基础比率和认知风格对贝叶斯推理影响的眼动研究

选取35名本科生为被试,采用EyeLink II眼动仪,考察了基础比率和认知风格对贝叶斯推理的影响,探讨了基础比率作用机制的争论。实验采用2（基础比率：高、低）×2（认知风格：场依存、场独立）双因素被试间设计,要求每位被试完成一道贝叶斯推理题,问题内容为疾病情境。将推理材料划为AOI1（描述基础比率）、AOI2（描述击中率）、AOI3（描述虚报率）、AOI4（提问）4个兴趣区,分别记录被试的总注视时间、注视次数等。结果发现：（1）在总注视时间和注视次数指标上,基础比率和认知风格的主效应均不显著,两者的交互作用显著;（2）在总注视时间和回视次数指标上,各兴趣区差异显著,关注程度从高到低依次为：AOI2＞AOI3＞AOI1＞AOI4。这说明,在贝叶斯推理中,并没有完全忽视基础比率;对于不同认知风格的个体而言,基础比率所起的作用是不同的。这也给我们一点启示：或许我们不能单一地去考虑基础比率的作用机制,而应该将它与个体的某些因素结合起来综合加以讨论。     

The base-rate fallacy in probability judgments

The base-rate fallacy is people's tendency to ignore base rates in favor of, e.g., individuating information (when such is available), rather than integrate the two. This tendency has important implications for understanding judgment phenomena in many clinical, legal, and social-psychological settings. An explanation of this phenomenon is offered, according to which people order information by its perceived degree of relevance, and let high-relevance information dominate low-relevance information. Information is deemed more relevant when it relates more specifically to a judged target case. Specificity is achieved either by providing information on a smaller set than the overall population, of which the target case is a member, or when information can be coded, via causality, as information about the specific members of a given population. The base-rate fallacy is thus the result of pitting what seem to be merely coincidental, therefore low-relevance, base rates against more specific, or causal, information. A series of probabilistic inference problems is presented in which relevance was manipulated with the means described above, and the empirical results confirm the above account. In particular, base rates will be combined with other information when the two kinds of information are perceived as being equally relevant to the judged case.     

A test of the optimal classifier's independence assumption in perceptual categorization

Observers completed perceptual categorization tasks that included separate base-rate/payoff manipulations, corresponding simultaneous base-rate/payoff manipulations, and conflicting simultaneous base-rate/payoff manipulations. Performance (1) was closer to optimal for 2:1 than for 3:1 base-rate/payoff ratios and when base rates as opposed to payoffs were manipulated, and (2) was more in line with the predictions from the flat-maxima hypothesis than from the independence assumption of the optimal classifier in corresponding and conflicting simultaneous base-rate/payoff conditions. A hybrid model that instantiated simultaneously the flat-maxima and the competition between reward and accuracy maximization (COBRA) hypotheses was applied to the data. The hybrid model was superior to a model that incorporated the independence assumption, suggesting that violations of the independence assumption are to be expected and are well captured by the flat-maxima hypothesis without requiring any additional assumptions. The parameters indicated that observers' reward-maximizing decision criterion rapidly approaches the optimal value and that more weight is placed on accuracy maximization in separate and corresponding simultaneous base-rate/payoff conditions than in conflicting simultaneous base-rate/payoff conditions.     

A test of the optimal classifier’s independence assumption in perceptual categorization

Observers completed perceptual categorization tasks that included separate base-rate/payoff manipulations, corresponding simultaneous base-rate/payoff manipulations, and conflicting simultaneous base-rate/payoff manipulations. Performance (1) was closer to optimal for 2:1 than for 3:1 baserate/ payoff ratios and when base rates as opposed to payoffs were manipulated, and (2) was more in line with the predictions from the flat-maxima hypothesis than from the independence assumption of the optimal classifier in corresponding and conflicting simultaneous base-rate/payoff conditions. A hybrid model that instantiated simultaneously the flat-maxima and the competition between reward and accuracy maximization (COBRA) hypotheses was applied to the data. The hybrid model was superior to a model that incorporated the independence assumption, suggesting that violations of the independence assumption are to be expected and are well captured by the flat-maxima hypothesis without requiring any additional assumptions. The parameters indicated that observers’ reward-maximizing decision criterion rapidly approaches the optimal value and that more weight is placed on accuracy maximization in separate and corresponding simultaneous base-rate/payoff conditions than in conflicting simultaneous base-rate/payoff conditions.     

Probability matching, accuracy maximization, and a test of the optimal classifier's independence assumption in perceptual categorization

Observers completed perceptual categorization tasks that included 25 base-rate/payoff conditions constructed from the factorial combination of five base-rate ratios (1:3, 1:2, 1:1, 2:1, and 3:1) with five payoff ratios (1:3, 1:2, 1:1, 2:1, and 3:1). This large database allowed an initial comparison of the competition between reward and accuracy maximization (COBRA) hypothesis with a competition between reward maximization and probability matching (COBRM) hypothesis, and an extensive and critical comparison of the flat-maxima hypothesis with the independence assumption of the optimal classifier. Model-based instantiations of the COBRA and COBRM hypotheses provided good accounts of the data, but there was a consistent advantage for the COBRM instantiation early in learning and for the COBRA instantiation later in learning. This pattern held in the present study and in a reanalysis of Bohil and Maddox (2003). Strong support was obtained for the flat-maxima hypothesis over the independence assumption, especially as the observers gained experience with the task. Model parameters indicated that observers' reward-maximizing decision criterion rapidly approaches the optimal value and that more weight is placed on accuracy maximization in separate base-rate/payoff conditions than in simultaneous base-rate/payoff conditions. The superiority of the flat-maxima hypothesis suggests that violations of the independence assumption are to be expected, and are well captured by the flat-maxima hypothesis, with no need for any additional assumptions.     

Probability matching, accuracy maximization, and a test of the optimal classifier’s independence assumption in perceptual categorization

Observers completed perceptual categorization tasks that included 25 base-rate/payoff conditions constructed from the factorial combination of five base-rate ratios (1:3, 1:2, 1:1, 2:1, and 3:1) with five payoff ratios (1:3, 1:2, 1:1, 2:1, and 3:1). This large database allowed an initial comparison of the competition between reward and accuracy maximization (COBRA) hypothesis with a competition between reward maximization and probability matching (COBRM) hypothesis, and an extensive and critical comparison of the flat-maxima hypothesis with the independence assumption of the optimal classifier. Model-based instantiations of the COBRA and COBRM hypotheses provided good accounts of the data, but there was a consistent advantage for the COBRM instantiation early in learning and for the COBRA instantiation later in learning. This pattern held in the present study and in a reanalysis of Bohil and Maddox (2003). Strong support was obtained for the flat-maxima hypothesis over the independence assumption, especially as the observers gained experience with the task. Model parameters indicated that observers’ reward-maximizing decision criterion rapidly approaches the optimal value and that more weight is placed on accuracy maximization in separate base-rate/payoff conditions than in simultaneous base-rate/payoff conditions. The superiority of the flat-maxima hypothesis suggests that violations of the independence assumption are to be expected, and are well captured by the flat-maxima hypothesis, with no need for any additional assumptions.     

Accentuation of information processes and biases in group judgments integrating base-rate and case-specific information

This article investigates differences in the ways that groups and individuals apply information-processing strategies and fall prey to biases in their judgments. Judgments were made on probabilistic inference problems that involved base-rate and case-specific information. Consistent with hypotheses, when individuals neglect base-rate information in their probability judgments, groups accentuate this tendency. Moreover, when the source of case-specific information is inaccurate, individuals neglect the case-specific information, and groups accentuate this tendency with the base-rate information dominating their probability judgments. In addition, groups accentuate the strategies used by individuals to integrate the base-rate and case-specific information. These results provide strong support for a group accentuation tendency for the application of information-processing biases and the strategies used to integrate information. Discussion reflects upon the relationship of the results of this experiment with other research on base-rate neglect and group judgment. Underlying mechanisms and potential moderators of the group accentuation pattern are also discussed.     

I know the rule,but I'll just go with my gut: is there a rational use of intuition?

ABSTRACT

Research has established that human thinking is often biased by intuitive judgement. The base-rate neglect effect provides such an example, so named because people often support their decisions in stereotypical individuating information, neglecting base-rates. Here, we test the hypothesis that reasoners acknowledge information provided by base-rates and may use individuating information in support of a “rational” decision process. Results from four experiments show that “base-rate neglecting” occurs when participants acknowledge sample distributions; participants who prefer individuating over base-rate information perceive base-rates as less diagnostic and are more confident in their individuating-based responses; and that posterior probabilities (assigned after all relevant information is considered) predict more individuating-based responses for individuating-preference participants (suggesting a rational process). However, data also show a deeper form of base-rate neglect: even when some participants report to prefer base-rate information, define individuating information as non-diagnostic, and their posterior probabilities suggest otherwise, they still provide individuating-based responses.     

基础概率在贝叶斯推理中的作用

针对贝叶斯推理研究中基础概率忽略现象的争论,直接操纵基础概率水平,考察被试在贝叶斯推理时是否加工了基础概率信息。结果表明,低基础概率组后验概率估计显著低,无基础概率组后验概率估计反应时显著短于有基础概率组。被试在各种条件下估计的正确率都较低,说明对基础概率在贝叶斯推理中的作用考虑不充分。     

Task Specificity in the Use of Words in Mathematics: Evidence from Bilingual Problem Solvers

Mathematics is often said to be a different language in itself. Three experiments were conducted to show some evidence for this common notion. It was hypothesized that in math word problem solving, people interpret words like “more” and “less” in specialized ways that are specific to the task of math word problem solving. Subjects were given texts with quantitative information, but the texts were framed either as math problems or as stories, and were written either in English or Filipino. Subjects were then asked to verify statements that describe quantitative relations given in the text; these relations either stated an exact or an inexact quantitative difference. The verification responses and verification times in three experiments show that subjects more often accepted the inexact difference as true when the text was framed as a story compared to when framed as a problem. These results support the hypothesis that the use of the specialized meaning is specific to the task of solving word problems in math. The data were equivocal about the role of the language used in the operation of this knowledge. The results were discussed in terms of the implications of specificity of knowledge, context sensitivity, and the possible role of language use in the process of learning and developing mathematical knowledge.     

Problem structure and the use of base-rate information from experience

This article is concerned with the use of base-rate information that is derived from experience in classifying examples of a category. The basic task involved simulated medical decision making in which participants learned to diagnose hypothetical diseases on the basis of symptom information. Alternative diseases differed in their relative frequency or base rates of occurrence. In five experiments initial learning was followed by a series of transfer tests designed to index the use of base-rate information. On these tests, patterns of symptoms were presented that suggested more than one disease and were therefore ambiguous. The alternative or candidate diseases on such tests could differ in their relative frequency of occurrence during learning. For example, a symptom might be presented that had appeared with both a relatively common and a relatively rare disease. If participants are using base-rate information appropriately (according to Bayes' theorem), then they should be more likely to predict that the common disease is present than that the rare disease is present on such ambiguous tests. Current classification models differ in their predictions concerning the use of base-rate information. For example, most prototype models imply an insensitivity to base-rate information, whereas many exemplar-based classification models predict appropriate use of base-rate information. The results reveal a consistent but complex pattern. Depending on the category structure and the nature of the ambiguous tests, participants use base-rate information appropriately, ignore base-rate information, or use base-rate information inappropriately (predict that the rare disease is more likely to be present). To our knowledge, no current categorization model predicts this pattern of results. To account for these results, a new model is described incorporating the ideas of property or symptom competition and context-sensitive retrieval.     

Relations between vocabulary development and verbal short-term memory: The relative importance of short-term memory for serial order and item information

Although many studies have shown an association between verbal short-term memory (STM) and vocabulary development, the precise nature of this association is not yet clear. The current study reexamined this relation in 4- to 6-year-olds by designing verbal STM tasks that maximized memory for either item or serial order information. Although empirical data suggest that distinct STM processes determine item and serial order recall, these were generally confounded in previous developmental studies. We observed that item and order memory tasks were independently related to vocabulary development. Furthermore, vocabulary development was more strongly associated with STM for order information in 4- and 6-year-olds and with STM for item information in 5-year-olds. These data highlight the specificity of verbal STM for serial order and item information and suggest a causal association between order STM processes and vocabulary development, at least in 4- and 6-year-olds.     

Base-rate respect: From ecological rationality to dual processes

The phenomenon of base-rate neglect has elicited much debate. One arena of debate concerns how people make judgments under conditions of uncertainty. Another more controversial arena concerns human rationality. In this target article, we attempt to unpack the perspectives in the literature on both kinds of issues and evaluate their ability to explain existing data and their conceptual coherence. From this evaluation we conclude that the best account of the data should be framed in terms of a dual-process model of judgment, which attributes base-rate neglect to associative judgment strategies that fail to adequately represent the set structure of the problem. Base-rate neglect is reduced when problems are presented in a format that affords accurate representation in terms of nested sets of individuals.     

行为决策中的基线比例忽略：心理机制与影响因素

基线比例忽略是指个体进行决策和判断时不能充分利用或者忽略基线比例而偏好新信息的现象。该现象普遍存在于日常行为与决策的许多领域,尤其显著表现在临床医疗领域,因此对这一现象的研究具有重要的应用价值。目前,基线比例忽略的心理机制主要有双加工理论和因果贝叶斯框架等。基线比例忽略的影响因素主要包括认知能力、年龄、基线比例的表述形式等。未来的研究需要从基线比例忽略的神经机制、影响因素以及应用研究的拓展等方面着手。     

A theoretical framework for understanding the effects of simultaneous base-rate and payoff manipulations on decision criterion learning in perceptual categorization

Observers completed perceptual categorization tasks in which base rates and payoffs were manipulated separately or simultaneously across a range of category discriminabilities. Decision criterion estimates from the simultaneous base-rate/payoff conditions were closer to optimal than those predicted from the independence assumption, in line with predictions from the flat-maxima hypothesis. A hybrid model that instantiated the flat-maxima and competition between reward and accuracy maximization hypotheses was applied to the data as well as used in a reanalysis of C. J. Bohil and W.J. Maddox's (2001) study. The hybrid model was superior to a model that incorporated the independence assumption, suggesting that violations of the independence assumption are to be expected and are well captured by the flat-maxima hypothesis, without requiring any additional assumptions.     

Freud’s dream of the double

While the motif of the double serves a prominent role in Freud’s writings from early on, this essay is an examination of the determinative power of the double in two key texts, texts in which specific, new sets doubles emerge for the first time in Freud’s career. Totem and Taboo features a double that manifests itself primarily in the form of ambivalence. Beyond the Pleasure Principle features a double that manifests itself primarily in the form of a very peculiar conflict that also entails complicity.     

Rehearsal in serial memory for visual-spatial information: Evidence from eye movements

It is well established that rote rehearsal plays a key role in serial memory for lists of verbal items. Although a great deal of research has informed us about the nature of verbal rehearsal, much less attention has been devoted to rehearsal in serial memory for visual-spatial information. By using the dot task—a visual-spatial analogue of the classical verbal serial recall task—with delayed recall, performance and eyetracking data were recorded in order to establish whether visual-spatial rehearsal could be evidenced by eye movement. The use of eye movement as a form of rehearsal is detectable (Experiment 1), and it seems to contribute to serial memory performance over and above rehearsal based on shifts of spatial attention (Experiments 1 and 2).