The role of potential loss in the influence of affect on risk-taking behavior

In three experiments the influence of positive affect on risk-taking behavior was examined. In Experiment 1 subjects who received a free gift of candy, compared to those in a control group, were willing to pay increasingly more for lottery tickets as the prize rose from $10 to $90 and as the probability of winning rose from .10 to .90. In Experiment 2 subjects who received a free gift of candy, compared to those in a control group, were willing to pay more to buy insurance against loss, and were particularly more likely to do so when the potential loss was large. A third study, which found that subjects who received a free gift of candy were not willing to pay more for an item than were control subjects, led us to conclude that the results of the first two experiments are not best interpreted as merely due to a general increase in the willingness to spend as a consequence of having received a gift. Instead it was concluded that positive feelings can foster both risk-prone behavior (Experiment 1) and risk-averse behavior (Experiment 2). When a positive-affect subject faces a risk situation in which the potential loss is emphasized, the subject demonstrates risk aversion; when the potential loss is minimized, then risk proneness is observed.     

Cognitive processes underlying lottery and sports gambling decisions: The role of stated probabilities and background knowledge

Two studies compared choice and underlying cognitive processes in equivalent decision tasks involving risk and uncertainty (lotteries versus sports gambles including displayed expert probability judgements). In sports gambles, background knowledge was triggered via information on team location, home or away. Otherwise, displayed risk information (stake, winnings, odds, and outcome probabilities) was controlled across gamble type. In a choice study, home win bets were chosen significantly more frequently than draws or away wins, compared to lottery equivalents. In a parallel study eliciting concurrent verbal protocols, participants made fewer evaluations of odds and probabilities, and more statements involving background knowledge in sports gambles. Furthermore, some sports gamble protocols indicated modifications of stated probabilities and decision strategies contingent on domain knowledge. It was concluded that stated probability revision and knowledge-based reasoning are key cognitive processes in sports gambling not normally applied in the lottery paradigms often employed in decision research.     

Subjective probability and delay.

Human subjects indicated their preference between a hypothetical $1,000 reward available with various probabilities or delays and a certain reward of variable amount available immediately. The function relating the amount of the certain-immediate reward subjectively equivalent to the delayed $1,000 reward had the same general shape (hyperbolic) as the function found by Mazur (1987) to describe pigeons' delay discounting. The function relating the certain-immediate amount of money subjectively equivalent to the probabilistic $1,000 reward was also hyperbolic, provided that the stated probability was transformed to odds against winning. In a second experiment, when human subjects chose between a delayed $1,000 reward and a probabilistic $1,000 reward, delay was proportional to the same odds-against transformation of the probability to which it was subjectively equivalent.     

Testing Credit and Blame Attributions as Explanation for Choices under Ambiguity

People make decisions every day based on their estimates of the chances of various events occurring. By their very nature, these subjective estimates are less certain, and thus more ambiguous, than objective probabilities such as those associated with roulette wheels or lotteries. In two experimental studies, we investigate choices between bets on the decision maker′s knowledge versus bets on a lottery with the same chance of winning. In Study 1, we partially replicate the Heath and Tversky (1991) finding that subjects have an increasing preference for betting on their own knowledge over the matched-chance lottery as probability increases. We also discover a significant minority of subjects who exhibit the opposite pattern and prefer the lottery as probability increases. In addition, we explicitly test the subjects′ attributions about the credit they would feel for a win and the blame they would feel for a loss, and these attributions do provide some explanation for their choice behavior. In Study 2, we manipulate knowledge and accountability, in an attempt to heighten the attributions of credit and blame, and we replicate the findings.     

"It Could Be Us!": Cognitive and Social Psychological Factors in UK National Lottery Play

This study examines the cognitive and social psychological factors underlying UK National Lottery play. A total of 384 respondents were asked about their own lottery playing behaviours, their knowledge of lottery odds and their beliefs about the role of skill, chance, luck and optimism in lottery play. Using hypothetical scenarios, respondents were also asked to rate the likelihood of winning the lottery jackpot (matching all six numbers) with number combinations reflecting different levels of apparent randomness, previous matches, near misses and prize size manipulations. Frequency of lottery play was found to be positively correlated with age, income, Instants scratchcard play, gambling on horse/greyhound racing, the football pools, and bingo as well as with beliefs about skill, luck and optimism. Frequency of lottery play was negatively correlated with general education and estimate of relative win likelihoods based on the perceived randomness of number combinations. Planned contrasts revealed that compared to individual (non‐syndicate) players, syndicate lottery players played more regularly and gambled more on the football pools. Results are discussed in the light of current cognitive theories surrounding the misperception of probability and their relation to lottery play and in the need for future models to recognise the social factors inherent in syndicate‐based lottery participation.     

公正世界信念对记忆偏差的影响

公正世界信念指人们需要相信他们所处的世界是一个公正有序的世界。本研究考察的是公正世界信念是否影响人们的记忆,让人产生记忆偏差。实验一中,被试首先阅读一则彩票中奖的新闻,然后阅读关于中奖者人品的描述,最后被试需要回忆中奖金额。结果发现,中奖者的个性品质影响对奖金数额的记忆。实验二中,两组被试分别阅读一则维护公正世界信念或威胁公正世界信念的无关故事,接下来程序与实验一相同。结果发现,预先激活的公正世界信念状态与中奖者个性品质在记忆结果上存在显著的交互效应。结果表明,公正世界信念能够导致记忆偏差。     

The same but different: an empirical investigation of the reducibility principle

According to classical utility theory the valuation of any lottery should depend only on its outcomes and their respective probabilities, and should not be affected by the nature, complexity and structure of the chance mechanism. Previous research has documented systematic violations of this principle. For example, most subjects prefer lotteries in which the payoffs are contingent on the joint occurrence of multiple (high probability) events to simple lotteries, and lotteries in which the earlier stages offer higher probabilities than the later stages. We review the various violations of this principle and suggest a classification into two major types associated with misunderstanding of chance mechanisms and attitude towards the chance mechanism and process. In the present study 40 subjects were presented with 30 pairs of binary gambles. In any given pair the lotteries had identical outcomes and equal ‘reduced’ probabilities (and thus equal expected values). However, the chance mechanisms varied along a variety of factors such as the size of the sample space, the number of stages, temporal ordering, order of probabilities, their transparency and time constraints. Half the subjects saw lotteries involving gains and the other half considered only losses. After choosing one lottery in each pair, the subjects were asked to explain and justify their choices. The findings revealed systematic violations of the reducibility principle: subjects displayed a preference for lotteries with larger sample spaces, and for lotteries that allow quicker resolutions in the earlier stages. A clear distinction between some patterns of preferences in the gains and loss domains was revealed. In gambles involving gains subjects preferred to have the highest probability on the first stage (and the lowest probability on the last stage), but displayed the opposite preferences for losses. A content analysis of the subjects' stated reasons for their choices identified eight major categories. The most frequently invoked were hope, fun, simplicity, stress and time. Copyright © 2001 John Wiley & Sons, Ltd.     

Choosing Between Lotteries: Remarkable Coordination Without Communication

The current research examines tacit coordination behavior in a lottery selection task. Two hundred participants in each of three experiments and 100 in a fourth choose to participate in one of two lotteries, where one lottery has a larger prize than the other. Independent of variations in the complexity of the mechanism of prize allocation, the prize amounts, and whether the lottery is the participant's first or second choice, we typically find that the percentage of participants who choose the high versus low‐prize lotteries does not significantly differ from the equilibrium predictions. This coordination is achieved without communication or experience. We additionally find that participants with an analytical thinking style and a risk‐averse tendency are more likely to choose the low‐prize lottery over the high‐prize lottery. This tendency seems to be stable across choices. The pattern of our results suggests that to achieve tacit coordination, having a subset of individuals who attend to the choices of others is sufficient. Copyright © 2012 John Wiley & Sons, Ltd.     

Cognitive strategies for coping with uncertain outcomes

It was proposed that, when faced with highly desirable but uncertain outcomes, people may employ cognitive strategies in an attempt to influence their future affective responses to the outcomes in question. The present study attempted to demonstrate the use of two such strategies. First, it was hypothesized that when people are faced with a low probability of obtaining a highly desirable outcome, they tend to derogate that outcome by perceiving it as less attractive. Second, it was proposed that when people are faced with uncertainty regarding the occurrence of a highly desirable outcome, they tend to underestimate the likelihood of its occurrence, in an attempt to avoid future disappointment. These hypotheses were tested within the context of a lottery in which subjects were given a low, moderate, or high chance of winning a prize that was either high or low in attractiveness. As predicted, subjects viewed the highly attractive prize as less valuable and attractive when they had a low probability of winning than when the probability of winning was moderate or high. Subjects also perceived themselves as less likely to win when the prize was high in attractiveness than when it was low in attractiveness. The relationship of these findings to studies of self-handicapping and attribute ambiguity is discussed.     

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.     

Probability and delay of reinforcement as factors in discrete-trial choice.

Pigeons chose between two alternatives that differed in the probability of reinforcement and the delay to reinforcement. A peck on the red key always produced a delay of 5 s and then a possible reinforcer. The probability of reinforcement for responding on this key varied from .05 to 1.0 in different conditions. A response on the green key produced a delay of adjustable duration and then a possible reinforcer, with the probability of reinforcement ranging from .25 to 1.0 in different conditions. The green-key delay was increased or decreased many times per session, depending on a subject's previous choices. The purpose of these adjustments was to estimate an indifference point, or a delay that resulted in a subject's choosing each alternative about equally often. In conditions where the probability of reinforcement was five times higher on the green key, the green-key delay averaged about 12 s at the indifference point. In conditions where the probability of reinforcement was twice as high on the green key, the green-key delay at the indifference point was about 8 s with high probabilities and about 6 s with low probabilities. An analysis based on these results and those from studies on delay of reinforcement suggests that pigeons' choices are relatively insensitive to variations in the probability of reinforcement between .2 and 1.0, but quite sensitive to variations in probability between .2 and 0.     

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.     

Risk preferences in young children: early evidence of individual differences in reaction to potential gains and losses

New methods were developed for studying risky decision making in children as young as age five. Each child was given a block of ‘gain’ trials, for example, a choice between a sure gain of one prize and a 50:50 chance of gaining either two prizes or no prize, and a block of ‘loss’ trials, for example, a choice between a sure loss of one prize and a 50:50 chance of losing either two prizes or no prize. We were thus able to compare risky choice for gains and losses at the level of the individual child. In each of two experiments a variety of individual difference variables were measured, including in Experiment 2, the child's parent's scores on the same task. Across experiments, the preponderance of choices was of the risky option. However, most children and adults made more risky choices in the domain of losses than in the domain of gains. Predictors of individual differences in children included shyness, impulsivity, and the risk taking of the child's parent. We suggest that methods are now in place to encourage further studies of decision processes in young children. Copyright © 2003 John Wiley & Sons, Ltd.     

The Effect of Catastrophe Potential on the Interpretation of Numerical Probabilities of the Occurrence of Hazards1

Two studies demonstrated that identical numerical probabilities of the occurrence of hazards are judged as higher when these involve potential catastrophes compared to noncatastrophic hazards. Fifteen hazards were presented that involve a potential catastrophe and 15 noncatastrophic hazards. Each hazard was given a numerical probability, which was either 1:10, 1:1,000, or 1:100,000. Numerical probabilities were rated as larger when these concerned hazards that have catastrophe potential compared to the noncatastrophic hazards, also when this effect was controlled for perceived benefits. Similar results were obtained in a second study, which controlled for possible confounds (e.g., base rate). The results suggest that verbal interpretations of numerical probabilities of the occurrence of hazards include more than only probability, for instance one's attitude toward the hazardous activity. Implications for risk communication are discussed.     

Impugning Randomness, Convincingly

John organized a state lottery and his wife won the main prize. You may feel that the event of her winning wasn’t particularly random, but how would you argue that in a fair court of law? Traditional probability theory does not even have the notion of random events. Algorithmic information theory does, but it is not applicable to real-world scenarios like the lottery one. We attempt to rectify that.     

When Equal Chances = Good Chances: Verbal Probabilities and the Equiprobability Effect

When six equally qualified candidates compete for the same position, p = 1/6 for each. People seem to accept this principle more readily for numerical than for verbal probabilities. Equal chances with three to six alternatives are often verbally described in a positive vein as "entirely possible" or "a good chance" and rarely negatively as "doubtful" or "improbable." This equiprobability effect of verbal probabilities is demonstrated in five studies describing job applicants, lottery players, competing athletes, and examination candidates. The equiprobability effect is consistent with a causal (propensity) view of probabilities, where chances are believed to reflect the relative strength of facilitating and preventive causes. If important conditions in support of the target outcome are present (the candidate is qualified for the position), and there is little to prevent it from occurring (no stronger candidates), chances appear to be good. In the presence of obstacles (one stronger candidate), or in the absence of facilitating conditions (the candidate is poorly qualified), chances appear to be poor, even when numerical p values remain constant. The findings indicate that verbal and numerical probability estimates can reflect different intuitions. Copyright 2001 Academic Press.     

Cognitive Biases in Playing the Lottery: Estimating the Odds and Choosing the Numbers

Three experiments were conducted to examine the operation of the representativeness and anchoring and adjustment heuristics in lottery play. Subjects in Experiments 1 and 2 indicated their chances of winning a lottery with an objective probability of 1 in 10. Consistent with the anchoring and adjustment heuristic, subjects (in both experiments) perceived their chances of winning to be greater when the lottery was based on a single event than when it was based on a disjunctive event. Subjects in these two experiments also selected numbers to play in a pick-3 (Experiment 1) or pick-4 (Experiment 2) lottery. Consistent with the representativeness heuristic, subjects in Experiment 2 demonstrated a preference for numbers without repeating digits. This also occurred in Experiment 3 wherein the numbers actually played in the Indiana daily Pick-3 lottery were examined.     

Delay or probability discounting in a model of impulsive behavior: effect of alcohol

Little is known about the acute effects of drugs of abuse on impulsivity and self-control. In this study, impulsivity was assessed in humans using a computer task that measured delay and probability discounting. Discounting describes how much the value of a reward (or punisher) is decreased when its occurrence is either delayed or uncertain. Twenty-four healthy adult volunteers ingested a moderate dose of ethanol (0.5 or 0.8 g/kg ethanol: n = 12 at each dose) or placebo before completing the discounting task. In the task the participants were given a series of choices between a small, immediate, certain amount of money and $10 that was either delayed (0, 2, 30, 180, or 365 days) or probabilistic (i.e., certainty of receipt was 1.0, .9, .75, .5, or .25). The point at which each individual was indifferent between the smaller immediate or certain reward and the $10 delayed or probabilistic reward was identified using an adjusting-amount procedure. The results indicated that (a) delay and probability discounting were well described by a hyperbolic function; (b) delay and probability discounting were positively correlated within subjects; (c) delay and probability discounting were moderately correlated with personality measures of impulsivity; and (d) alcohol had no effect on discounting.     

The priority heuristic: making choices without trade-offs

Bernoulli's framework of expected utility serves as a model for various psychological processes, including motivation, moral sense, attitudes, and decision making. To account for evidence at variance with expected utility, the authors generalize the framework of fast and frugal heuristics from inferences to preferences. The priority heuristic predicts (a) the Allais paradox, (b) risk aversion for gains if probabilities are high, (c) risk seeking for gains if probabilities are low (e.g., lottery tickets), (d) risk aversion for losses if probabilities are low (e.g., buying insurance), (e) risk seeking for losses if probabilities are high, (f) the certainty effect, (g) the possibility effect, and (h) intransitivities. The authors test how accurately the heuristic predicts people's choices, compared with previously proposed heuristics and 3 modifications of expected utility theory: security-potential/aspiration theory, transfer-of-attention-exchange model, and cumulative prospect theory.     

The effect of order of presentation of verbal probability expressions on numerical estimates in a medical context

Many medical decisions are made on a probability estimate. Models of risk benefit calculations in health behaviour rarely articulate how people perceive and appraise such probability. Cognitive processes may mediate the processing of probability expressions and may be important to understand the meaning or the range of meanings that probability statements portray to patients. Past studies have indicated that verbal expressions of probability are vague and subject to individual interpretation. On the theoretical level when subjects are asked to translate a set of verbal probability expressions, ranging from high to low, into their equivalent numerical expressions subjects usually produce a continuum of numerical equivalents also ranging from high to low. In practice clinicians frequently communicate information about uncertainty to the patients by verbal probability estimates. This study explored the effect of the order of presentation of the verbal expressions on the numerical probabilities produced by a group of medical students (n?=?87) in relation to medical probabilities. The results showed that the order of presentation (descending vs. random) of the verbal probability expressions was found to have a significant effect on three of the seven numerical probabilities produced by the subjects. The order effect is discussed to together with implications for clinical practice.