An evidential support accumulation model of subjective probability

A model of cue-based probability judgment is developed within the framework of support theory. Cue diagnosticity is evaluated from experience as represented by error-free frequency counts. When presented with a pattern of cues, the diagnostic implications of each cue are assessed independently and then summed to arrive at an assessment of the support for a hypothesis, with greater weight placed on present than on absent cues. The model can also accommodate adjustment of support in light of the baserate or prior probability of a hypothesis. Support for alternatives packed together in a "residual" hypothesis is discounted; fewer cues are consulted in assessing support for alternatives as support for the focal hypothesis increases. Results of fitting this and several alternative models to data from four new multiple-cue probability learning experiments are reported.     

Probability, logic and the cognitive foundations of rational belief

Since Pascal introduced the idea of mathematical probability in the 17th century discussions of uncertainty and “rational” belief have been dogged by philosophical and technical disputes. Furthermore, the last quarter century has seen an explosion of new questions and ideas, stimulated by developments in the computer and cognitive sciences. Competing ideas about probability are often driven by different intuitions about the nature of belief that arise from the needs of different domains (e.g., economics, management theory, engineering, medicine, the life sciences etc). Taking medicine as our focus we develop three lines of argument (historical, practical and cognitive) that suggest that traditional views of probability cannot accommodate all the competing demands and diverse constraints that arise in complex real-world domains. A model of uncertain reasoning based on a form of logical argumentation appears to unify many diverse ideas. The model has precursors in informal discussions of argumentation due to Toulmin, and the notion of logical probability advocated by Keynes, but recent developments in artificial intelligence and cognitive science suggest ways of resolving epistemological and technical issues that they could not address.     

Patterns of Preference for Numerical and Verbal Probabilities

We report results of an experiment designed to test a principle formulated by Budescu and Wallsten (1995), that, when communicating uncertainty information, mode choices are sensitive to sources and degrees of vagueness. In addition, we examined subjects’ efficacy in using such uncertainty information as a function of communication mode, source, and vagueness. In phase one of the experiment, subjects in a dyad used precise (numerical) or imprecise (verbal) expressions to communicate to a remote partner precise or vague uncertainty about the likelihoods of events. Spinner outcomes were used to generate precise uncertainty while answers to almanac questions were used to elicit vague uncertainty. In phase two, subjects saw the events paired with their partners’ estimates of similar events, and were asked to gamble on one event from each pair. Communication mode preferences were measured as the relative frequency that subjects chose the numerical mode to either express or receive uncertainty information regarding the events. Efficacy was measured as the relative frequency that subjects choose from the pair the event associated with the objectively more probable uncertainty expression. Underlying uncertainty interacted with direction of communication to affect preferences for modes of expression of the probabilities. Subjects preferred precise (numerical) information, especially for precise events (spinners). For vague events (questions), their preference for precise (numerical) information was stronger when receiving than when communicating information. Similar preferences were reflected in the efficiency of subsequent gamble decisions based on the probability estimates. Specifically, decisions were more efficacious (i.e. consistent with Expected Utility) when degrees of precision in events and estimates matched. © 1997 by John Wiley & Sons, Ltd.     

Upward versus Downward Anchoring in Frequency Judgments of Social Facts

Frequency estimation of social facts in two methods of judgment elicitation was investigated. In the “narrow-range” condition, subjects answered questions in the format: “Out of 100 incidents, how many belong to category X?” In the “wide-range” condition, the frequency for the same event was assessed with respect to “Out of 10,000”. Judged frequencies in the wide-range condition were divided by 100, and were compared with the corresponding judgments in the narrow-range condition. Such comparisons were made for low-frequency and high-frequency events. Previous research has shown that, for low-frequency events, judged frequencies are proportionally greater in the narrow-range than in the wide-range condition. These results reflect cognitive processes of implicit anchoring, whereby judged frequencies lie close to small numbers within the response ranges provided. I call this process “downward anchoring,” and predicted that this tendency would be replicated in the present study. Moreover, I predicted that assessments about high-frequency events would evoke similar cognitive processes operating in the opposite direction. By such “upward anchoring,” judged frequencies would lie close to relatively larger numbers within the given response ranges. Consequently, I predicted that judged frequencies for high-frequency events would be proportionally greater in the wide-range condition than in the narrow-range condition. These predictions were confirmed.     

Choice with delayed and probabilistic reinforcers: effects of variability, time between trials, and conditioned reinforcers.

In a discrete-trials procedure with pigeons, a response on a green key led to a 4-s delay (during which green houselights were lit) and then a reinforcer might or might not be delivered. A response on a red key led to a delay of adjustable duration (during which red houselights were lit) and then a certain reinforcer. The delay was adjusted so as to estimate an indifference point--a duration for which the two alternatives were equally preferred. Once the green key was chosen, a subject had to continue to respond on the green key until a reinforcer was delivered. Each response on the green key, plus the 4-s delay that followed every response, was called one "link" of the green-key schedule. Subjects showed much greater preference for the green key when the number of links before reinforcement was variable (averaging four) than when it was fixed (always exactly four). These findings are consistent with the view that probabilistic reinforcers are analogous to reinforcers delivered after variable delays. When successive links were separated by 4-s or 8-s "interlink intervals" with white houselights, preference for the probabilistic alternative decreased somewhat for 2 subjects but was unaffected for the other 2 subjects. When the interlink intervals had the same green houselights that were present during the 4-s delays, preference for the green key decreased substantially for all subjects. These results provided mixed support for the view that preference for a probabilistic reinforcer is inversely related to the duration of conditioned reinforcers that precede the delivery of food.     

Calibration of sensory and cognitive judgments: A single model for both

In a recent issue of this journal, Winman and Juslin (34 , 135–148, 1993) present a model of the calibration of subjective probability judgments for sensory discrimination tasks. They claim that the model predicts a pervasive underconfidence bias observed in such tasks, and present evidence from a training experiment that they interpret as supporting the notion that different models are needed to describe judgment of confidence in sensory and in cognitive tasks. The model is actually part of the more comprehensive decision variable partition model of subjective probability calibration that was originally proposed in Ferrell and McGoey (Organizational Behavior and Human Performance, 26 , 32–53, 1980). The characteristics of the model are described and it is demonstrated that the model does not predict underconfidence, that it is fully compatible with the overconfidence frequently found in calibration studies with cognitive tasks, and that it well represents experimental results from such studies. It is concluded that only a single model is needed for both types of task.     

Imprecise Epistemic Values and Imprecise Credences

A number of recent arguments purport to show that imprecise credences are incompatible with accuracy-first epistemology. If correct, this conclusion suggests a conflict between evidential and alethic epistemic norms. In the first part of the paper, I claim that these arguments fail if we understand imprecise credences as indeterminate credences. In the second part, I explore why agents with entirely alethic epistemic values can end up in an indeterminate credal state. Following William James, I argue that there are many distinct alethic values that a rational agent can have. Furthermore, such an agent is rationally permitted not to have settled on one fully precise value function. This indeterminacy in value will sometimes result in indeterminacy in epistemic behaviour—that is, because the agent’s values aren’t settled, what she believes might not be.     

基于非逻辑机制的条件推理模式：P—Q映射模型及其实证检验

研究结合数学分析方法,提出了基于非逻辑机制的条件推理模型：P-Q映射模型。并根据这个模型,对人们在不同命题类型奈件下的推理行为进行了预测。预测结果显示,当推理前提为LH和HL型命题时,基于P-Q映射模型的预测结果与基于条件概率模型的预测结果完全一致。但当推理前提为LL和HH型命题时,两种模型给出的预测结果存在差异。实验结果表明,当前提命题为LL和HH型命题时,被试的条件推理行为与P-Q映射模型的预言完全一致。     

Comprehending Semantic and Grammatical Violations in Italian. N400 and P600 Comparison with Visual and Auditory Stimuli

Arguments about the existence of language-specific neural systems and specifically about the independence of syntactic and semantic processing have focused on the event-related brain measures (ERPs) as tool to monitoring moment-by-moment the cognitive processes underlaid. In the present experiments, the available evidence indicates that the ERP response to semantic anomalies is at least partially distinct from the ERP response to syntactic anomalies and that two distinct processes are activated in sentences comprehension. ERPs were recorded from 10 electrodes while subjects read (Experiment 1) or listened (Experiment 2) to sentences containing semantic or syntactic violations. Final-words that were inconsistent with the sentence context elicited a negative-going wave at about 400 ms poststimulus, whereas penultimate-word incongruous with the grammatical structure (subject–verb non-agreement) elicited a positive-going wave about 600 ms poststimulus. No differences based on the perceptual modality of the stimulus (visual or auditory) nor different ERP correlates as a function of task-relevance (explicit/implicit task induction) were found. The implications of our results for Italian language are explained.