Sympathetic magic and perceptions of randomness: The hot hand versus the gambler's fallacy

The gambler's fallacy and hot hand were studied in predictions about outcomes of coin tosses. A critical trial occurred when participants made predictions after a “run” of four heads or tails. Participants' attention was manipulated to focus on the person flipping the coin, the coin, or neither (control group) as a possible cause of the run. We also manipulated whether or not there was a change in who tossed the coin. In the control condition the standard reversal was observed (gambler's fallacy); however, when participants focused on the person, and it was that same person who conducted the run and critical coin toss, more people chose in the direction of continuation (hot hand). Directing attention to the person tossing the run seemed to prompt participants to behave as if that individual was “hot” in terms of getting a specific outcome (e.g., heads), as if by sympathetic magic, thus eliminating the gambler's fallacy.     

Deductive schemas with uncertain premises using qualitative probability expressions

The new paradigm in the psychology of reasoning redirects the investigation of deduction conceptually and methodologically because the premises and the conclusion of the inferences are assumed to be uncertain. A probabilistic counterpart of the concept of logical validity and a method to assess whether individuals comply with it must be defined. Conceptually, we used de Finetti's coherence as a normative framework to assess individuals' performance. Methodologically, we presented inference schemas whose premises had various levels of probability that contained non-numerical expressions (e.g., “the chances are high”) and, as a control, sure levels. Depending on the inference schemas, from 60% to 80% of the participants produced coherent conclusions when the premises were uncertain. The data also show that (1) except for schemas involving conjunction, performance was consistently lower with certain than uncertain premises, (2) the rate of conjunction fallacy was consistently low (not exceeding 20%, even with sure premises), and (3) participants' interpretation of the conditional agreed with de Finetti's “conditional event” but not with the material conditional.     

Explaining the gambler's fallacy: Testing a gestalt explanation versus the “law of small numbers”

The present study tests a gestalt (closure) explanation for the gambler's fallacy which posits that runs in random events will be expected to reverse only when the run is open or ongoing. This is contrasted with the law of small numbers explanation suggesting that people expect random outcomes to balance out generally. Sixty-one university students placed hypothetical guesses and bets on a series of coin tosses. Either heads or tails were dominant (8 versus 4). In a closed run condition the run ended prior to the critical trial (e.g., HHHT), and in an open run condition the run remained open (e.g., THHH). As hypothesised, participants showed the gambler's fallacy in the open run condition, but not in the closed run condition. This difference is not due to differential memory for the outcomes. Men, and people with more previous experience gambling, were also found to be more prone to the gambler's fallacy. It is argued that the gestalt explanation best explains the results.     

Detecting and predicting changes

When required to predict sequential events, such as random coin tosses or basketball free throws, people reliably use inappropriate strategies, such as inferring temporal structure when none is present. We investigate the ability of observers to predict sequential events in dynamically changing environments, where there is an opportunity to detect true temporal structure. In two experiments we demonstrate that participants often make correct statistical decisions when asked to infer the hidden state of the data generating process. However, when asked to make predictions about future outcomes, accuracy decreased even though normatively correct responses in the two tasks were identical. A particle filter model accounts for all data, describing performance in terms of a plausible psychological process. By varying the number of particles, and the prior belief about the probability of a change occurring in the data generating process, we were able to model most of the observed individual differences.     

热手谬误和赌徒谬误心理机制研究述评

在知觉随机序列时,人们倾向于把序列中实际上各自独立的相邻结果看作是存在正相关或负相关的,而出现热手谬误或赌徒谬误,又称为随机序列中的正负近因效应。有关这两谬误最早的心理机制的探索中,Kahneman 和Tversky采用局部代表性启发法对此进行了解释。但是这种解释也存在诸多不足,因此近期的一些模型（因果模型、Urn模型、记忆模型、适应模型和两阶段格式塔模型）分别从不同角度对两种谬误提出了新的解释。最后文章指出研究方法、神经机制、个体差异以及生活中的应用是该领域研究的几个未来发展方向     

A process model of the understanding of uncertain conditionals

To build a process model of the understanding of conditionals we extract a common core of three semantics of if-then sentences: (a) the conditional event interpretation in the coherencebased probability logic, (b) the discourse processingtheory of Hans Kamp, and (c) the game-theoretical approach of Jaakko Hintikka. The empirical part reports three experiments in which each participant assessed the probability of 52 if-then sentencesin a truth table task. Each experiment included a second task: An n-back task relating the interpretation of conditionals to working memory, a Bayesian bookbag and poker chip task relating the interpretation of conditionals to probability updating, and a probabilistic modus ponens task relating the interpretation of conditionals to a classical inference task. Data analysis shows that the way in which the conditionals are interpreted correlates with each of the supplementary tasks. The results are discussed within the process model proposed in the introduction.     

Fallacies in probability judgments for conjunctions and disjunctions of everyday events

The conjunction fallacy occurs when people judge a conjunction B‐and‐A as more probable than a constituent B, contrary to probability theory's ‘conjunction rule’ that a conjunction cannot be more probable than either constituent. Many studies have demonstrated this fallacy in people's reasoning about various experimental materials. Gigerenzer objects that from a ‘frequentist’ standpoint probability theory is not valid for these materials, and so failure to follow the conjunction rule is not a fallacy. This paper describes three experiments showing that the conjunction fallacy occurs as consistently for conjunctions where frequentist probability theory is valid (conjunctions of everyday weather events) as for other conjunctions. These experiments also demonstrate a reliable correlation between the occurrence of the conjunction fallacy and the disjunction fallacy (which arises when a disjunction B‐or‐A is judged less probable than a constituent B). This supports a probability theory + random variation account of probabilistic reasoning. Copyright © 2008 John Wiley & Sons, Ltd.     

Personality moderates the interaction between positive and negative daily events predicting negative affect and stress

A 30-day diary study examined personality moderators (neuroticism and extraversion) of the interaction between positive and negative daily events predicting daily negative affect and night-time stress. Multilevel analyses revealed positive daily events buffered the effect of negative daily events on negative affect for individuals low in neuroticism and individuals high in extraversion, but not for individuals high in neuroticism or individuals low in extraversion. Positive daily events also buffered the effect of negative daily events on that night’s stress, but only for participants low in neuroticism. As such, this research linked today’s events to tonight’s stressfulness. This study advances our understanding of how neuroticism and extraversion influence within-person associations between positive and negative events predicting negative affect and stress.     

An account of subjective probability judgment for joint events: Conjunctive and disjunctive

Probability judgment is a vital part of many aspects of everyday life. In the present paper, we present a new theory of the way in which individuals produce probability estimates for joint events: conjunctive and disjunctive. We propose that a majority of individuals produce conjunctive (disjunctive) estimates by making a quasi‐random adjustment, positive or negative, from the less (more) likely component probability with the other component playing no obvious role. In two studies, we produce evidence supporting propositions that follow from our theory. First, the component probabilities do appear to play the distinct roles we propose in determining the joint event probabilities. Second, contrary to probability theory and other accounts of probability judgment, we show that the conjunctive‐less likely probability difference is unrelated to the more likely disjunctive probability difference (in normative theory these quantities are identical). In conclusion, while violating the norms of probability judgment, we argue that estimates produced in the manner we propose will be close enough to the normative values especially given the changing nature of the external environment and the incomplete nature of available information.     

An improved method for counting stressful life events (SLEs) when predicting mental health and wellness

Objective: Checklists for registering stressful life events (SLEs) generally correlate negatively, but weakly, with mental health outcome measures. Thus, the present study examined various methodological approaches for improving these relationships.

Design: A total of 1679 participants (women?=?943, men?=?736, M age-39.8) were randomly drawn from the general Norwegian population (response rate 34%). This prospective cohort study included two follow-ups at 10 (n?=?1181) and 23 months (n?=?942).

Main outcome measures: Satisfaction with life and absence of psychological distress (i.e. anxiety and depression) represented a joint measure for indexing ‘mental wellness’ (MW).

Results: A simple count of SLEs weakly predicted MW, as expected, whereas the addition of a moderator (i.e. manageability of the event) substantially improved predictive power. Four additional moderators were examined: duration, impact, help-seeking and time since onset, but these were non-significant after inserting manageability into the model. This SLE counting method also retained its predictive power after including multiple criterion-related variables that substantially adjusted the longitudinal statistical model.

Conclusion: This new SLE counting method exhibited a considerable improvement to predicting mental health and well-being. It is well suited for use in epidemiological research requiring a short SLE checklist format with high predictive power.     

Updating beliefs in light of uncertain evidence: Descriptive assessment of Jeffrey's rule

Jeffrey (1983) proposed a generalisation of conditioning as a means of updating probability distributions when new evidence drives no event to certainty. His rule requires the stability of certain conditional probabilities through time. We tested this assumption (“invariance”) from the psychological point of view. In Experiment 1 participants offered probability estimates for events in Jeffrey's candlelight example. Two further scenarios were investigated in Experiment 2, one in which invariance seems justified, the other in which it does not. Results were in rough conformity to Jeffrey's (1983) principle.     

Childhood remembered: Reports of both unique and repeated events

To explore the significance of repeated memories for individuals' personal histories, we compared the characteristics of young adults' unique and repeated memories of childhood experiences. Memory type (unique vs. repeated) was a within-participant variable. In Experiment 1, college-age participants generated as many early memories as possible in 4 minutes; in Experiment 2, another sample provided complete reports of five early memories in each condition. In both experiments, participants rated the vividness, biographical importance and personal meaning of each memory and labelled the accompanying emotion. Unique memories were more vivid than repeated memories as well as more likely to include negative emotion, regardless of the method of reporting. Most importantly, college students rated their memories for unique and repeated events as equivalently infused with personal meaning. Analysis of the content of the memories reported in Experiment 2 established that unique and repeated memories did not differ in word count or percentages of perceptual terms or words indicating positive affect, although unique memories contained a greater percentage of negative affect. Additional analyses of content provided evidence for differences in the functions served by unique and repeated memories. The results have implications for the study of autobiographical memory and for identifying over-general memories.     

Measuring inaccuracy of uncertain doxastic states in many-valued logical systems

I will propose an alternative philosophical approach to the representation of uncertain doxastic states. I will argue that the current account of measuring inaccuracy of uncertain doxastic states is inadequate for Belnap's four-valued logic. Specifically, a situation can be found in which either an inaccuracy measure returns a completely wrong result or an agent's inaccuracy score is inadequate relative to the mistake in her doxastic attitude. This will motivate an alternative representation of uncertain doxastic states based on ordered pairs. I will describe a possible inaccuracy measure that is suitable for ordered pairs, and I will show that it has all the qualities that are required for an inaccuracy measure to be legitimate. Finally, I will introduce conditions of rationality for uncertain doxastic states represented by ordered pairs.     

Assessment and treatment of self-control with aversive events

Self-control can be defined as choosing a smaller, immediate aversive event over a larger, delayed aversive event (e.g., flossing daily instead of risking major dental problems later). Children with developmental disabilities have been found to respond impulsively when given the choice between aversive events that differ based on magnitude and difficulty. However, qualitative differences between events may also impact aversiveness. This study attempted to replicate and extend prior research by (i) empirically identifying a hierarchy of qualitatively different aversive tasks for three individuals with developmental disabilities by evaluating their average latency to escape responses when presented with each task, (ii) assessing baseline levels of self-control (i.e., selection of immediate, low-aversive tasks over delayed, high-aversive tasks), and (iii) implementing an empirically validated treatment (i.e., adding a delay to both tasks). Each participant initially made impulsive choices, but self-control increased following treatment.     

Culture,Perception, and Artistic Visualization: A Comparative Study of Children's Drawings in Three Siberian Cultural Groups

In a study of three indigenous and non‐indigenous cultural groups in northwestern and northeastern Siberia, framed line tests and a landscape drawing task were used to examine the hypotheses that test‐based assessments of context sensitivity and independence are correlated with the amount of contextual information contained in drawings, and with the order in which the focal and background objects are drawn. The results supported these hypotheses, and inspection of the regression relationships suggested that the intergroup variations in test performance were likely to result from differences in the attention accorded to contextual information, as revealed by the drawings. Social and environmental explanations for the group differences in context sensitivity are also discussed. The conclusions support the argument that cultural differences in artistic styles and perceptual tests reflect the same underlying perceptual tendencies, and they are consistent with the argument that these tendencies reflect corresponding differences in patterns of social and environmental interaction.     

Heuristics as beliefs and as behaviors: the adaptiveness of the "hot hand"

and analyzed reasoning by asking: what are the reasoner's goals? This emphasizes the adaptiveness of behavior rather than whether a belief is normative. Belief in the "hot hand" in basketball suggests that players experiencing streaks should be given more shots, but this has been seen as a fallacy due to failure to find dependencies between players' shots. Based on their findings, I demonstrate by Markov modeling and simulation that streaks are valid allocation cues for deciding who to give shots to, because this behavior achieves the team goal of scoring more. Empirically I show that this adaptive heuristic is supported by the fallacious belief in dependency, more so as skill level increases. I extend the theoretical analysis to identify general conditions under which following streaks should be beneficial. Overall, this approach illustrates the advantages of analyzing reasoning in terms of adaptiveness.     

Personality,life events and the course of anxiety and depression

Using data from the Netherlands Study of Depression and Anxiety, we examined among 1322 participants with a DSM‐IV diagnosis of depression or anxiety: (i) whether positive and negative life events influence 1‐year course of anxiety and depressive symptoms; (ii) whether personality traits (neuroticism and extraversion) predict symptom course and moderate the impact of life events on symptom course; and (iii) whether life events mediate relationships of neuroticism and extraversion with symptom course. Negative life events were predictive of both anxiety and depressive symptoms, while positive life events predicted the course of depressive symptoms only. Personality traits had significant predictive and moderating effects on symptom course, though these effects were rather small. Copyright © 2011 John Wiley & Sons, Ltd.     

Relationship between the number of life events and memory capacity in children

Stressful life events can result into declined memory performance at later age. One hypothesis suggests that stress affects the hippocampus, a brain area important for memory functioning. This study explored a potential relationship between the number of negative stressful life events and hippocampus-dependent declarative but not hippocampus-independent procedural memory performance in a community sample of 255 children, aged 6–12 years. The findings revealed that negative stressful life events were negatively related to verbal declarative memory, but not to nonverbal declarative and procedural memory. The memory impairments could not be accounted for by attention and sleep disturbances, and parenting characteristics as perceived by the child did not influence the vulnerability for the stress-related memory impairments. These findings provide further insight into the deleterious effects of negative stressful life events on learning in school-aged children.