Naive Probability: Model‐Based Estimates of Unique Events

We describe a dual‐process theory of how individuals estimate the probabilities of unique events, such as Hillary Clinton becoming U.S. President. It postulates that uncertainty is a guide to improbability. In its computer implementation, an intuitive system 1 simulates evidence in mental models and forms analog non‐numerical representations of the magnitude of degrees of belief. This system has minimal computational power and combines evidence using a small repertoire of primitive operations. It resolves the uncertainty of divergent evidence for single events, for conjunctions of events, and for inclusive disjunctions of events, by taking a primitive average of non‐numerical probabilities. It computes conditional probabilities in a tractable way, treating the given event as evidence that may be relevant to the probability of the dependent event. A deliberative system 2 maps the resulting representations into numerical probabilities. With access to working memory, it carries out arithmetical operations in combining numerical estimates. Experiments corroborated the theory's predictions. Participants concurred in estimates of real possibilities. They violated the complete joint probability distribution in the predicted ways, when they made estimates about conjunctions: P(A), P(B), P(A and B), disjunctions: P(A), P(B), P(A or B or both), and conditional probabilities P(A), P(B), P(B|A). They were faster to estimate the probabilities of compound propositions when they had already estimated the probabilities of each of their components. We discuss the implications of these results for theories of probabilistic reasoning.     

When the Unreal is More Likely Than the Real: Post Hoc Probability Judgements and Counterfactual Closeness

Occasionally, people are called upon to estimate probabilities after an event has occurred. In hindsight, was this an outcome we could have expected? Could things easily have turned out differently? One strategy for performing post hoc probability judgements would be to mentally turn the clock back and reconstruct one's expectations before the event. But if asked about the probability of an alternative, counterfactual outcome, a simpler strategy is available, based on this outcome's perceived closeness to what actually happened. The article presents five studies exploring the relationship between counterfactual closeness and counterfactual probability. The first study indicates that post hoc probabilities typically refer to the counterfactual rather than the factual outcome. Studies 2-5 show that physical, temporal, or conceptual proximity play a decisive role for post hoc probability assessments of counterfactual events. When margins are narrow, the probabilities of, for instance, winning a match (when losing), and of losing (when actually winning) may even be rated higher than the corresponding probabilities of what really happened. Closeness is also more often referred to, and rated to be a better reason for believing there is a “good chance” of the counterfactual rather than of the factual result occurring. Finally, the closeness of the alternative outcome in success and failure stories is shown to be significantly correlated to its rated probability.     

Attending to the execution of a complex sensorimotor skill: expertise differences, choking, and slumps

A simulated baseball batting task was used to compare the relative effects of attending to extraneous information (tone frequency) and attending to skill execution (direction of bat movement) on performance and swing kinematics and to evaluate how these effects differ as a function of expertise. The extraneous dual task degraded batting performance in novices but had no significant effect on experts. The skill-focused dual task increased batting errors and movement variability for experts but had no significant effect on novices. For expert batters, accuracy in the skill-focused dual task was inversely related to the current level of performance. Expert batters were significantly more accurate in the skill-focused dual task when placed under pressure. These findings indicate that the attentional focus varies substantially across and within performers with different levels of expertise.     

Verbal probabilities: Ambiguous, context-dependent, or both?

To investigate the communication value of verbal probabilistic phrases, like “possibly,” “probably,” and “perhaps,” three experiments were conducted. Subjects were asked to judge the degree of probability expressed by such phrases in different contexts: in sentences reflecting opinions on current events, in a medical discussion of treatment effectiveness, and in videotaped news reports. Judgments of degree of probability were performed in the first study on a 0–100% probability scale and in the other two on 7-point rating scales. Results indicated that different contexts influence the interpretation of probability terms and in many cases, but not always, lead to higher between-subject variability than when the terms are judged in isolation, presumably because the interpretation of probability terms tends to be correlated with the judges' personal opinions on the topics. Special communication problems arise from the fact that most people are not fully aware of the ambiguity of these phrases and underestimate the variability of such ratings in the general population. Miscommunication between experts and the general public was illustrated by answers to a questionnaire given to general medical practitioners and to parents of small children. The latter preferred numerical probabilities to words, but thinking from an individual-oriented perspective, they often misunderstood the intended statistical meanings.     

The elusive wishful thinking effect

Abstract

We define a desirability effect as the inflation of the judged probability of desirable events or the diminution of the judged probability of undersirable events. A series of studies of this effect are reported. In the first four experiments, subjects were presented with visual stimuli (a grid matrix in two colours, or a jar containing beads in two colours), and asked to estimate the probability of drawing at random one of the colours), and asked to estimate the probability of drawing at random one of the colours. The estimated probabilities for a defined draw were not higher when the draw entailed a gain than when it entailed a loss. In the fifth and sixth experiments, subjects read short stories each describing two contestants competing for some desirable outcome (e.g. parents fighting for child custody, or firms bidding for a contract). Some judged the probability that A would win, others judged the Desirability that A would win. Story elements that enhanced a contestant's desirability did not cause the favoured contestant to be judged more likely to win. Only when a contestant's desirability was enhanced by promising the subject of payoff contingent on that contestant's victory was there some slight evidence for a desirability effect: contestants were judged more likely to win when the subject expected a monetary prize if they won than when the subject expected a prize if the other contestant won. In the last experiment, subjects estimated the probability of an over-20-point weekly change in the Dow Jones average, and were promised prizes contingent on such a change either occurring, or failing to occur. They were also given a monetary incentive for accuracy. Subjects who desired a small change. We conclude that desirability effects, when they exist, operate by biasing the evidence brought to mind regarding the event in question, but when a given body of evidence is considered, its judged probability is not influenced by desirability considerations.     

Experimental test of the prospect theory value function: A stochastic dominance approach

According to prospect theory, individuals are risk averse regarding gains but risk seeking regarding losses, implying an S-shaped value function. The S-shaped value function hypothesis is based on experiments in which subjects are asked to choose separately between alternatives with either only positive or only negative outcomes, alternatives which rarely exist in the capital market. In addition, the S-shaped findings may be biased by the “certainty effect” and by probability distortion. In this paper we employ the recently developed prospect stochastic dominance criterion to test the prospect theory S-shaped value function hypothesis with mixed outcomes and with no “certainty effect.” Assuming that subjects do not distort moderate probabilities, we strongly reject the prospect theory S-shaped value function, with at least 76–86% of the choices being inconsistent with such preferences. When possible subjective probability distortions are taken into account, we find that at least 50–66% of the choices are inconsistent with an S-shaped value function.     

Feature cues in probability learning: Data base information and judgment

Judgments of probabilistic events are often based partly on some information about past similar events. This study investigates the impact of summarized historical data termed a feature cue on performance in a cue probability learning task. Judges (n = 64) made 150 predictions of a criterion variable (Y_e) from a single cue variable (X). The feature cue variable (Z) provided judges with the “average past criterion” for the cue value on trial i, i.e., the conditional mean . Availability of the feature cue was varied with an AB-BA transfer design. Results demonstrate that the presence of the feature cue greatly imporved prediction achievement and accuracy. Under certain conditions, consistency and cue weighting were also improved by the feature cue aid. Although the feature cue value itself was not used as a prediction, it served as an anchor, around which judgments were dispersed. Implications for decision making with data base information are discussed.     

Time stamp in conditioned place avoidance can be set to different circadian phases

We have reported that the expression of conditioned place avoidance (CPA) in the golden hamster is regulated in a circadian pattern such that the preference is exhibited strongly at the circadian time of prior training but not at other circadian times [Cain, S. W., Chou, T., & Ralph, M. R. (2004a). Circadian modulation of performance on an aversion-based place learning task in hamsters. Behavioural Brain Research, 150(1–2), 201–205]. In that study, animals that were trained at a specific circadian time to discriminate between a “safe” context and one paired with foot shock, showed strong avoidance of the paired context at 24 and 48 h following the last training session, and showed no avoidance at 32 and 40 h following training. In the present study, we hypothesized that this “time stamp” effect is settable to any circadian phase. This was tested by training animals at one of two times of day (ZT13 or ZT4) and testing whether a time stamp would be observed, with avoidance occurring only when training and testing times match. Results confirmed our hypothesis, suggesting that the time stamp in the performance of learned tasks can be set to any circadian phase. Such an ability may allow animals in nature to predict the recurrence of 24 h events, regardless of the time of day the event was encountered.     

Perceptual Expertise as a Shift from Strategic Interference to Automatic Holistic Processing

Holistic processing was initially characterized a unique hallmark of face perception (e.g., Young et al., 1987) and later argued a domain-general marker of perceptual expertise (e.g., Gauthier et al., 1998). More recently, evidence for holistic processing - measured by interference from task-irrelevant parts - was obtained in novices, raising questions for its usefulness as a test of expertise. Indeed, recent studies use the same task to make opposite claims: Hsiao & Cottrell (2009) found more interference in novices than experts for Chinese characters, while Wong, Palmeri & Gauthier (2009) found more interference in experts than novices with objects. Offering a resolution to this paradox, our work on the perception of musical notation (Wong & Gauthier, in press) suggests that expert and novice interference effects represent two ends of a continuum: interference is initially strategic and contextual, but becomes more automatic as holistic processing develops with the acquisition of perceptual expertise.     

On estimating inter-subject variability of choice probabilities under observability constraints

Methods are presented for estimating inter-subject variability of the probability of a given event defined in terms of subject's behavior (e.g., probability of a given choice in a discrimination experiment). The constraints consist of using no more than two independent observations for each subject. Estimators are provided for assessing the inter-subject “variance” of the analyzed probabilities; also, a method is given for testing the hypothesis that the average probability is the same for two groups of subjects.     

The Effects of Expertise on the Hindsight Bias

We present data from three experiments examining the effects of objective and subjective expertise on the hindsight bias. In Experiment 1, participants read an essay about baseball or dogs and then answered questions about the baseball essay to the best of their ability, as if they had not read the essay, or to the best of their ability, although they read about dogs. Participants also completed a quiz about baseball rules and terminology, which was an objective measure of expertise. Results demonstrated that as participants' baseball expertise increased, their inability to act as if they never read the essay also increased; expertise exacerbated the hindsight bias. To test the effects of subjective expertise on hindsight bias and investigate factors underlying the relationship, participants in Experiment 2 ranked five topics in order of expertise and gave feeling‐of‐knowing (FOK) ratings for questions from these topics. Foresight participants then saw each question again and answered the questions; hindsight participants saw the questions and answers and gave the probability they would have known the answers had they not been provided. Hindsight bias increased with subjective expertise as did average FOK ratings. In Experiment 3, we experimentally manipulated perceived expertise but found that neither average FOK ratings nor hindsight bias was affected by experimentally induced expertise. Taken together, the results demonstrate that expertise exacerbates both objective and subjective hindsight bias but that an FOK, which likely exists only when expertise is naturally acquired, is necessary to engender the detrimental effect of expertise on the hindsight bias. Copyright © 2016 John Wiley & Sons, Ltd.     

Priming of future States in complex motor skills

The ability to anticipate future states of perceived actions is an important faculty for motor control and the generation of coordinated social interaction. Here, we studied whether the perception of a static posture of a complex movement automatically activates representations of future states of this particular movement event. We did this by using a priming paradigm with photographs of a high-jump movement. Participants judged whether a picture depicted a posture from the approach or flight phase of that movement. To evaluate expertise-dependent effects of priming, non-athletes and athletes were compared. Results revealed faster responding when prime and target pictures were assigned to the same motor response (response priming), and when the temporal order of prime and target matched the temporal order of the depicted postures in a real high jump (temporal-order priming). Whereas experts showed a temporal-order effect even within the same response category, such an effect occurred for novices only between response categories. A second experiment confirmed that these between-group differences are due to domain-specific motor expertise (i.e., high jump) rather than to general motor experiences. Altogether our results suggest that motor expertise results in a more fine-grained posture-based movement representation.     

Hierarchical structure in perceptual representation

A theoretical framework for perceptual representation is presented which proposes that information is coded in hierarchical networks of nonverbal propositions. The hierarchical structure of the representations implies selective organization: Some subsets of a figure will be encoded as integral, structural units of that figure, while others will not. A context-sensitive metric for the “goodness” of a part within a figure is developed, corresponding to the probability that the subset will be encoded as a structural unit. Converging evidence supporting this position is presented from four different tasks using simple, straight-line figures. The tasks studied are (a) dividing figures into “natural” parts, (b) rating the “goodness” of parts within figures, (c) timed verification of parts within figures, and (d) timed mental synthesis of spatially separated parts into unitary figures. The results are discussed in terms of the proposed theory of representation, the processes that operate on those representations, and the general implications of the data for perceptual theories.     

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.     

Bets and Boundaries: Assigning Probabilities to Imprecisely Specified Events

Uncertainty and vagueness/imprecision are not the same: one can be certain about events described using vague predicates and about imprecisely specified events, just as one can be uncertain about precisely specified events. Exactly because of this, a question arises about how one ought to assign probabilities to imprecisely specified events in the case when no possible available evidence will eradicate the imprecision (because, say, of the limits of accuracy of a measuring device). Modelling imprecision by rough sets over an approximation space presents an especially tractable case to help get one’s bearings. Two solutions present themselves: the first takes as upper and lower probabilities of the event X the (exact) probabilities assigned X’s upper and lower rough-set approximations; the second, motivated both by formal considerations and by a simple betting argument, is to treat X’s rough-set approximation as a conditional event and assign to it a point-valued (conditional) probability. With rough sets over an approximation space we get a lot of good behaviour. For example, in the first construction mentioned the lower probabilities are n-monotone, for every . When we examine other models of approximation/imprecision/vagueness, and in particular, proximity spaces, we lose a lot of that good behaviour. In the literature there is not (even) agreement on the definition of upper and lower approximations for events (subsets) in the underlying domain. Betting considerations suggest one choice and, again, ways to assign upper and lower and point-valued probabilities, but nothing works well. Special Issue on Vagueness Edited by Rosanna Keefe and Libor Bêhounek     

Experts in fast-ball sports reduce anticipation timing cost by developing inhibitory control

The present study was conducted to examine the relationship between expertise in movement correction and rate of movement reprogramming within limited time periods, and to clarify the specific cognitive processes regarding superior reprogramming ability in experts. Event-related potentials (ERPs) were recorded in baseball experts (n=7) and novices (n=7) while they completed a predictive task. The task was to manually press a button to coincide with the arrival of a moving target. The target moved at a constant velocity, and its velocity was suddenly decreased in some trials. Under changed velocity conditions, the baseball experts showed significantly smaller timing errors and a higher rate of timing reprogramming than the novices. Moreover, ERPs in baseball experts revealed faster central negative deflection and augmented frontal positive deflection at 200ms (N200) and 300ms (Pd300) after target deceleration, respectively. Following this, peak latency of the next positive component in the central region (P300b) was delayed. The negative deflection at 200ms, augmented frontal positive deflection, and late positive deflection at 300ms have been interpreted as reflecting stimulus detection, motor inhibition, and stimulus-response translation processes. Taken together, these findings suggest that the experts have developed movement reprogramming to avoid anticipation cost, and this is characterized by quick detection of target velocity change, stronger inhibition of the planned, incorrect response, and update of the stimulus-response relationship in the changed environment.     

Expert anticipation from deceptive action

Expertise in sports enhances the ability to anticipate forthcoming events from the observation of a player’s actions. In the present study, we investigated whether this ability is applicable to deceptive action. In three experiments, performance at anticipating the direction change of a running opponent was examined with experienced rugby players and novice counterparts. These experiments were conducted with reaction-time and temporal-occlusion tasks, in combination with eye movement recordings and the presentation of filmed actions and their point-light representations. The main finding was that the experienced players were superior to the novices in their anticipation of deceptive actions, although their performance was still impaired by the deception, in comparison with their anticipation of nondeceptive actions. We also found that the experienced players anticipated nondeceptive actions less accurately than the novices, suggesting that the players’ expectations of deceptive actions worked negatively on their judgments of nondeceptive actions. The results obtained with the point-light representations closely resembled those obtained with the filmed sequences, indicating that anticipation was based on the kinematics of the running action. These results are discussed in the context of recent developments in research on expertise and deception in sports.     

Probabilistic judgment on a coarser scale

We hypothesize that when assessing the likelihood of uncertain events, statistically unsophisticated people utilize a coarse internal scale that only has a limited number of categories. The present paper reports two experiments on probabilistic judgment to test this hypothesis. In Experiment 1, participants estimated event probabilities freely and we found that their responses were highly clustered despite the even and nearly continuous distribution of the target probabilities. In Experiment 2, participants made forced comparisons using two different external response scales (coarser versus finer). We found that their performance did not measure up to the requirement of the finer scale. These findings indicate that besides the systematic biases, a certain portion of human errors in probabilistic judgment may be due to the low resolution of the internal representations.     

Who is crossing where? Infants' discrimination of figures and grounds in events

To learn relational terms such as verbs and prepositions, children must first dissect and process dynamic event components. This paper investigates the way in which 8- to 14-month-old English-reared infants notice the event components, figure (i.e., the moving entity) and ground (i.e., stationary setting), in both dynamic (Experiment 1) and static representations of events (Experiment 2) for categorical ground distinctions expressed in Japanese, but not in English. We then compare both 14- and 19-month-old English- and Japanese-reared infants’ processing of grounds to understand how language learning interacts with the conceptualization of these constructs (Experiment 3). Results suggest that (1) infants distinguish between figures and grounds in events; (2) they do so differently for static vs. dynamic displays; (3) early in the second year, children from diverse language environments form nonnative – perhaps universal – event categories; and (4) these event categories shift over time as children have more exposure to their native tongue.