Partition priming in judgment under uncertainty

We show that likelihood judgments are biased toward an ignorance-prior probability that assigns equal credence to each mutually exclusive event considered by the judge. The value of the ignorance prior depends crucially on how the set of possibilities (i.e., the state space) is subjectively partitioned by the judge. For instance, asking "what is the probability that Sunday will be hotter than any other day next week?" facilitates a two-fold case partition, [Sunday hotter, Sunday not hotter], thus priming an ignorance prior of 1/2. In contrast, asking "what is the probability that the hottest day of the week will be Sunday?" facilitates a seven-fold class partition, [Sunday hottest, Monday hottest, etc.], priming an ignorance prior of 1/7. In four studies, we observed systematic partition dependence: Judgments made by participants presented with either case or class formulations of the same query were biased toward the corresponding ignorance prior.     

Interevent relationships and judgment under uncertainty: structure determines strategy

A fundamental empirical question regarding judgments about events is whether experienced absolute frequencies or relative frequencies are relied on when the likelihood of a particular occurrence is judged. The present research explicates the conditions under which people rely on remembered raw absolute frequencies versus on inferred relative frequencies or proportions when making predictions. Participants saw opinion poll results for candidates prior to an election and, on the basis of these, made judgments concerning the likelihood of each candidate's winning this election. Certain candidates demonstrated a high absolute frequency of winning in the polls, whereas other candidates had high relative win frequencies. The results indicated that adults are cognitively flexible with regard to the inputs used in this judgment. Certain stimulus event configurations induced reasoning by way of absolute frequencies, whereas other configurations elicited judgments based on relative frequencies. More specifically, as the relational complexity of the event structure increased and more inferences were required to make predictions, the tendency to rely on absolute, as opposed to relative, frequencies also increased.     

Pseudodiagnosticity

Subjects selected data in order to decide from which of two ‘islands’ an ‘archeological find’ had come. The results replicated two established phenomena in cognitive psychology: (1) the tendency to ignore base rate data given individuating information, and (2) the tendency to seek confirmatory evidence.The major outcome of the study was, however, to reveal a new phenomenon in information search. Subjects displayed a surprising and strong tendency to seek diagnostically worthless information. They then altered their conclusion based on that information. For example, subjects who had already obtained P(D₁/H₁) selected P(D₂/H₁) when P(D₁/H₂) was equally easily available, and when they had no relevant experience to bring to bear on the estimation of P(D₁/H₂). This phenomenon, which appears to be a wholly dysfunctional cognitive tendency, was labeled pseudodiagnosticity.     

Causal explanation improves judgment under uncertainty,but rarely in a Bayesian way

Three studies reexamined the claim that clarifying the causal origin of key statistics can increase normative performance on Bayesian problems involving judgment under uncertainty. Experiments 1 and 2 found that causal explanation did not increase the rate of normative solutions. However, certain types of causal explanation did lead to a reduction in the magnitude of errors in probability estimation. This effect was most pronounced when problem statistics were expressed in percentage formats. Experiment 3 used process-tracing methods to examine the impact of causal explanation of false positives on solution strategies. Changes in probability estimation following causal explanation were the result of a mixture of individual reasoning strategies, including non-Bayesian mechanisms, such as increased attention to explained statistics and approximations of subcomponents of Bayes’ rule. The results show that although causal explanation of statistics can affect the way that a problem is mentally represented, this does not necessarily lead to an increased rate of normative responding.     

Between ignorance and truth: Partition dependence and learning in judgment under uncertainty

In 3 studies, participants viewed sequences of multiattribute objects (e.g., colored shapes) appearing with varying frequencies and judged the likelihood of the attributes of those objects. Judged probabilities reflected a compromise between (a) the frequency with which each attribute appeared and (b) the ignorance prior probability cued by the number of distinct values that the focal attribute could take on. Thus, judged probabilities were partition dependent, varying with the number of events into which the state space was subjectively divided. This bias was diminished among participants more confident in what they learned, was strong and insensitive to level of confidence when ignorance priors were especially salient, and required ignorance priors to be salient only when probabilities were elicited (not during encoding).     

The role of short-term memory capacity and task experience for overconfidence in judgment under uncertainty

Research with general knowledge items demonstrates extreme overconfidence when people estimate confidence intervals for unknown quantities, but close to zero overconfidence when the same intervals are assessed by probability judgment. In 3 experiments, the authors investigated if the overconfidence specific to confidence intervals derives from limited task experience or from short-term memory limitations. As predicted by the naive sampling model (P. Juslin, A. Winman, & P. Hansson, 2007), overconfidence with probability judgment is rapidly reduced by additional task experience, whereas overconfidence with intuitive confidence intervals is minimally affected even by extensive task experience. In contrast to the minor bias with probability judgment, the extreme overconfidence bias with intuitive confidence intervals is correlated with short-term memory capacity. The proposed interpretation is that increased task experience is not sufficient to cure the overconfidence with confidence intervals because it stems from short-term memory limitations.     

Inconsistency and uncertainty in multi-attribute judgment of human performance

This paper examines the effect of uncertainty and inconsistency on the judgment of human performance. The results indicate that the effect of inconsistency on judgment is not mediated by subjective uncertainty. We find that both the level and the extremity of judgment decrease with uncertainty. These effects are explained, respectively, by uncertainty aversion and by regressiveness. We also find that both the level and the extremity of judgment of human performance increase with inconsistency. These effects are explained by reliance on integration rules in which judgment is based primarily on some aspects of the information, while other aspects are, to some extent, ignored.     

Path planning under spatial uncertainty

In this article, we present experiments studying path planning under spatial uncertainties. In the main experiment, the participants' task was to navigate the shortest possible path to find an object hidden in one of four places and to bring it to the final destination. The probability of finding the object (probability matrix) was different for each of the four places and varied between conditions. Givensuch uncertainties about the object's location, planning a single path is not sufficient. Participants had to generate multiple consecutive plans (metaplans)--for example: If the object is found in A, proceed to the destination; if the object is not found, proceed to B; and so on. The optimal solution depends on the specific probability matrix. In each condition, participants learned a different probability matrix and were then asked to report the optimal metaplan. Results demonstrate effective integration of the probabilistic information about the object's location during planning. We present a hierarchical planning scheme that could account for participants' behavior, as well as for systematic errors and differences between conditions.     

Coherent choice functions under uncertainty

We discuss several features of coherent choice functions—where the admissible options in a decision problem are exactly those that maximize expected utility for some probability/utility pair in fixed set S of probability/utility pairs. In this paper we consider, primarily, normal form decision problems under uncertainty—where only the probability component of S is indeterminate and utility for two privileged outcomes is determinate. Coherent choice distinguishes between each pair of sets of probabilities regardless the “shape” or “connectedness” of the sets of probabilities. We axiomatize the theory of choice functions and show these axioms are necessary for coherence. The axioms are sufficient for coherence using a set of probability/almost-state-independent utility pairs. We give sufficient conditions when a choice function satisfying our axioms is represented by a set of probability/state-independent utility pairs with a common utility.     

Instrumental judgment and performance under variations in action-outcome contingency and contiguity

The intentional theory of instrumental performance proposes that performance of an action is determined in part by a belief about its causal effectiveness in producing a desired outcome. At variance with this notion, previous implicit learning experiments appear to have yielded dissociations between subjects' performance and beliefs. In two experiments, subjects were given an opportunity to perform an action--pressing a key on a computer keyboard--which was associated with an outcome on the computer screen according to a free-operant contingency. The subjects in one group were asked to judge the effectiveness of the action in causing the outcome, while those in a second group were asked to maximize their points score under a payoff schedule. In the first study, the effect of varying the contingency between the action and outcome was examined by keeping the probability of an outcome contiguous with an action constant and varying the probability of an outcome in the absence of an action. Performance and judgments showed a comparable sensitivity to variations of the instrumental contingency. In the second study, the delay between the action and the resultant outcome was varied. Increasing the action-outcome delay from 0 sec up to 4 sec produced a systematic decline in both causal judgments and performance relative to noncontingent, control conditions. These results are in accord with the intentional theory of performance, but they present difficulties for the notion of implicit learning.     

Decision-making under uncertainty: biases and Bayesians

Animals (including humans) often face circumstances in which the best choice of action is not certain. Environmental cues may be ambiguous, and choices may be risky. This paper reviews the theoretical side of decision-making under uncertainty, particularly with regard to unknown risk (ambiguity). We use simple models to show that, irrespective of pay-offs, whether it is optimal to bias probability estimates depends upon how those estimates have been generated. In particular, if estimates have been calculated in a Bayesian framework with a sensible prior, it is best to use unbiased estimates. We review the extent of evidence for and against viewing animals (including humans) as Bayesian decision-makers. We pay particular attention to the Ellsberg Paradox, a classic result from experimental economics, in which human subjects appear to deviate from optimal decision-making by demonstrating an apparent aversion to ambiguity in a choice between two options with equal expected rewards. The paradox initially seems to be an example where decision-making estimates are biased relative to the Bayesian optimum. We discuss the extent to which the Bayesian paradigm might be applied to the evolution of decision-makers and how the Ellsberg Paradox may, with a deeper understanding, be resolved.     

Confidence in judgment

Experiments have shown that, generally, people are overconfident about the correctness of their answers to questions. Cognitive psychologists have attributed this to biases in the way people generate and handle evidence for and against their views. The overconfidence phenomenon and cognitive psychologists' accounts of its origins have recently given rise to three debates. Firstly, ecological psychologists have proposed that overconfidence is an artefact that has arisen because experimenters have used question material not representative of the natural environment. However, it now appears that some overconfidence remains even after this problem has been remedied. Secondly, it has been proposed that overconfidence is an artefactual regression effect that arises because judgments contain an inherently random component. However, those claiming this appear to use the term overconfidence to refer to a phenomenon quite different from the one that the cognitive psychologists set out to explain. Finally, a debate has arisen about the status of perceptual judgments. Some claim that these evince only underconfidence and must, therefore, depend on mechanisms fundamentally different from those subserving other types of judgment. Others have obtained overconfidence with perceptual judgments and argue that a unitary theory is more appropriate. At present, however, no single theory provides an adequate account of the many diverse factors that influence confidence in judgment.     

Probability matching in choice under uncertainty: Intuition versus deliberation

Gaissmaier and Schooler (2008) [Gaissmaier, W., & Schooler, L. J. (2008). The smart potential behind probability matching. Cognition, 109, 416-422] argue that probability matching, which has traditionally been viewed as a decision making error, may instead reflect an adaptive response to environments in which outcomes potentially follow predictable patterns. In choices involving monetary stakes, we find that probability matching persists even when it is not possible to identify or exploit outcome patterns and that many “probability matchers” rate an alternative strategy (maximizing) as superior when it is described to them. Probability matching appears to reflect a mistaken intuition that can be, but often is not, overridden by deliberate consideration of alternative choice strategies.     

The role of causal models in multiple judgments under uncertainty

Two studies examined a novel prediction of the causal Bayes net approach to judgments under uncertainty, namely that causal knowledge affects the interpretation of statistical evidence obtained over multiple observations. Participants estimated the conditional probability of an uncertain event (breast cancer) given information about the base rate, hit rate (probability of a positive mammogram given cancer) and false positive rate (probability of a positive mammogram in the absence of cancer). Conditional probability estimates were made after observing one or two positive mammograms. Participants exhibited a causal stability effect: there was a smaller increase in estimates of the probability of cancer over multiple positive mammograms when a causal explanation of false positives was provided. This was the case when the judgments were made by different participants (Experiment 1) or by the same participants (Experiment 2). These results show that identical patterns of observed events can lead to different estimates of event probability depending on beliefs about the generative causes of the observations.     

Public good provision under environmental and social uncertainty

Social dilemmas face people with various kinds of uncertainty. To extend earlier research on environmental uncertainty in resource dilemmas (i.e. uncertainty about the resource size), the present experiment examines the effects of Environmental Uncertainty (low, high uncertainty about the provision point) and Social Uncertainty (low, high uncertainty about others' cooperation) in a public goods dilemma. In line with Social Comparison Theory, it was predicted and found that Environmental Uncertainty decreases cooperation only under High Social Uncertainty, but not under Low Social Uncertainty. The detrimental effects of Environmental Uncertainty can be counteracted by uncertainty reducing information on the provision point and/or on others' contributions as well. © 1998 John Wiley & Sons, Ltd.     

Rapid word learning under uncertainty via cross-situational statistics

There are an infinite number of possible word-to-word pairings in naturalistic learning environments. Previous proposals to solve this mapping problem have focused on linguistic, social, representational, and attentional constraints at a single moment. This article discusses a cross-situational learning strategy based on computing distributional statistics across words, across referents, and, most important, across the co-occurrences of words and referents at multiple moments. We briefly exposed adults to a set of trials that each contained multiple spoken words and multiple pictures of individual objects; no information about word-picture correspondences was given within a trial. Nonetheless, over trials, subjects learned the word-picture mappings through cross-trial statistical relations. Different learning conditions varied the degree of within-trial reference uncertainty, the number of trials, and the length of trials. Overall, the remarkable performance of learners in various learning conditions suggests that they calculate cross-trial statistics with sufficient fidelity and by doing so rapidly learn word-referent pairs even in highly ambiguous learning contexts.