Considering too few alternatives: The mental model theory of extensional reasoning

When solving a simple probabilistic problem, people tend to build an incomplete mental representation. We observe this pattern in responses to probabilistic problems over a set of premises using the conjunction, disjunction, and conditional propositional connectives. The mental model theory of extensional reasoning explains this bias towards underestimating the number of possibilities: In reckoning with different interpretations of the premises (logical rules, mental model theoretical, and, specific to conditional premises, conjunction and biconditional interpretation) the mental model theory accounts for the majority of observations. Different interpretations of a premise result in a build-up of mental models that are often incomplete. These mental models are processed using either an extensional strategy relying on proportions amongst models, or a conflict monitoring strategy. The consequence of considering too few possibilities is an erroneous probability estimate akin to that faced by decision makers who fail to generate and consider all alternatives, a characteristic of bounded rationality. We compare our results to the results published by Johnson-Laird, Legrenzi, Girotto, Legrenzi, and Caverni [Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar], 62 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]–88 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]. doi:10 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].1037 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]/0033 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]-295X Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].106 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].1 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].62 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]], and we observe lower performance levels than those in the original article.     

Evidence for a young adult face bias in accuracy and consensus of age estimates

Adults' face processing may be specialized for the dimensions of young adult faces. For example, young and older adults exhibit increased accuracy in normality judgments and greater agreement in attractiveness ratings for young versus older adult faces. The present study was designed to examine whether there is a similar young adult face bias in facial age estimates. In Experiment 1, we created a face age continuum by morphing an averaged young adult face with an averaged older adult face in 5% increments, for a total of 21 faces ranging from 0 to 100% old. Young and older adults estimated facial age for three stimulus age categories [young (morphs 0–30%), middle‐aged (morphs 35–65%), and older adult (morphs 70–100%)]. Both age groups showed the least differentiation in age estimates for young adult faces, despite showing greater consensus across participants in estimates for young faces. In Experiment 2, young and older adults made age estimates for individual young and older adult identities. Both age groups were more accurate and showed greater consensus in age estimates for young faces. Collectively, these results provide evidence for a bias in processing young adult faces beyond that which is often observed in recognition and normality/attractiveness judgment tasks.     

Scarce Foods are Perceived as Having More Calories

People vary dramatically in their calorie estimates of food depending on the information available to them. Prior research has focused on information that is normatively relevant to the number of calories a food contains (e.g., fat content, serving size). The current research examines whether information that is normatively irrelevant to the number of calories a food contains—such as its availability—might also shape people's calorie estimates. Three studies found that a food perceived as limited in availability leads people to estimate the food to contain more calories. Serial mediation analyses revealed that this effect occurs because scarce food is seen as more valuable and expensive, which subsequently induces feelings of resource deprivation. This sense of resource deprivation, in turn, leads to motivated perception, whereby higher calorie estimates are the result of people wanting to acquire more resources. The findings provide insight into the psychology of scarcity and underscore the importance of understanding how contextual factors shape people's calorie estimates and the psychological mechanisms that drive them.     

用不同外部表征方式集中呈现信息条件下的因果力判断

在分别用文字陈述、表格和图形三种外部表征方式集中呈现因果信息的条件下,用直接估计因果力大小的实验范式考察单一因果关系因果力估计的特点,检验概率对比模型,效力PC理论和pCI规则。让287名大学生被试估计不同化学药物影响动物基因变异的能力。结果发现,对单一因果关系因果力估计具有以下4个特点：⑴不对称性：在预防原因条件下的因果力估计较多符合效力PC理论,而在产生原因条件下的因果力估计一般符合概率对比模型;⑵文字陈述、表格和图形三种信息外部表征方式,不影响产生原因条件下的因果力估计,但影响预防原因条件下的因果力估计。在预防原因条件下,与文字陈述和表格表征相比,图形表征会促使更多被试按效力PC理论来做因果力估计;⑶没有被试使用pCI规则;⑷被试估计因果力所使用的规则存在明显的个体差异。     

The change probability effect: incidental learning, adaptability, and shared visual working memory resources

Statistical properties in the visual environment can be used to improve performance on visual working memory (VWM) tasks. The current study examined the ability to incidentally learn that a change is more likely to occur to a particular feature dimension (shape, color, or location) and use this information to improve change detection performance for that dimension (the change probability effect). Participants completed a change detection task in which one change type was more probable than others. Change probability effects were found for color and shape changes, but not location changes, and intentional strategies did not improve the effect. Furthermore, the change probability effect developed and adapted to new probability information quickly. Finally, in some conditions, an improvement in change detection performance for a probable change led to an impairment in change detection for improbable changes.     

任务情境与概率知识经验对中学生合取判断的影响研究

本研究采用了一套由不同任务情境(数字情境和日常情境)组成的合取判断问卷与一套概率基础知识问卷,对106名中学生的合取判断情况进行调查,结果显示:(1)无论在哪种任务情境下,概率知识经验均未对合取判断成绩产生显著影响。(2)不同概率知识经验的被试在数字任务情境下采用的策略有所不同。     

Intolerance of uncertainty and perceived threat

The present study examined the relations between dimensions of intolerance of uncertainty (i.e., desire for predictability and uncertainty paralysis) and perceptions of threat (i.e., perceptions of the probabilities and costs of future undesirable outcomes) in a sample of 239 college students. Uncertainty paralysis was positively associated with both perceived probabilities and perceived costs for negative outcomes. Desire for predictability was positively associated with perceived costs for negative outcomes but was not associated with perceived probabilities for negative outcomes. When probability estimates for low base rate outcomes were examined separately, desire for predictability was negatively associated with perceived probabilities. Finally, perceived threat partially mediated the relations between dimensions of intolerance of uncertainty and worry. The results of the present study suggest mechanisms through which dimensions of intolerance of uncertainty might lead to excessive worry.     

Violations of coherence in subjective probability: a representational and assessment processes account

Coherent judgment is a cardinal feature of rational cognition. Six experiments revealed systematic violations of coherence in probability judgment in which participants assigned different probabilities to mathematically equiprobable events. Experiments 1-5 revealed a strict refocusing effect: Compared to an occurrence frame, a non-occurrence frame resulted in higher estimates if base-rate evidence favored occurrence, lower estimates if evidence favored non-occurrence, and similar estimates if evidence supported indifference. Moreover, Experiments 5 and 6 revealed a pessimistic bias in which the less favorable of two equiprobable events was assigned greater probability. The findings support a Representational and Assessment Processes account (RAP) in which subjective probability is influenced by the perceived compatibility between representations of focal events and representations of evidence.     

Testing boundary conditions for the conjunction fallacy: effects of response mode, conceptual focus, and problem type

Two experiments used within-subject designs to examine how conjunction errors depend on the use of (1) choice versus estimation tasks, (2) probability versus frequency language, and (3) conjunctions of two likely events versus conjunctions of likely and unlikely events. All problems included a three-option format verified to minimize misinterpretation of the base event. In both experiments, conjunction errors were reduced when likely events were conjoined. Conjunction errors were also reduced for estimations compared with choices, with this reduction greater for likely conjuncts, an interaction effect. Shifting conceptual focus from probabilities to frequencies did not affect conjunction error rates. Analyses of numerical estimates for a subset of the problems provided support for the use of three general models by participants for generating estimates. Strikingly, the order in which the two tasks were carried out did not affect the pattern of results, supporting the idea that the mode of responding strongly determines the mode of thinking about conjunctions and hence the occurrence of the conjunction fallacy. These findings were evaluated in terms of implications for rationality of human judgment and reasoning.