An approach to combine the logistic threshold model of psychophysics with the Bradley-Terry-Luce models of choice theory

The paper presents a straightforward extension of the Bradley-Terry-Luce model (BTL model) that can be derived from the logistic threshold model of psychophysics which assumes that psychometric functions are logistic probability functions. It is shown that (under weak side conditions) the logistic threshold model is a submodel of the extended BTL model. Moreover, representation and uniqueness theorems are proven that provide some evidence that the extended BTL model is a useful and widely applicable generalization of the ordinary BTL model. Finally, the logistic shape of the psychometric function is derived from axioms about binary choice probabilities. This characterization of the logistic threshold model can replace goodness of fit tests for the logistic probability distribution.     

Psychophysics without physics: extension of Fechnerian scaling from continuous to discrete and discrete-continuous stimulus spaces

The computation of subjective (Fechnerian) distances from discrimination probabilities involves cumulation of appropriately transformed psychometric increments along smooth arcs (in continuous stimulus spaces) or chains of stimuli (in discrete spaces). In a space where any two stimuli that are each other's points of subjective equality are given identical physical labels, psychometric increments are positive differences ψ(x,y)-ψ(x,x) and ψ(y,x)-ψ(x,x), where x≠y and ψ is the probability of judging two stimuli different. In continuous stimulus spaces the appropriate monotone transformation of these increments (called overall psychometric transformation) is determined uniquely in the vicinity of zero, and its extension to larger values of its argument is immaterial. In discrete stimulus spaces, however, Fechnerian distances critically depend on this extension. We show that if overall psychometric transformation is assumed (A) to be the same for a sufficiently rich class of discrete stimulus spaces, (B) to ensure the validity of the Second Main Theorem of Fechnerian Scaling in this class of spaces, and (C) to agree in the vicinity of zero with one of the possible transformations in continuous spaces, then this transformation can only be identity. This result is generalized to the broad class of “discrete-continuous” stimulus spaces, of which continuous and discrete spaces are proper subclasses.     

命题内容对青少年条件推理的影响

选取3个具体内容的条件命题作为实验材料,以小四、初一、高一、大三的学生为被试,探讨了命题内容对青少年条件推理的影响机制及其发展特点。结果表明:(1)对同一年级而言,不同内容的条件命题的相同推理(MP、MT、DA、AC)之间表现出显著的差异;对不同年级而言,相同内容的条件命题的四种推理之间也存在显著的差异。(2)青少年的条件推理过程似乎是一种基于对事件发生概率估计的直觉判断,这一判断过程主要取决于个体知识经验的增长和主体认知水平的提高,而用形式逻辑的标准来衡量个体条件推理能力的高低似乎并不妥当。     

A quantum probability account of order effects in inference

Order of information plays a crucial role in the process of updating beliefs across time. In fact, the presence of order effects makes a classical or Bayesian approach to inference difficult. As a result, the existing models of inference, such as the belief-adjustment model, merely provide an ad hoc explanation for these effects. We postulate a quantum inference model for order effects based on the axiomatic principles of quantum probability theory. The quantum inference model explains order effects by transforming a state vector with different sequences of operators for different orderings of information. We demonstrate this process by fitting the quantum model to data collected in a medical diagnostic task and a jury decision-making task. To further test the quantum inference model, a new jury decision-making experiment is developed. Using the results of this experiment, we compare the quantum inference model with two versions of the belief-adjustment model, the adding model and the averaging model. We show that both the quantum model and the adding model provide good fits to the data. To distinguish the quantum model from the adding model, we develop a new experiment involving extreme evidence. The results from this new experiment suggest that the adding model faces limitations when accounting for tasks involving extreme evidence, whereas the quantum inference model does not. Ultimately, we argue that the quantum model provides a more coherent account for order effects that was not possible before.     

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.     

人非理性且难教化?论支持自由家长主义的证据

基于心理学的研究, 自由家长主义者认为人们的思维有个体难以克服的、根深蒂固的系统性缺陷, 并难以通过教育来避免和消除, 因此主张因势利导, 仰仗外部专家的“助推”把人们的行为引导到正确方向。然而, 从生态理性的角度看, 人们依照自由家长主义者所谓的认知偏差做出的选择未必导致糟糕的结果, 而依照自由家长主义者所推崇的理性方法做出的选择也未必导致理想的结果。本文分析了自由家长主义者用来支持助推的证据后发现：(1)它们源于一些研究者对“何为理性”的狭隘定义, 误解了人类理性的本质; (2)它们对研究结果进行了选择性的报告, 忽视了与这些证据相反的证据。通过这些分析, 我们认为“人非理性且难教化”这一自由家长主义者的论断过于武断并有失偏颇。投入教育, 教会人们如何精明老练地处理风险不仅是可行的, 而且是替代助推的一个更为持久有效的解决方案。     

风险决策的概率权重偏差：心理机制与优化策略

概率权重偏差指人对事件发生的主观概率估计与客观概率的差异。它影响投资、投保、医患沟通等方面。“重结果轻概率”的非补偿性策略和参照点诱发的情绪波动会引发概率权重偏差; 改变“概率”的描述形式、“结果”的情绪体验、“损益”的参照点、风险的心理距离等可调整权重偏差、优化决策。未来需深究权重偏差的适用情境、机制关联及偏差辨别等问题。     

Which statistical formats facilitate what decisions? The perception and influence of different statistical information formats

Research suggesting both a superiority of frequencies over single‐event probabilities and of smaller reference classes over very large reference classes have utilized tasks that vary in computational complexity. The present research sought to simply and directly evaluate if—apart from simplifying statistical inference tasks—frequencies and small reference classes are clearer than other formats. After eliminating possible computational confounds, simple frequencies (based on small reference classes, e.g. 1/3) and to some extent relative frequencies (percentages, e.g. 33%) were perceived as clearer than absolute frequencies (based on very large reference classes, e.g. 90 million Americans) and single‐event probabilities (e.g. 0.33). Concurrently, these different formats were evaluated in terms of their relative influence. Absolute frequencies were relatively more persuasive for smaller magnitudes (e.g. 2.7 million) but less persuasive for larger magnitudes (e.g. 267 million), as compared to analogous presentations. Single‐event probabilities were judged to minimize the significance of information. Copyright © 2002 John Wiley & Sons, Ltd.     

Measuring Inconsistency

I provide a method of measuring the inconsistency of a set of sentences – from 1-consistency, corresponding to complete consistency, to 0-consistency, corresponding to the explicit presence of a contradiction. Using this notion to analyze the lottery paradox, one can see that the set of sentences capturing the paradox has a high degree of consistency (assuming, of course, a sufficiently large lottery). The measure of consistency, however, is not limited to paradoxes. I also provide results for general sets of sentences.     

Accuracy of discrimination,rate of responding,and resistance to change

Pigeons were trained on multiple schedules in which responding on a center key produced matching-to-sample trials according to the same variable-interval 30-s schedules in both components. Matching trials consisted of a vertical or tilted line sample on the center key followed by vertical and tilted comparisons on the side keys. Correct responses to comparison stimuli were reinforced with probability .80 in the rich component and .20 in the lean component. Baseline response rates and matching accuracies generally were higher in the rich component, consistent with previous research. When performance was disrupted by prefeeding, response-independent food during intercomponent intervals, intrusion of a delay between sample and comparison stimuli, or extinction, both response rates and matching accuracies generally decreased. Proportions of baseline response rate were greater in the rich component for all disrupters except delay, which had relatively small and inconsistent effects on response rate. By contrast, delay had large and consistent effects on matching accuracy, and proportions of baseline matching accuracy were greater in the rich component for all four disrupters. The dissociation of response rate and accuracy with delay reflects the localized impact of delay on matching performance. The similarity of the data for response rate and accuracy with prefeeding, response-independent food, and extinction shows that matching performance, like response rate, is more resistant to change in a rich than in a lean component. This result extends resistance to change analyses from the frequency of response emission to the degree of stimulus control, and suggests that the strength of discriminating, like the strength of responding, is positively related to rate of reinforcement.