Deduction from Uncertain Premises

We investigate how the perceived uncertainty of a conditional affects a person's choice of conclusion. We use a novel procedure to introduce uncertainty by manipulating the conditional probability of the consequent given the antecedent. In Experiment 1, we show first that subjects reduce their choice of valid conclusions when a conditional is followed by an additional premise that makes the major premise uncertain. In this we replicate Byrne (1989). These subjects choose, instead, a qualified conclusion expressing uncertainty. If subjects are given a third statement that qualifies the likelihood of the additional premise, then the uncertainty of the conclusions they choose is systematically related to the suggested uncertainty. Experiment 2 confirms these observations in problems that omit the additional premise and qualify the first premise directly. Experiment 3 shows that the qualifying statement also affects the perceived probability of the consequent given the antecedent of the conditional. Experiment 4 investigates the effect of suggested uncertainty on the fallacies and shows that increases in uncertainty reduce the number of certain conclusions that are chosen while affirming the consequent but have no effect on denying the antecedent. We discuss our results in terms of rule theories and mental models and conclude that the latter give the most natural account of our results.     

Underdetermination,Model-ensembles and Surprises: On the Epistemology of Scenario-analysis in Climatology

As climate policy decisions are decisions under uncertainty, being based on a range of future climate change scenarios, it becomes a crucial question how to set up this scenario range. Failing to comply with the precautionary principle, the scenario methodology widely used in the Third Assessment Report of the International Panel on Climate Change (IPCC) seems to violate international environmental law, in particular a provision of the United Nations Framework Convention on Climate Change. To place climate policy advice on a sound methodological basis would imply that climate simulations which are based on complex climate models had, in stark contrast to their current hegemony, hardly an epistemic role to play in climate scenario analysis at all. Their main function might actually consist in ‘foreseeing future ozone-holes’. In order to argue for these theses, I explain first of all the plurality of climate models used in climate science by the failure to avoid the problem of underdetermination. As a consequence, climate simulation results have to be interpreted as modal sentences, stating what is possibly true of our climate system. This indicates that climate policy decisions are decisions under uncertainty. Two general methodological principles which may guide the construction of the scenario range are formulated and contrasted with each other: modal inductivism and modal falsificationism. I argue that modal inductivism, being the methodology implicitly underlying the third IPCC report, is severely flawed. Modal falsificationism, representing the sound alternative, would in turn require an overhaul of the IPCC practice.     

Timed magnitude comparisons of numerical and nonnumerical expressions of uncertainty

Two experiments involving paired comparisons of numerical and nonnumerical expressions of uncertainty are reported. Subjects were timed under two opposing sets of instructions ("choose higher probability" vs. "choose lower probability"). Numerical comparisons were consistently faster and easier than their nonnumerical counterparts. Consistent distance and congruity effects were obtained, illustrating that both numerical and nonnumerical expressions of uncertainty contain subjective magnitude information, and suggesting that similar processes are employed in manipulating and comparing numerical and verbal terms. To account for the general pattern of results obtained, Holyoak's reference point model (1978) was generalized by explicitly including the vagueness of the nonnumerical expressions. This generalized model is based on the notion that probability expressions can be represented by membership functions (Wallsten, Budescu, Rapoport, Zwick, & Forsyth, 1986) from which measures of location for each word, and measures of overlap for each pair can be derived. A good level of fit was obtained for this model at the individual level.     

Uncertainty and the Ethics of Clinical Trials

A probabilistic explication is offered of equipoise and uncertainty in clinical trials. In order to be useful in the justification of clinical trials, equipoise has to be interpreted in terms of overlapping probability distributions of possible treatment outcomes, rather than point estimates representing expectation values. Uncertainty about treatment outcomes is shown to be a necessary but insufficient condition for the ethical defensibility of clinical trials. Additional requirements are proposed for the nature of that uncertainty. The indecisiveness of our criteria for cautious decision-making under uncertainty creates the leeway that makes clinical trials defensible.     

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.     

Probability all the Way Up

Richard Jeffrey’s radical probabilism (‘probability all the way down’) is augmented by the claim that probability cannot be turned into certainty, except by data that logically exclude all alternatives. Once we start being uncertain, no amount of updating will free us from the treadmill of uncertainty. This claim is cast first in objectivist and then in subjectivist terms.     

Psychological management intervention guidelines for rape survivors with post-traumatic stress disorder (PTSD): A brief exploratory systematic literature review

This exploratory systematic literature review aimed to characterise the current evidence on psychological management intervention guidelines for use with rape survivors with post-traumatic stress disorder (PTSD) symptoms. For the data searches we accessed the following electronic databases: Google Scholar, Science Direct, EBSCOhost, and PsychInfo. We utilised search terms with variations of the following key words: psychological management guidelines of PTSD*, rape survivors*. Inclusion criteria were guidelines for rape survivors with PTSD that consider referral, treatment, and preventive and health promotion in an international setting. We excluded guidelines that did not address PTSD resulting from rape in an international setting. We employed a narrative synthesis data analysis approach to integrate the evidence from across studies. Findings suggest prevalent guidelines for rape survivors with PTSD focus on cognitive behavioural therapy and other psychological management interventions in highly specialised areas and Primary Health Care (PHC) settings in international countries, but not in other countries such as South Africa. Emerging guidelines are needed for PTSD psychological management interventions in rape care clinics situated in South Africa.     

Toward a new conceptualization and operationalization of risk perception within the genetic counseling domain

The purpose of this paper is twofold. First, it provides an historical overview of studies of risk, risk perception, and decision making under risk within the genetic counseling domain. Second, it proposes an alternative conceptualization and operationalization for the study of risk perception. The conceptualization involves probability, adversity, incompleteness, and ambiguity. Prior studies of risk perception focus on the recurrence risk and operationalize risk perception by asking for interpretations of the magnitude of the probability of the outcome. Their focus is on the probability of a particular outcome. We formulate the problem in terms of a gamble and suggest that risk perception be operationalized in terms of the riskiness of the gamble. Our focus is on the riskiness of a decision option which entails two or more outcomes.     

Understanding ‘Unlikely (20% Likelihood)’ or ‘20% Likelihood (Unlikely)’ Outcomes: The Robustness of the Extremity Effect

Calls to communicate uncertainty using mixed, verbal‐numerical formats (‘unlikely [0–33%]’) have stemmed from research comparing mixed with solely verbal communications. Research using the new ‘which outcome’ approach to investigate understanding of verbal probability expressions suggests, however, that mixed formats might convey disadvantages compared with purely numerical communications. When asked to indicate an outcome that is ‘unlikely’, participants have been shown to often indicate outcomes with a value exceeding the maximum value shown, equivalent to a 0% probability —an ‘extremity effect’. Recognising the potential consequences of communication recipients expecting an ‘unlikely’ event to never occur, we extend the ‘which outcome’ work across four experiments, using verbal, numerical, and verbal‐numerical communication formats, as well as a previously unconsidered numerical‐verbal format. We examine how robust the effect is in the context of consequential outcomes and over non‐normal distributions. We also investigate whether participants are aware of the inconsistency in their responses from a traditional ‘how likely’ and ‘which outcome’ task. We replicate and extend previous findings, with preference for extreme outcomes (including above maximum values) observed in both verbal and verbal‐numerical formats. Our results suggest caution in blanket usage of recently recommended verbal‐numerical formats for the communication of uncertainty. Copyright © 2018 John Wiley & Sons, Ltd.     

Patients' interpretations of verbal expressions of probability: implications for securing informed consent to medical interventions

Physicians often use verbal expressions of probability to characterize their uncertainty about outcomes and the risks or side effects of proposed therapies. However, there is an extensive literature that documents the inherent vagueness of such expressions. Because of the potential importance of probability terms to physician-patient communication and decision-making, we asked patients to tell us the odds they thought applicable to the term "rare," as used by their physician to discuss the likelihood of an adverse outcome from surgery. Patients were randomly assigned to one of three outcome groups: death, severe heart attack, or severe pneumonia. Demographic data were elicited from each subject, as were indicators of present health status, medical history for certain diseases and surgery, and life expectancy. Linear regression and ANOVA analyses of the responses indicate that patient age, education level, perceived health status, and recency of experience with disease and medical care influence patients' numeric interpretations. We discuss the implications of these results.     

Aggregate and individual replication probability within an explicit model of the research process

We study a model of the research process in which the true effect size, the replication jitter due to changes in experimental procedure, and the statistical error of effect size measurement are all normally distributed random variables. Within this model, we analyze the probability of successfully replicating an initial experimental result by obtaining either a statistically significant result in the same direction or any effect in that direction. We analyze both the probability of successfully replicating a particular experimental effect (i.e., the individual replication probability) and the average probability of successful replication across different studies within some research context (i.e., the aggregate replication probability), and we identify the conditions under which the latter can be approximated using the formulas of Killeen (2005a, 2007). We show how both of these probabilities depend on parameters of the research context that would rarely be known in practice. In addition, we show that the statistical uncertainty associated with the size of an initial observed effect would often prevent accurate estimation of the desired individual replication probability even if these research context parameters were known exactly. We conclude that accurate estimates of replication probability are generally unattainable.     

Treatment of Time in the TAT

Part of a larger empirical investigation to identify and classify subjective probability notions and explore their relationship to personality variables (Lipgar, 1965). Four factors that distinguished four types of subjective probability notions had been obtained from a matrix of intercorrelations among 30 Ss' Q sort ratings on patterns of “head-tail” guesses. To investigate the possibility that subjective probability notions are associated with other orientational activities in situations of uncertainty, a typology of time orientations and rating scales was derived from TAT stories by those Ss who best represented the four subjective probability factors. These and other stories were rated by four judges independently, and an association between treatment of time in the TAT and subjective probability notions was substantiated.     

Judgement under uncertainty and conjunction fallacy inhibition training

Intuitive predictions and judgements under uncertainty are often mediated by judgemental heuristics that sometimes lead to biases. Our micro-developmental study suggests that a presumption of rationality is justified for adult subjects, in so far as their systematic judgemental biases appear to be due to a specific executive-inhibition failure in working memory, and not necessarily to a lack of understanding of the fundamental principles of probability. This hypothesis was tested using an experimental procedure in which 60 adult subjects were trained to inhibit the classical conjunction bias on a frequency judgement task derived from Tversky and Kahneman's work. Pre- and post-test performance was assessed via a probability judgement task. The data indicated a training effect, suggesting that subjects traditionally labelled as “irrational” with respect to the classical rules of inductive reasoning are in fact “inefficient inhibitors”. These findings are discussed in terms of a polymorphous view of rationality.     

Calibration accuracy of a judgmental process that predicts the commercial success of new product ideas

We examine the accuracy of forecasts of the commercial potential of new product ideas by experts at an Inventor's Assistance Program (IAP). Each idea is evaluated in terms of 37 attributes or cues, which are subjectively rated and intuitively combined by an IAP expert to arrive at a forecast of the idea's commercialization prospects. Data regarding actual commercialization outcomes for 559 new product ideas were collected to examine the accuracy of the IAP forecasts. The intensive evaluation of each idea conducted by the IAP produces forecasts that accurately rank order the ideas in terms of their probability of commercialization. The focus of the evaluation process on case‐specific evidence that distinguishes one idea from another, however, and the corresponding neglect of aggregate considerations such as the base rate (BR) and predictability of commercialization for new product ideas in general, yields forecasts that are systematically miscalibrated in terms of their correspondence to the actual probability of commercialization. Copyright © 2007 John Wiley & Sons, Ltd.     

Children's understanding of posterior probability

Do young children have a basic intuition of posterior probability? Do they update their decisions and judgments in the light of new evidence? We hypothesized that they can do so extensionally, by considering and counting the various ways in which an event may or may not occur. The results reported in this paper showed that from the age of five, children's decisions under uncertainty (Study 1) and judgments about random outcomes (Study 2) are correctly affected by posterior information. From the same age, children correctly revise their decisions in situations in which they face a single, uncertain event, produced by an intentional agent (Study 3). The finding that young children have some understanding of posterior probability supports the theory of naive extensional reasoning, and contravenes some pessimistic views of probabilistic reasoning, in particular the evolutionary claim that the human mind cannot deal with single-case probability.     

Reconsidering the aims of analysis in a probabilistic universe: Containment and coniunctio

Abstract

This paper explores the relationship between our attempts to define the aims of analysis and the acceptance of probability in New Physics. It draws attention to the influence of physicists on both Jung and Bion, which is well documented. It presents an argument for process-based aims rather than the recognition of innate knowledge as an aim. Two processes from different traditions (Jungian and Kleinian) are suggested as central to the aims of analysis: containment and coniunctio. The coniunctio/disiunctio axis in Jung's writing is paralleled with the axis PS<->D of the post-Kleinians. Clinical material is presented supporting the necessity of differential aims and illustrating development/stasis along this axis. A case is made for analysis to embrace the reality of uncertainty and to work with the psychic obstacles in patients, and in analysts, that result from coming to terms with probability.     

Making sense of surprise: an investigation of the factors influencing surprise judgments

Surprise is often defined in terms of disconfirmed expectations, whereby the surprisingness of an event is thought to be dependent on the degree to which it contrasts with a more likely, or expected, outcome. The authors investigated the alternative hypothesis that surprise is more accurately modeled as a manifestation of an ongoing sense-making process. In a series of experiments, participants were given a number of scenarios and rated surprise and probability for various hypothetical outcomes that either confirmed or disconfirmed an expectation. Experiment 1 demonstrated that representational specificity influences the relationship that holds between surprise and probability ratings. Experiment 2 demonstrated that the inclusion of an enabling event lowers surprise ratings for disconfirming outcomes. Experiment 3 explored the reason for this effect, revealing that enabling events lower surprise by reducing uncertainty, thus enhancing ease of integration. Experiment 4 evaluated the contrast hypothesis directly, showing that differences in contrast are not correlated with differences in surprise. These results provide converging support for the view that the level of surprise experienced for an event is related to the difficulty of integrating that event with an existing representation. (PsycINFO Database Record (c) 2010 APA, all rights reserved).     

用文字概率衡量不确定性：特征和问题

文字概率是衡量不确定性的方式之一, 即人们使用诸如“也许”、“未必”的词汇来描述特定事件发生的可能性。文字概率不同于数字概率, 主要体现在文字概率的模糊性、非概率运算性和语义特性上。这使得相对于数字概率, 用文字概率衡量不确定性既有优势也有问题, 进而对人们的不确定信息沟通和风险决策造成影响。虽然文字概率与数字概率存在特征上的差异并且人们在日常交流中偏爱文字概率, 但是大部分风险领域的研究却仅局限于数字概率, 今后有必要研究使用文字概率测量的风险决策。在已有文字概率特征研究的基础上, 还可以进一步探究其不同于数字概率的其它特征(文字/数字概率与双系统模型的联系、文字概率的跨文化差异等)及其对风险决策的影响。     

Verbal and Numerical Expressions of Probability: "It's a Fifty-Fifty Chance"

When estimating risks, people may use "50" as an expression of the verbal phrase "fifty-fifty chance," without intending the associated number of 50%. The result is an excess of 50s in the response distribution. The present study examined factors determining the magnitude of such a "50 blip," using a large sample of adolescents and adults. We found that phrasing probability questions in a distributional format (asking about risks as a percentage in a population) rather than in a singular format (asking about risks to an individual) reduced the use of "50." Less numerate respondents, children, and less educated adults were more likely to say "50." Finally, events that evoked feelings of less perceived control led to more 50s. The results are discussed in terms of what they reveal about how people express epistemic uncertainty. Copyright 2000 Academic Press.