Directional verbal probabilities: inconsistencies between preferential judgments and numerical meanings

Verbal probability expressions (e.g., it is possible or doubtful) convey not only vague numerical meanings (i.e., probability) but also semantic functions, called directionality. We performed two experiments to examine whether preferential judgments are consistent with numerical meanings of verbal probabilities regardless of directionality. The results showed that because of the effects of directionality, perceived degrees of certainty for verbal probabilities differed between a binary choice and a numerical translation (Experiment 1), and decisions based on a verbal probability do not correspond to those based on a numerical translation for verbal probabilities (Experiment 2). These findings suggest that directionality of verbal probabilities is an independent feature from numerical meanings; hence numerical meanings of verbal probability alone remain insufficient to explain the effects of directionality on preferential judgments.     

Motivated reasoning and verbal vs. numerical probability assessment: Evidence from an accounting context

A perplexing yet persistent empirical finding is that individuals assess probabilities in words and in numbers nearly equivalently, and theorists have called for future research to search for factors that cause differences. This study uses an accounting context in which individuals are commonly motivated to reach preferred (rather than accurate) conclusions. Within this context, I predict new differences between verbal and numerical probability assessments, as follows: first, individuals will justify an optimistic verbal assessment (e.g., somewhat possible) by retaining the option of re-defining it, in case of negative outcomes, as though the phrase really means something different, and, for that matter, means more things. This re-definition will maintain some connection to the original meaning of the phrase, but de-emphasized relative to the new meaning. Second, based on this behavior, I also predict individuals’ verbal probability assessments to be (1) more biased and yet (2) perceived as more justifiable than their numerical assessments. I find supportive evidence in an experiment designed to test the hypotheses. This study contributes to motivated reasoning and probability assessment theories (1) with new evidence of how individuals can word-smith in multiple attributes of a phrase to justify reaching a preferred conclusion, and (2) with new, reliable differences between verbal and numerical probability assessments. This study has important theoretical and practical implications relevant to organizational contexts in which people assess the likelihoods of uncertainties in words or numbers, and with motivations to reach a preferred conclusion.     

Predicting the directionality of probability words from their membership functions

Teigen and Brun have suggested that distinct from their numerical implications, most probability phrases are either positive or negative, in that they encourage one to think of reasons why the target event will or will not occur. We report two experiments testing our hypotheses that (a) the direction of a phrase can be predicted from properties of its membership function, and (b) this relation is invariant across contexts, and (c) —originally formulated by Teigen and Brun (1999)—that strong modifiers intensify phrase directionality. For each phrase, participants encoded membership functions by judging the degree to which it described the numerical probabilities 0.0, 0.1, …, 1.0, and also completed sentences including the target phrase. The types of reasons given in the sentence completion task were used to determine the phrase's directionality. The results support our hypotheses (a) and (b) regarding the relation between directionality and the membership functions, but we found only limited support for hypothesis (c) regarding the effects of modifiers on directionality. A secondary goal, to validate an efficient method of encoding membership functions, was also achieved. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

Selection of verbal probabilities: A solution for some problems of verbal probability expression

A method for verbal expression of degree of uncertainty is described. It requires the subject to select a phrase from a list that spans the full range of probabilities. In a second, optional, step, the subject indicates the numerical meaning of each phrase. The method avoids two problems of verbal probabilities—the indefinitely large lexicon and the individual differences in the interpretation of words. To test whether context and ordinal position might bias subjects' selection or interpretation of the verbal expressions in the list, the list order was varied. When the verbal expressions were arranged in random order, ordinal position had a significant effect on the selection of expressions. However, these effects did not occur when the phrases were listed in ascending or descending order. Considerations of accuracy and interpersonal agreement also support the use of ordered phrase lists.     

Reversal of the preference reversal phenomenon

The widely replicated preference reversal phenomenon (PRP) violates most theories of decision under risk. People exhibiting PRP choose a safe bet (with a large chance of a small gain) over a long shot (with a small chance of a larger gain). But, when bidding to buy or sell each bet, they bid more for the long shot. Surprisingly, in Experiment 1, a new opposite reversal pattern (NPRP) was found: Safe bets typically received larger bids than long shots and reversals were far more frequent when the long shot was chosen. In Experiment 2, NPRP was found for $100 expected value bets, but PRP occurred for bets with $3 expected values. The task characteristics apparently necessary to produce NPRP are (1) bids in the form of maximum buying prices, (2) possibility of loss in bidding, but not in choice, and (3) large payoffs. It is argued that wealth effects predicted by expected utility theory are too small to explain NPRP. Instead, it is hypothesized that a contingent decision process underlies the shift in reveral patterns and that aspiration levels exert increased influence in bidding to buy when payoffs are large.     

Are Arabic and verbal numbers processed in different ways?

Four experiments were conducted in order to examine effects of notation--Arabic and verbal numbers--on relevant and irrelevant numerical processing. In Experiment 1, notation interacted with the numerical distance effect, and irrelevant physical size affected numerical processing (i.e., size congruity effect) for both notations but to a lesser degree for verbal numbers. In contrast, size congruity had no effect when verbal numbers were the irrelevant dimension. In Experiments 2 and 3, different parameters that could possibly affect the results, such as discriminability and variability (Experiment 2) and the block design (Experiment 3), were controlled. The results replicated the effects obtained in Experiment 1. In Experiment 4, in which physical size was made more difficult to process, size congruity for irrelevant verbal numbers was observed. The present results imply that notation affects numerical processing and that Arabic and verbal numbers are represented separately, and thus it is suggested that current models of numerical processing should have separate comparison mechanisms for verbal and Arabic numbers.     

Verbal probabilities: An alternative approach

Previous studies of verbal probabilities have tried to place expressions like a chance, possible, and certain on 0–1 numerical probability scales. We ask instead, out of a range of outcomes, which outcome a verbal probability suggests. When, for instance, a sample of laptop batteries lasts from 1.5 to 3.5 hours, what is a certain and what is a possible duration? Experiment 1 showed that speakers associate certain with low values and possible with (unlikely) high or maximal values. In Experiment 2, this methodology was applied to several positive and negative verbal probability phrases, showing a preference for high rather than low or middle values in a distribution. Experiment 3 showed that such maxima are not universally described by large numbers. For instance, maximum speed is often described in terms of a small number of time units. What can (possibly) happen is accordingly sometimes described with very low and sometimes with very high values, depending upon focus of interest. Finally, participants in Experiment 4 were given the role of hearers rather than speakers and were asked to infer outcome ranges from verbal probabilities. Hearers appeared to be partly aware of speakers' tendencies to describe outcomes at the top of the range.     

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.     

Multi-attribute sequential search

This article describes empirical and theoretical results from two multi-attribute sequential search tasks. In both tasks, the DM sequentially encounters options described by two attributes and must pay to learn the values of the attributes. In the continuous version of the task the DM learns the precise numerical value of an attribute when she pays to view it. In the threshold version the DM learns only whether the value of an attribute is above or below a threshold that she sets herself. Results from the continuous condition reveal that DMs tended to terminate their searches too early relative to the optimal policy. The pattern reversed in the threshold condition: DMs searched for too long. Maximum likelihood comparisons of two different stochastic decision models showed that DMs under both information conditions performed in ways consistent with the optimal policies. Those offered continuous-valued attribute information did not, however, spontaneously degrade this information into binary (acceptable/unacceptable) form, despite the theoretical finding that satisficing can be a very effective and efficient search strategy.     

The effect of order of presentation of verbal probability expressions on numerical estimates in a medical context

Many medical decisions are made on a probability estimate. Models of risk benefit calculations in health behaviour rarely articulate how people perceive and appraise such probability. Cognitive processes may mediate the processing of probability expressions and may be important to understand the meaning or the range of meanings that probability statements portray to patients. Past studies have indicated that verbal expressions of probability are vague and subject to individual interpretation. On the theoretical level when subjects are asked to translate a set of verbal probability expressions, ranging from high to low, into their equivalent numerical expressions subjects usually produce a continuum of numerical equivalents also ranging from high to low. In practice clinicians frequently communicate information about uncertainty to the patients by verbal probability estimates. This study explored the effect of the order of presentation of the verbal expressions on the numerical probabilities produced by a group of medical students (n?=?87) in relation to medical probabilities. The results showed that the order of presentation (descending vs. random) of the verbal probability expressions was found to have a significant effect on three of the seven numerical probabilities produced by the subjects. The order effect is discussed to together with implications for clinical practice.     

Fuzzy MCDM based on the concept of α‐cut

In a fuzzy multiple criteria decision‐making (MCDM) problem, with a hierarchical structure of more than two levels and involving multiple decision‐makers (DMs), to find the exact membership functions of the final aggregation ratings of all feasible alternatives is almost impossible. Thus, ranking methods based on exact membership functions cannot be utilized to rank the feasible alternatives and complete the optimal selection. To resolve the above‐mentioned complexity and to incorporate assessments of all DMs' viewpoints, in this paper a fuzzy MCDM method with multiple DMs, based on the concepts of fuzzy set theory and α‐cut, is developed. This method incorporates a number of perspectives on how to approach the fuzzy MCDM problem with multiple DMs, as follows: (1) combining quantitative and qualitative criteria as well as negative and positive ones; (2) using the generalized means to develop the aggregation method of multiple DMs' opinions; (3) incorporating the risk attitude index β to convey the total risk attitude of all DMs by using the estimation data obtained at the data input stage; (4) employing the algebraic operations of fuzzy numbers based on the concept of α‐cut to calculate the final aggregation ratings and develop a matching ranking method for proposed fuzzy MCDM method with multiple DMs. Furthermore, we use this method to survey the site selection for free port zone (FPZ) in Taiwan as an empirical study to demonstrate the proposed fuzzy MCDM algorithm. The result of this empirical investigation shows that the port of Kaohsiung, the largest international port of Taiwan as well as the sixth container port in the world in 2004, is optimal for the Taiwan government in enacting the plan of FPZ. Copyright © 2005 John Wiley & Sons, Ltd.     

The Effect of Catastrophe Potential on the Interpretation of Numerical Probabilities of the Occurrence of Hazards1

Two studies demonstrated that identical numerical probabilities of the occurrence of hazards are judged as higher when these involve potential catastrophes compared to noncatastrophic hazards. Fifteen hazards were presented that involve a potential catastrophe and 15 noncatastrophic hazards. Each hazard was given a numerical probability, which was either 1:10, 1:1,000, or 1:100,000. Numerical probabilities were rated as larger when these concerned hazards that have catastrophe potential compared to the noncatastrophic hazards, also when this effect was controlled for perceived benefits. Similar results were obtained in a second study, which controlled for possible confounds (e.g., base rate). The results suggest that verbal interpretations of numerical probabilities of the occurrence of hazards include more than only probability, for instance one's attitude toward the hazardous activity. Implications for risk communication are discussed.     

Signing enhances memory like performing actions

In three experiments, we investigated the influence of the overt performance of signs on memory. Deaf and hearing participants studied lists of action phrases (Experiment 1) or nouns (Experiment 2) under standard verbal instruction, under the instructions to sign the verbal phrase, to symbolically perform the denoted action, or to carry out a prototypical action corresponding to each noun. Higher recall and recognition performances were observed when actions were performed than in the verbal encoding condition, and signing was as effective for memory as was enactment. Thus, overt signing can induce an enactment effect. In contrast, Experiment 3 demonstrated that performing an unrelated action did not. A unique but unrelated action was not memory efficient.     

Written object naming,spelling to dictation,and immediate copying: Different tasks,different pathways?

Politeness theory posits that speakers can use verbal probabilities (e.g., there is a chance, it is likely) to hedge bad news. So far, only indirect evidence supports that claim: From the hearer's standpoint, verbal probabilities are interpreted either as plain likelihood-communication devices or as face-management devices, resulting in different risk perceptions. The present research aims to test more directly the postulate of politeness theory by focusing on the effects of speakers' intentions on risk communication. In three experiments, participants communicated a probability by choosing an expression from a list of verbal probabilities. Results consistently showed that polite speakers communicated a different risk magnitude than informative speakers. Further findings indicate that the effect of the speakers' intention depends on the valence of the uncertain outcome. The theoretical and applied implications of these findings are discussed.     

Effects of event structure on retrospective duration judgments

Two experiments examined whether varying degrees of event coherence influence the remembering of an event’s actual duration. Relying on musical compositions (Experiment 1) or filmed narratives (Experiment 2) as experimental stimuli, the underlying hierarchy of information within events (i.e., melodic intervals or story elements) was either attentionally highlighted or obscured by placing a varying number of accents (i.e., prolonged notes or commercial breaks) at locations that either coincided or conflicted with grammatical phrase boundaries. When subjects were unexpectedly asked to judge the actual duration of events, through a reproduction (Experiment 1) or verbal estimation (Experiment 2) task, duration estimates became more accurate and less variable when the pattern of accentuation increasingly outlined the events’ nested relationships. Conversely, when the events’ organization was increasingly obscured through accentuation, time judgments not only became less accurate and more variable, but were consistently overestimated. These findings support a theoretical framework emphasizing the effects of event structure on attending and remembering activities.     

The Binary Additivity of Subjective Probability Does not Indicate the Binary Complementarity of Perceived Certainty

People's numeric probability estimates for 2 mutually exclusive and exhaustive events commonly sum to 1.0, which seems to indicate the full complementarity of subjective certainty in the 2 events (i.e., increases in certainty for one event are accompanied by decreases in certainty for the other). In this article, however, a distinction is made between the additivity of probability estimates and the complementarity of internal perceptions of certainty. In Experiment 1, responses on a verbal measure of certainty provide evidence of binary noncomplementarity in the perceived likelihoods of possible scenario outcomes, and a comparison of verbal and numeric certainty estimates suggests that numeric probabilities overestimated the complementarity of people's certainty. Experiment 2 used a choice task to detect binary noncomplementarity. Soliciting numeric probability estimates prior to the choice task changed the participants' choices in a direction consistent with complementarity. Possible mechanisms yielding (non)complementarity are discussed.     

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.