The Directionality of Verbal Probability Expressions: Effects on Decisions,Predictions, and Probabilistic Reasoning

Verbal phrases denoting uncertainty are of two kinds: positive, suggesting the occurrence of a target outcome, and negative, drawing attention to its nonoccurrence (Teigen & Brun, 1995). This directionality is correlated with, but not identical to, high and low p values. Choice of phrase will in turn influence predictions and decisions. A treatment described as having “some possibility” of success will be recommended, as opposed to when it is described as “quite uncertain,” even if the probability of cure referred to by these two expressions is judged to be the same (Experiment 1). Individuals who formulate their chances of achieving a successful outcome in positive terms are supposed to make different decisions than individuals who use equivalent, but negatively formulated, phrases (Experiments 2 and 3). Finally, negative phrases lead to fewer conjunction errors in probabilistic reasoning than do positive phrases (Experiment 4). For instance, a combination of 2 “uncertain” outcomes is readily seen to be “very uncertain.” But positive phrases lead to fewer disjunction errors than do negative phrases. Thus verbal probabilistic phrases differ from numerical probabilities not primarily by being more “vague,” but by suggesting more clearly the kind of inferences that should be drawn.     

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.     

Is guilt ‘likely’ or ‘not certain’?: Contrast with previous probabilities determines choice of verbal terms

This research focuses on what determines speakers' choice of positive and negative probability phrases (e.g., “a chance” vs. “not certain”) in a legal context. We argue that choice of phrase to describe an event's probability of occurrence can be determined by the contrast between its current p value and an earlier p value, and not by that current value alone. Three experiments were conducted describing scenarios where profilers communicated a suspect's probability of guilt to the police. In the first study, a probability estimate is revised upwards or downwards. In the second one, the probability estimate of a speaker is higher or lower than that given by a previous speaker. In both cases, participants expected upward trends to lead to positive phrases, whereas downward trends were associated with negative phrases. In a third study, participants had to select probability phrases to characterize two different suspects. No contrast effects were found. We conclude that verbal probability directionality has primarily an argumentative function, where positive phrases are selected when probabilities are contrasted with smaller p values, and negative when contrasted with higher p values.     

You say "probable" and I say "likely": improving interpersonal communication with verbal probability phrases

When forecasters and decision makers describe uncertain events using verbal probability terms, there is a risk of miscommunication because people use different probability phrases and interpret them in different ways. In an effort to facilitate the communication process, the authors investigated various ways of converting the forecasters' verbal probabilities to the decision maker's terms. The authors present 3 studies in which participants judged the probabilities of distinct events using both numerical and verbal probabilities. They define several indexes of interindividual coassignment of phrases to the same events and evaluate the conversion methods by comparing the values of these indexes for the converted and the unconverted judgments. In all the cases studied, the conversion methods significantly reduced the error rates in communicating uncertainties.     

Verbal Style,Gubernatorial Strategies,and Legislative Success

This article examines the relationship between a governor's verbal style and his success in achieving his legislative goals. We add a measure of verbal style developed by Roderick Hart to a traditional model used by scholars of political chief executives to explain legislative success. We apply this model to the State of the State addresses of six governors of Florida who served between 1966 and 2006. Our findings reflect the validity of the truism “words matter.” Governors who use words and phrases that connote enthusiasm, activity, and realism are more successful in the legislative arena than those who do not.     

Consistency in interpretation of probabilistic phrases

It is occasionally claimed in both applied decision analysis and in basic research that people can better use and understand probabilistic opinions expressed by nonnumerical phrases, such as “unlikely” or “probably,” than by numbers. It is important for practical and theoretical reasons to evaluate this claim. The available literature indicates that there is large variability in the mapping of phrases to numbers, but provides no indication as to its cause. This study asks (a) whether the variability can be attributed to how people interpret the phrases per se, rather than to how they use the number scale and (b) whether the variability is due primarily to between-subject or to within-subject factors. In order to answer these questions, 32 subjects ranked and compared 19 probability phrases on each of three occasions. The results show that individuals have a relatively stable rank ordering of the phrases over time, but that different individuals have different rank orderings. Practical and methodological implications of these data are discussed.     

The Influence of Positive Affect on the Decision Rule in Risk Situations: Focus on Outcome (and Especially Avoidance of Loss) Rather Than Probability

Two experiments examined the influence of positive affect on probability estimation and choice. Participants in whom positive affect had been induced, as well as no-manipulation controls, were asked to make both numerical evaluations of verbal probabilities in three-outcome gambles and actual betting decisions about similar gambles. Results from Experiment 1 showed the phenomenon labeledcautious optimism:Positive affect participants significantly overestimated the probabilities associated with phrases for winning relative to their estimates of probability of losing for the same phrases (optimism), while participants in a control condition did not; yet, in actual gambling situations, affect condition participants were much less likely to gamble than were controls when a real loss was possible (caution). Results of the betting task from Experiment 2 further indicated that affect participants used a betting-decision rule that was different from that of controls: They bet less than controls in gambles where potential losses were large, even though probability of loss was small, and they bet more than controls in gambles where the amount of the potential loss was small, even though the probability of loss was moderate or large. These findings suggest that positive affect can promote an overt shift from a decision rule focusing primarily on probabilities to one focusing on utilities or outcome values, especially for losses. Taken together, the results are compatible with an interpretation of the influence of positive affect in terms of an elaboration of positive cognitive material, and purposive behavior in decisions, rather than in terms of mere response bias.     

Brain functions associated with verbal working memory tasks among young males with alcohol use disorders

This study aimed to investigate the differences in brain functions during verbal working memory between individuals with alcohol use disorders (AUD) and normal controls. fMRI was used to scan brain activations associated with verbal working memory while participants performed 2-back and 0-back tasks. A total of 21 young male college students participated in the study. Eleven of those who clinically met the criteria for AUD were assigned to the AUD group, whereas ten demographically similar subjects who were social drinkers but not AUD were assigned to the normal control group. The AUD group showed less activation in bilateral frontal and precentral, left superior temporal, left superior parietal, and left cerebellar cortex during the 2-back task relative to 0-back task compared to the normal control group. In contrast, the control group showed less activation only in the right uncus than the AUD group. These results suggest that subjects with AUD present abnormality in brain functioning during verbal working memory.     

Framing experts' (dis)agreements about uncertain environmental events

Agreements and disagreements between expert statements influence lay people's beliefs. But few studies have examined what is perceived as a disagreement. We report six experiments where people rated agreement between pairs of probabilistic statements about environmental events, attributed to two different experts or to the same expert at two different points in time. The statements differed in frame, by focusing on complementary outcomes (45% probability that smog will have negative health effects vs. 55% probability that it will not have such effects), in probability level (45% vs. 55% probability of negative effects), or in both respects. Opposite frames strengthened disagreement when combined with different probability levels. Approximate probabilities can be “framed” in yet another way by indicating reference values they are “over” or “under”. Statements that use different directional verbal terms (over vs. under 50%) indicated greater disagreement than statements with the same directional term but different probability levels (over 50% vs. over 70%). Framing and directional terms similarly affected consistency judgments when both statements were issued by the same expert at different occasions. The effect of framing on perceived agreement was significant for medium (10 and 20 percentage points) differences between probabilities, whereas the effect of directional term was stable for numerical differences up to 40 percentage points. To emphasize agreement between different estimates, they should be framed in the same way. To accentuate disagreements or changes of opinion, opposite framings should be used.     

Diagnostic causal reasoning with verbal information

In diagnostic causal reasoning, the goal is to infer the probability of causes from one or multiple observed effects. Typically, studies investigating such tasks provide subjects with precise quantitative information regarding the strength of the relations between causes and effects or sample data from which the relevant quantities can be learned. By contrast, we sought to examine people’s inferences when causal information is communicated through qualitative, rather vague verbal expressions (e.g., “X occasionally causes A”). We conducted three experiments using a sequential diagnostic inference task, where multiple pieces of evidence were obtained one after the other. Quantitative predictions of different probabilistic models were derived using the numerical equivalents of the verbal terms, taken from an unrelated study with different subjects. We present a novel Bayesian model that allows for incorporating the temporal weighting of information in sequential diagnostic reasoning, which can be used to model both primacy and recency effects. On the basis of 19,848 judgments from 292 subjects, we found a remarkably close correspondence between the diagnostic inferences made by subjects who received only verbal information and those of a matched control group to whom information was presented numerically. Whether information was conveyed through verbal terms or numerical estimates, diagnostic judgments closely resembled the posterior probabilities entailed by the causes’ prior probabilities and the effects’ likelihoods. We observed interindividual differences regarding the temporal weighting of evidence in sequential diagnostic reasoning. Our work provides pathways for investigating judgment and decision making with verbal information within a computational modeling framework.     

Verbal probabilities: a question of frame?

Verbal expressions of probability and uncertainty are of two kinds: positive (‘probable’, ‘possible’) and negative (‘not certain’, ‘doubtful’). Choice of term has implications for predictions and decisions. The present studies show that positive phrases are rated to be more optimistic (when the target outcome is positive), and more correct, when the target outcome actually occurs, even in cases where positive and negative phrases are perceived to convey the same probabilities (Experiments 1 and 2). Selection of phrase can be determined by linguistic frame. Positive quantifiers (‘some’, ‘several’) support positive probability phrases, whereas negative quantifiers (‘not all’) suggest negative phrases (Experiment 3). Positive frames induced by numeric frequencies (e.g. the number of students to be admitted) imply positive probability phrases, whereas negative frames (e.g. the number of students to be rejected) call for negative probability phrases (Experiment 4). It is concluded that choice of verbal phrase is based not only on level of probability, but also on situational and linguistic cues. Copyright © 2002 John Wiley & Sons, Ltd.     

Non-verbal and verbal judgements of length invariance by young children.

One hundred and fifty non-conservers in length were assessed for their ability to make a non-verbal judgement of length invariance on a task employing a train-transfer design in which the stimuli were pairs of pencils. Seventy per cent of the children from the group who had to respond to length equality as opposed to inequality made the correct invariance judgement and could, moreover, characterize their choices in invariance language (e.g. 'same size') whilst still failing the standard verbal task in which such phrases were used by the experimenter. This is regarded as supporting the hypothesis that the non-conserver's linguistic difficulty is not with framing the verbal judgement but in interpreting a question which he believes has to be interpreted unidimensionally in such a context of perceptual change.     

Verbalization of Decision Strategies in Multiple‐Cue Probabilistic Inference

In multiple‐cue probabilistic inference, people choose between alternatives based on several cues, each of which is differentially associated with an alternative's overall value. Various strategies have been proposed for probabilistic inference (e.g., weighted additive, tally, and take‐the‐best). These strategies differ in how many cue values they require to enact and in how they weight each cue. Do decision makers actually use any of these strategies? Ways to investigate this question include analyzing people's choices and the cues that they reveal. However, different strategies often predict the same decisions, and search behavior says nothing about whether or how people use the information that they acquire. In this research, we attempt to elucidate which strategies participants use in a multiple‐cue probabilistic inference task by examining verbal protocols, a high‐density source of process data. The promise of verbal data is in their utility for testing detailed information processing models. To that end, we apply protocol analysis in conjunction with computational simulations. We find converging evidence across outcome measures, search measures, and verbal reports that most participants use simplifying heuristics, namely take‐the‐best. Copyright © 2015 John Wiley & Sons, Ltd.     

Outcome trees and baseball: A study of expertise and list-length effects

When people estimate the probability of an event using a list that includes all or most of the possible events, their estimate of that probability is lower than if the other possible events are not explicitly identified on the list (i.e., are collapsed into an all-other-possibilities category). This list-length (or pruning) effect has been demonstrated to occur even for people who have expertise or considerable knowledge in the event domain. We reasoned that the experts used in previous studies would be unlikely to have probabilistic representations of their problem domains (e.g., auto mechanics, auditors, hospitality managers). We used baseball experts (n= 35) and novices (n = 56) on the assumption that expertise in baseball almost certainly involves mental representations of probability for various baseball events. Subjects estimated the frequency of hits, walks, strikeouts, putouts, and “all other” outcomes for an average major league player in 100 times at bat. Other subjects estimated these event outcome frequencies in a short-list condition (e.g., strikeouts, walks, and “all other”). Strong list-length effects were observed with novices; the frequency estimate for strikeouts, for example, was nearly twice as high in the short-list condition as in the long-list condition. Experts, however, showed no list-length effect and their estimated probabilities were very near the actual (normatively correct) probabilities in all conditions. We argue that the omission effect can be overridden by strong mental representations of the family of possible events and/or a clear knowledge of the probabilities associated with the events. As well, we argue that list-length effects seem to result at least in part from an anchoring-and-adjustment strategy.     

Predicting binary choices from probability phrase meanings

The issues of how individuals decide which of two events is more likely and of how they understand probability phrases both involve judging relative likelihoods. In this study, we investigated whether derived scales representing probability phrase meanings could be used within a choice model to predict independently observed binary choices. If they can, this simultaneously provides support for our model and suggests that the phrase meanings are measured meaningfully. The model assumes that, when deciding which of two events is more likely, judges take a single sample from memory regarding each event and respond accordingly. The model predicts choice probabilities by using the scaled meanings of individually selected probability phrases as proxies for confidence distributions associated with sampling from memory. Predictions are sustained for 34 of 41 participants but, nevertheless, are biased slightly low. Sequential sampling models improve the fit. The results have both theoretical and applied implications.     

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。     

Successful detection of verbal and visual concealed knowledge using an RT‐based paradigm

An increasing number of researchers are exploring variations of the Concealed Knowledge Test (CKT) as alternatives to traditional ‘lie‐detector’ tests. For example, the response times (RT)‐based CKT has been previously shown to accurately detect participants who possess privileged knowledge. Although several studies have reported successful RT‐based tests, they have focused on verbal stimuli despite the prevalence of photographic evidence in forensic investigations. Related studies comparing pictures and phrases have yielded inconsistent results. The present work compared an RT‐CKT using verbal phrases as stimuli to one using pictures of faces. This led to equally accurate and efficient tests using either stimulus type. Results also suggest that previous inconsistent findings may be attributable to study procedures that led to better memory for verbal than visual items. When memory for verbal phrases and pictures were equated, we found nearly identical detection accuracies. Copyright © 2007 John Wiley & Sons, Ltd.     

Probabilistic argumentation

Argumentation in the sense of a process of logical reasoning is a very intuitive and general methodology of establishing conclusions from defeasible premises. The core of any argumentative process is the systematical elaboration, exhibition, and weighting of possible arguments and counter-arguments. This paper presents the formal theory of probabilistic argumentation, which is conceived to deal with uncertain premises for which respective probabilities are known. With respect to possible arguments and counter-arguments of a hypothesis, this leads to probabilistic weights in the first place, and finally to an overall probabilistic judgment of the uncertain proposition in question. The resulting probabilistic measure is called degree of support and possesses the desired properties of non-monotonicity and non-additivity. Reasoning according to the proposed formalism is an simple and natural generalization of the two classical forms of probabilistic and logical reasoning, in which the two traditional questions of the probability and the logical deducibility of a hypothesis are replaced by the more general question of the probability of a hypothesis being logically deducible from the available knowledge base. From this perspective, probabilistic argumentation also contributes to the emerging area of probabilistic logics.     

Time complexity and consistency issues in using the AHP for making group decisions

Two different ways of using the AHP in making group decisions are compared and evaluated. The first method combines different experts’ opinions before applying an eigenvalue method to obtain final weights for decision alternatives. The second, in contrast, derives each expert's rating for the decision alternatives before combining them. Both methods take into account the relative importance of different experts in making decisions. Comparison and evaluation of these two methods are made by using two criteria: time complexity and consistency indices. A numerical example is provided to illustrate the use of these two methods, and results of a mathematical simulation are presented for comparing the time complexity in different-sized problems. © 1998 John Wiley & Sons, Ltd.     

Another look at gender-related differences in leadership behavior

This investigation examined self-related behavioral differences in terms of broad leadership styles using a methodology that minimized biases inherent in research designs previously employed to investigate this area. Subjects consisted of 40 males and 41 females who served in the role of leader, and who instructed both a male and a female subordinate in a card-sorting task. Experimental sessions were tape-recorded and transcribed, after which judges classified word phrases into various language categories. Factor analysis of the language categories yielded two factors of verbal behavior within a leadership situation: a socially oriented style and a task-oriented style. In contrast to generally accepted stereotypes, results indicated that within the present experimental context male leaders preferred to use phrases that indicated a more social style than female leaders. However, both male and female leaders used language that indicated a task-oriented approach to a significantly greater degree when instructing a female rather than a male subordinate. Implications and interpretations of the results are discussed.