negative, drawing attention to its nonoccurrence (Teigen & Brun, 1995). This directionality is correlated with, but not identical to, high and low p values. Choice of phrase will in turn influence predictions and decisions. A treatment described as having “some possibility” of success will be recommended, as opposed to when it is described as “quite uncertain,” even if the probability of cure referred to by these two expressions is judged to be the same (Experiment 1). Individuals who formulate their chances of achieving a successful outcome in positive terms are supposed to make different decisions than individuals who use equivalent, but negatively formulated, phrases (Experiments 2 and 3). Finally, negative phrases lead to fewer conjunction errors in probabilistic reasoning than do positive phrases (Experiment 4). For instance, a combination of 2 “uncertain” outcomes is readily seen to be “very uncertain.” But positive phrases lead to fewer disjunction errors than do negative phrases. Thus verbal probabilistic phrases differ from numerical probabilities not primarily by being more “vague,” but by suggesting more clearly the kind of inferences that should be drawn.     

Gambles vs. quasi-realistic scenarios: expectations to find probability and risk-defusing information

The paper investigates predecisional information search in risky decisions, specifically information concerning the probability of a negative outcome and whether a risk-defusing operator (RDO) is available. Experiment 1 (54 participants) tested the hypothesis that search for such information is triggered by expectations that it can be obtained in the situation. Cues for the availability of information were manipulated. It was predicted that cues mentioning possible information sources raise expectations and consequently increase search activity. Furthermore, gambles were expected to differ from other real world contexts, with lower expectations for RDOs and higher ones for probabilities. The Method of Active Information Search was employed. The number of questions asked about probability and RDOs in different conditions confirmed the hypotheses. Experiment 2 (36 participants) ruled out the alternative interpretation that the expectation to actually find favorable probabilities or applicable RDOs respectively, rather than the expectation to obtain information, determined information search.     

The agony of victory and thrill of defeat: Mixed emotional reactions to disappointing wins and relieving losses

Because of counterfactual comparisons, good outcomes that could have been better (i.e., disappointing wins) and bad outcomes that could have been worse (i.e., relieving losses) elicit relatively middling ratings on bipolar emotion scales. We conducted two experiments with gambles to examine whether such outcomes elicit neutral emotions, sequentially mixed emotions of positive and negative affect, or simultaneously mixed emotions. In Experiment 1, static unipolar measures of positive and negative affect revealed that disappointing wins and relieving losses elicit mixed emotions, rather than relatively neutral emotions. In Experiment 2, participants provided continuous unipolar measures of positive and negative affect by pressing one button whenever they felt good and another button whenever they felt bad. Results revealed that disappointing wins and relieving losses elicit positive and negative affect simultaneously, rather than in alternation.     

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.     

The effects of control on betting: paradoxical betting on items of high confidence with low value

Traditional decision theories emphasize the probabilities and values of possible outcomes, but decisions may also be influenced by perceived control, with control defined as probability alterability. In 3 experiments, participants were offered bets on their own answers to general knowledge questions, bets that are characterized by control. The bets were fair if participants' reported confidence was well calibrated, positively valued if participants were underconfident, but unfavorable when participants were overconfident. Bet acceptance was a steep, linear, increasing function of confidence that is termed paradoxical betting. This pattern was generally contrary to the value of bets (considered either as average outcome or as subjective utility) and was steeper in slope than matched bets on apparently random events in Experiment 3. The author argues that control is a fundamental determinant of decision making that is readily incorporated in some existing models of decision weighting.     

Verbal probabilities: a question of frame?

Verbal expressions of probability and uncertainty are of two kinds: positive (‘probable’, ‘possible’) and negative (‘not certain’, ‘doubtful’). Choice of term has implications for predictions and decisions. The present studies show that positive phrases are rated to be more optimistic (when the target outcome is positive), and more correct, when the target outcome actually occurs, even in cases where positive and negative phrases are perceived to convey the same probabilities (Experiments 1 and 2). Selection of phrase can be determined by linguistic frame. Positive quantifiers (‘some’, ‘several’) support positive probability phrases, whereas negative quantifiers (‘not all’) suggest negative phrases (Experiment 3). Positive frames induced by numeric frequencies (e.g. the number of students to be admitted) imply positive probability phrases, whereas negative frames (e.g. the number of students to be rejected) call for negative probability phrases (Experiment 4). It is concluded that choice of verbal phrase is based not only on level of probability, but also on situational and linguistic cues. Copyright © 2002 John Wiley & Sons, Ltd.     

概率水平与模糊性对短视损失规避的影响

短视损失规避是指如果投资者频繁地评估其投资回报,那么他就会经常改变其投资决策,进而减少对风险资产的投入。本文采用实验法探讨了任务概率水平以及模糊性对短视损失规避的影响。结果发现短视损失规避只存在于中等损失概率任务中,说明该现象并非普遍存在;当概率模糊时,高损失概率任务中出现短视损失规避,而低损失概率任务中则出现反向的短视损失规避,说明模糊性能扩展“短视”起作用的概率范围。     

Is guilt ‘likely’ or ‘not certain’?: Contrast with previous probabilities determines choice of verbal terms

This research focuses on what determines speakers' choice of positive and negative probability phrases (e.g., “a chance” vs. “not certain”) in a legal context. We argue that choice of phrase to describe an event's probability of occurrence can be determined by the contrast between its current p value and an earlier p value, and not by that current value alone. Three experiments were conducted describing scenarios where profilers communicated a suspect's probability of guilt to the police. In the first study, a probability estimate is revised upwards or downwards. In the second one, the probability estimate of a speaker is higher or lower than that given by a previous speaker. In both cases, participants expected upward trends to lead to positive phrases, whereas downward trends were associated with negative phrases. In a third study, participants had to select probability phrases to characterize two different suspects. No contrast effects were found. We conclude that verbal probability directionality has primarily an argumentative function, where positive phrases are selected when probabilities are contrasted with smaller p values, and negative when contrasted with higher p values.     

Riskier for me or for others? The role of domain and probability in self-other differences,in risky decision-making

Abstract

In social and economic interactions, people often decide differently for others, as against for themselves, under situations involving risks. This sometimes leads to conflicts or contradictions. Although previous studies have explored such contradictions, the findings have been inconsistent. To reconcile these inconsistencies, this paper investigates the role played by the different domains and probabilities in the self-other differences under risk. Two groups of participants completed a gambling task combining different domains (gain vs. loss) and probabilities (small vs. large). One group made decisions for others and the other group made decisions for themselves. The results revealed a four pattern of discrepancy: the ones who made decisions for others were less risk-seeking than those who made decisions for themselves over the small probability gains. This was reversed over the large probability gains. Conversely, the participants who made decisions for others were more risk-seeking than those who made decisions for themselves over the small probability losses. The results were reversed over the large probability losses. These results reconcile the contradictory findings of the previous studies and suggest the significant role played by contextual factors in such discrepancies.     

Do people really believe they are above average?

A question that has plagued self-enhancement research is whether participants truly believe the overly positive self-assessments they report, or whether better-than-average effects reflect mere hopes or self-presentation. In a test of people’s belief in the accuracy of their self-enhancing trait ratings, participants made a series of bets, each time choosing between betting that they had scored at least as high on a personality test as a random other participant, or betting on a random drawing in which the probability of success was matched to their self-assigned percentile rank on the test. They also reported the point at which they would switch their bet from their self-rating to the drawing, or vice versa. Participants were indifferent between betting on themselves or on the drawing, and it took only a slight change in the drawing’s probability for them to switch their bet, indicating that people truly believe their self-enhancing self-assessments.     

The effect of constant outcome value on judgments and decision making given linguistic probabilities

Two experiments were performed to determine whether judgments of the relative chances of two independent events occurring are biased by constant outcome values contingent on the events when the uncertainties are specified by linguistic expressions (e.g. doubtful). In Experiment 1, subjects directly judged the relative chances of the two events, of which one was represented by a spinner and the other by a linguistic probability expression. In Experiment 2, only linguistic probability expressions were used to describe the two events and a betting procedure was used. A bias was evident in both studies, such that the relative judgments tended to favour the event with the positive rather than the negative contingent outcome. The bias was smaller for the low- than for the high-probability phrases. Individual differences were great, with the bias appearing strongly in only about one-third of the population. Theoretical implications of the present and related results are discussed.     

Too good to be true? Psychological responses to uncommon options in risk–reward environments

Risks and rewards, or payoffs and probabilities, are inversely related in many choice environments. We investigated people's psychological responses to uncommon combinations of risk and reward that deviate from learned regularities (e.g., options that offer a high payoff with an unusually high probability) as they evaluated risky options. In two experiments (N = 183), participants first priced monetary gambles drawn from environments in which risks and rewards were negatively correlated, positively correlated, or uncorrelated. In later trials, they evaluated gambles with uncommon combinations of risk and reward—that is, options that deviated from the respective environment's risk–reward structure. Pricing, response times, and (in Experiment 2) pupil dilation were recorded. In both experiments, participants took more time when responding to uncommon compared to foreseeable options or when the same options were presented in an uncorrelated risk–reward environment. This result was most pronounced when the uncommon gambles offered higher expected values compared to the other gambles in the set. Moreover, these uncommon, high‐value options were associated with an increase in pupil size. These results suggest that people's evaluations of risky options are based not only on the options' payoffs and probabilities but also on the extent to which they fit the risk–reward structure of the environment.     

Confidence in judgments based on incomplete information: An investigation using both hypothetical and real gambles

This study assessed how confidence in judgments is affected by the need to make inferences about missing information. Subjects indicated their likelihood of taking each of a series of gambles based on both probability and payoff information or only one of these sources of information. They also rated their confidence in each likelihood judgment. Subjects in the Explicit Inference condition were asked to explicitly estimate the values of missing information before making their responses while subjects in the Implicit Inference condition were not. The manner in which probability information was framed was also manipulated. Experiment 1 employed hypothetical gambles and Experiment 2 employed gambles with real money. Expressed likelihood of taking gambles was higher when probability was phrased in terms of '% chance of winning' rather than '% chance of losing', but this difference was somewhat less with real gambles than with hypothetical gambles. Confidence ratings in each experiment were actually higher on incomplete information trials than on complete information trials in the Explicit Inference condition. Results were related to the general issue of confidence in judgments.     

Thinking styles and risky decision‐making: Further exploration of the affect–probability weighting link

People usually overweight small probabilities and underweight large probabilities leading to the familiar inverse S‐shaped weighting function. This research explores the link between affect and the structure of probability weighting from the perspective of thinking dispositions, a concept central to dual system theories of reasoning. The effects of affective priming and cognitive load on both probability weighting and the value function are also examined. The evidence suggests that thinking styles do have predictive implications for risky decision‐making. Participants with a more affective thinking style tend to be more risk‐seeking in small probability gambles. However, increasing access to the affective system by affective priming or cognitive load manipulations tend to reduce risk‐seeking behavior in small probability gambles as well as reduce risk averse behavior in large probability gambles. Previous research, manipulating the affective nature of lottery outcomes, found evidence for an increase in curvature (more overweighting of small probabilities and more underweighting of large probabilities) of the weighting function for affect‐rich outcomes, lending support to a hope‐and‐fear deconstruction of probability weighting. The present research suggests that increased anticipatory emotions characterized by the elevation of the weighting function (more overweighting at all probabilities) is also important and could sometimes be more significant than hope‐and‐fear in decision‐making under risk. An integrated approach incorporating the impact of affect on all three, the elevation and curvature of probability weighting as well as the curvature of the value function explains the empirical findings. Copyright © 2010 John Wiley & Sons, Ltd.