Can membership-functions capture the directionality of verbal probabilities?

Verbal probabilities are a common mean for communicating risk and uncertainties in many decision-making settings (e.g., finance, medicine, military). They are considered directional because they elicit a focus on either the outcome occurrence (e.g., there is a chance) or on its non-occurrence (e.g., it is unlikely). According to a quantitative perspective, directionality is dependent on the vague probabilistic meaning conveyed by verbal probabilities—e.g., p(outcome) > .50 = > focus on outcome occurrence. In contrast a more qualitative perspective suggests that directionality depends on contextual factors. The present study tested whether the directionality of verbal probabilities was determined by their vague probabilistic meaning, by contextually manipulated variables (i.e., representativeness and base rate), or by a combination of both. Participants provided their own expressions to describe the guilt of a suspect and then assessed the vague probabilistic meaning and directionality associated with those expressions. Results showed that directionality was mainly determined by the vague probabilistic meaning but also by the base rate of guilt. Although attention focus on the occurrence or the non-occurrence of the target outcome is dependent on vague probabilistic meaning, it cannot be fully accounted for by it.     

The effectiveness of feedback in multiple-cue probability learning

How effective are different types of feedback in helping us to learn multiple contingencies? This article attempts to resolve a paradox whereby, in comparison to simple outcome feedback, additional feedback either fails to enhance or is actually detrimental to performance in nonmetric multiple-cue probability learning (MCPL), while in contrast the majority of studies of metric MCPL reveal improvements at least with some forms of feedback. In three experiments we demonstrate that if feedback assists participants to infer cue polarity then it can in fact be effective in nonmetric MCPL. Participants appeared to use cue polarity information to adopt a linear judgement strategy, even though the environment was nonlinear. The results reconcile the paradoxical contrast between metric and nonmetric MCPL and support previous findings of people's tendency to assume linearity and additivity in probabilistic cue learning.     

Estimating the effect of word predictability on eye movements in Chinese reading using latent semantic analysis and transitional probability

Latent semantic analysis (LSA) and transitional probability (TP), two computational methods used to reflect lexical semantic representation from large text corpora, were employed to examine the effects of word predictability on Chinese reading. Participants' eye movements were monitored, and the influence of word complexity (number of strokes), word frequency, and word predictability on different eye movement measures (first-fixation duration, gaze duration, and total time) were examined. We found influences of TP on first-fixation duration and gaze duration and of LSA on total time. The results suggest that TP reflects an early stage of lexical processing while LSA reflects a later stage.     

A cognitive‐emotional account of the shape of the probability weighting function

Research has shown a tendency of decision makers to overweight small probabilities and to underweight moderate and large probabilities. In standard treatments this is graphically modeled by an inverse S‐shaped probability weighting function. We suggest that emotions play a significant role in the shaping of the probability weighting function. In particular, the weighting function is proposed to be some function of objective probability, expected elation, and expected disappointment. The overweighting of small probabilities results from the anticipated elation after having won, given that winning was very unlikely. The underweighting of large probabilities results from anticipated disappointment after having failed to win, given that winning was very likely. Hence, probability is assumed to influence utility. Three experiments investigate these hypotheses. Experiments 1 and 2 show that a convex function relates probability to surprise. Experiment 3 elicits choice data and further supports the proposed hypotheses. The model adds to the understanding of the cognitive and emotional processes underlying the shape of the probability weighting function. Copyright © 2002 John Wiley & Sons, Ltd.     

Are there degrees of belief?

John Maynard Keynes claimed that not all probabilities were comparable. Frank Ramsey argued that they were, and that Keynes's views to the contrary rested on a confusion of degree of entailment and degree of belief. We will argue that Keynes and Ramsey largely talked past each other, and yet that there are issues of great significance underlying their dispute. In particular, the simple principle of maximizing expected utility may be seen in a new light as one step of a rich and complex process.     

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.     

Choice with delayed and probabilistic reinforcers: effects of prereinforcer and postreinforcer stimuli.

In Experiment 1, pigeons' pecks on a green key led to a 5-s delay with green houselights, and then food was delivered on 20% (or, in other conditions, 50%) of the trials. Pecks on a red key led to an adjusting delay with red houselights, and then food was delivered on every trial. The adjusting delay was used to estimate indifference points: delays at which the two alternatives were chosen about equally often. Varying the presence or absence of green houselights during the delays that preceded possible food deliveries had large effects on choice. In contrast, varying the presence of the green or red houselights in the intertrial intervals had no effects on choice. In Experiment 2, pecks on the green key led to delays of either 5 s or 30 s with green houselights, and then food was delivered on 20% of the trials. Varying the duration of the green houselights on nonreinforced trials had no effect on choice. The results suggest that the green houselights served as a conditioned reinforcer at some times but not at others, depending on whether or not there was a possibility that a primary reinforcer might be delivered. Given this interpretation of what constitutes a conditioned reinforcer, most of the results were consistent with the view that the strength of a conditioned reinforcer is inversely related to its duration.     

Second-order schedules of token reinforcement: effects of varying the schedule of food presentation

In the initial link of a complex schedule, one discriminative stimulus was presented and lever pressing produced tokens on fixed-ratio schedules. In the terminal link, signalled by a second discriminative stimulus, deposits of the tokens produced food. With two rats, the terminal link was presented after each sixth component schedule of token reinforcement was completed. With the other two rats, the terminal link was presented following the first component schedule completed after a fixed interval. During the terminal link, each token deposit initially produced food. The schedule of food presentation was subsequently increased such that an increasing number of token deposits in the terminal link was required for each food presentation. Rates of lever pressing in the initial link were inversely related to the schedule of food presentation in the terminal link. These results are similar to those of experiments that have varied schedules of food presentation in chained schedules. Rates and patterns of responding controlled throughout the initial link were more similar to those ordinarily controlled by second-order brief-stimulus schedules than to those controlled by comparable extended chained schedules.     

Rewording the Rules on Disjunctive Probability

Logic is a central and highly useful part of philosophy. Its value is particularly evident when it comes to keeping our thinking about disjunctive probabilities clear. Because of the two meanings of “or” (“just one of these statements is true,” “at least one of these statements is true”), logic can show how the likelihood of a disjunction being true can be determined quite easily. To gauge the chance that one of two or more exclusive alternatives is true, one need only sum up their respective likelihoods. And to know the chance that at least one of two or more compatible alternatives is true, one simply has to figure the chance that it is false that all of them are false!