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

Is guilt ‘likely’ or ‘not certain’? 1 Running head: IS GUILT “LIKELY” OR “NOT CERTAIN”? Is guilt ‘likely’ or ‘not certain’? Contrast with previous probabilities determines choice of verbal terms Marie Juanchich University of Toulouse Karl Halvor Teigen University of Oslo Gaëlle Villejoubert Kingston University London Correspondence should be addressed to: Marie Juanchich Université de Toulouse, CLLE-LTC (CNRS, UTM, EPHE), Maison de la recherche 5 allées A. Machado 31058 Toulouse Cedex 9 France Phone: +33 5 61 50 39 87 E-mail: marie.juanchich@univ-tlse2.fr Is guilt ‘likely’ or ‘not certain’? 2 Abstract 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 comparisons to lead to positive phrases, whereas downward comparisons 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. Keywords: Uncertainty; verbal probabilities; directionality; legal context; judgments of guilt; upward and downward comparisons; communication. PsyclNFO classification: 27.20: Linguistics & Language & Speech; 30.20: Group and Interpersonal Processes; 30.40: Social Perception & Cognition Is guilt ‘likely’ or ‘not certain’? 3 1. Introduction We live in a probabilistic world, where our expectations about tomorrow and beliefs about yesterday are held with various degrees of certainty. The topic of the present research is to explore how this certainty, or lack of it, is expressed and communicated to others. In formal contexts, degrees of certainty can be expressed as numeric probabilities on a scale from 0 to 1.0 or 0% to 100%. In daily life, people spontaneously use a wide variety of verbal phrases to describe chances and uncertainties (Budescu, Weinberg, & Wallsten, 1988). In fact, they prefer using verbal probability expressions, such as “it is possible” or “it is doubtful” (Erev & Cohen, 1990; Wallsten, Budescu, Zwick, & Kemp, 1993). These expressions convey imprecise degrees of likelihood. Thus, “a very good chance” describes a higher probability than simply “a chance”. Attempts to “translate” verbal probabilities into numeric equivalents have invariably concluded that verbal probability phrases convey “vague” likelihood levels (for reviews see Diez & Druzdzel, in press; Teigen & Brun, 2003a; Theil, 2002). As an elaboration of this view, Budescu and Wallsten (1995) suggested a fuzzy set model, where verbal phrases can be mapped with a membership function on the 0-1 probability scale. Such membership functions can differ from person to person, and should ideally be studied within a given individual’s preferred lexicon of phrases (Karelitz & Budescu, 2004). Verbal terms, however, do more than describing a particular level of probability. They also guide the listeners’ attention in one of two directions, either towards the possible occurrence or truth of the target outcome (“there is a chance that X is guilty”), or towards its potential non-occurrence or falsehood (“it is not certain that X is guilty”). This property is called directionality (Teigen & Brun, 1995). To determine phrases’ directionality, Teigen and Brun (1995) adapted a sentence completion technique first used by Moxey and Sanford (1987) with quantifiers. This technique consists of asking participants to provide plausible Is guilt ‘likely’ or ‘not certain’? 4 reasons for why an event was possible, probable, uncertain, doubtful, and so on. Sentences like “there is a chance that the market will remain stable, because…” were completed with reasons in favor of the market stability (pro reasons). In contrast, negative phrases such as “it is uncertain that the market will remain stable, because…” were consistently completed with reasons against market stability (con reasons). Very few phrases (e.g., “fifty-fifty”) seemed to invite respondents to consider both pro and con reasons at the same time. Thus, despite communicating vague numerical meanings, most verbal probability phrases are either unambiguously positive or unambiguously negative, regardless of probability magnitude. Directionality has many important pragmatic functions in conversation. They direct the listeners’ attention towards one among two possible outcomes, making arguments for or against the target event’s truth or occurrence more or less salient. They also are taken to reveal the speaker’s degree of optimism or pessimism (Teigen & Brun, 2003b), and might influence the listener’s subsequent decisions. For example, Teigen and Brun (1999) showed that nearly 70% of individuals decided against recommending a medical treatment after being told it was “quite uncertain” that it would be helpful. By contrast, nearly all of those told that there was “some possibility” that the treatment could be helpful, decided to recommend it. The directionality of verbal probability is therefore taken to act like a pragmatic signal indicating the speaker’s view on which action to undertake and aiming to coordinate speakers and listeners, not just for sharing of information, but also to establish a common platform for subsequent planning and action (Hilton, 2008). Little is known, however, about what makes speakers select a positive or a negative probability phrase in the first place. The present studies were designed to investigate, from a conversational perspective, when positive or negative phrases are chosen. 1. 1. Determinants of Directionality Is guilt ‘likely’ or ‘not certain’? 5 The main concern of the present paper is how verbal probabilities are selected, rather than how they are understood. Past research on the meaning of verbal probabilities suggests that one determinant of phrases choice will be the magnitude of the probability in the speaker’s mind. For example, a probability of .80 should be described as “a good chance” rather than as “a slight hope”. One could argue that this probability magnitude could also predict the directionality of the phrase chosen. As a matter of fact, high probabilities are generally described by positive terms (Teigen & Brun, 1995). Moreover, previous studies have found that negative phrases are more often used to describe events with a probability below .50 whereas positive phrases refer more often to probabilities above .50 (Teigen, 1988a, 1988b; Teigen & Brun, 1995). In fact, Budescu, Karelitz, and Wallsten (2003) suggested that the directionality of verbal phrases could be predicted by their membership functions on a 0-1 probability scale. Their results showed that positive phrases typically convey numerical meanings above .50 whereas negative phrases typically convey numerical meanings below the .50 mark. Budescu et al., however, did not include critical test phrases such as positive phrases communicating small probabilities (e.g., “a slight possibility”) or negative phrases communicating high probabilities (e.g., “not completely certain”) in the sample of phrases they tested, as pointed out by Honda and Yamagishi (2006). Their results therefore do not preclude the possibility that people will occasionally prefer negative phrases to communicate high probabilities or, conversely, positive phrases to convey low probabilities. Moreover, the apparent correlation between probability magnitude and directionality of verbal probabilities is at odds with the finding that a given uncertain event (e.g., a medical treatment which may or may not be helpful) can be described by a positive or a negative word as illustrated above (Teigen & Brun, 1999). In a recent study, Piercey (2009) made use of this observation in constructing a list from lower to higher probabilities with both kinds of phrases alternating throughout the list. Is guilt ‘likely’ or ‘not certain’? 6 Another argument against the view that choice of directionality is determined by the magnitude of the probability communicated comes from the observation that positive and negative probability expressions are not equally frequent. Most lists of verbal probabilities contain more positive than negative phrases. This may be a natural consequence of a stronger focus on what will happen rather than on what will not happen, independently of events’ probability of occurrence. Negative probability phrases seem to have a similar function as linguistic negations, which according to linguists presuppose the existence of a belief or an assertion that is being denied (Gilbert, 1991; Horn, 1989). Similar asymmetries can be found with other frames as well, for instance glasses filled with liquid will be more often described as “half full” rather than as “half empty” (McKenzie & Nelson, 2003), and a quantity of 1.5 million is more often described as “more than one million” than “less than two millions” (Halberg & Teigen, 2009). We may think of this predominance of positive descriptions as manifestation of a general positivity bias (in an informational rather than an evaluative sense) where affirmations are more widespread than negations (McGuire & McGuire, 1992; Peeters, 1971). This suggests that individuals would prefer using a positive verbal phrase by default, whatever the magnitude of the probability they wish to communicate. Negative phrases, by contrast, would be chosen when the speaker wishes to express a contrast between a target probability magnitude and its expected or previous value. Thus, we consider the choice between positive and negative phrases to communicate a given probability magnitude as a choice between different perspectives, or different frames. In their studies of natural language quantifiers, Moxey and colleagues (Moxey, 2006; Moxey & Sanford, 1987; Moxey, Sanford, & Dawydiak, 2001) have argued that the same quantity can be described using positive or negative polarity quantifiers, directing the reader’s attention either to the set of reference or to its complement. Thus, saying “a few people came to the party” focuses attention on those who came, whereas saying “few people came to the party” Is guilt ‘likely’ or ‘not certain’? 7 calls attention to the complementary set, namely those who were absent. The authors argued that directionality choice depends on the relation between the amount expected and the amount actually observed (Moxey & Sanford, 1993). Accordingly, the speaker who opts to say “a few people came to the party” presumably expected a lower turnout. Thus, positive quantifiers allow comparisons with lower amounts. The literature on frames and framing effects in decisions and choices offers a discussion of similar phenomena, in cases where identical quantities can be described alternatively in terms of numerical probabilities of success vs. failures (Mandel, 2008), survival vs. mortality rates (McNeil, Pauker, Sox, & Tversky, 1982), work done or work left to do (Teigen & Karevold, 2005), and glasses half full or half empty (McKenzie & Nelson, 2003). The relation between frames and choice of verbal probabilities was demonstrated by Teigen and Brun (2003b, Experiment 4). When a quantity was described in a positive frame (e.g., the number of students admitted to an educational program), participants preferred using positive probability phrases to describe the chances of a candidate being admitted on the same program. Conversely, complementary negative frames (e.g., the number of students not admitted on the program) led to choices of negative phrases to describe the candidate’s probability of admission. McKenzie and Nelson (2003) proposed an account of choice of frame as a function of reference point. Participants in their experiments described a glass as “half full” when it had been previously empty, and as “half empty” when it had been previously full. Accordingly, we expect people to choose positive verbal probabilities whenever they are comparing the probability of a target event with a smaller probability, and, conversely, choose negative phrases when they have a higher probability as their reference point. We propose, in other words, that directionality of verbal phrase is chosen not to express the absolute, but rather the Is guilt ‘likely’ or ‘not certain’? 8 relative magnitude of the probabilities involved. Positive and negative phrases accordingly emerge as the result of a comparison process. 1. 2. Experiments We propose that positive verbal probabilities will be chosen whenever the speaker wants to stress that chances are greater than zero, and more generally to compare and contrast a target probability with a lower one as reference point. Negative verbal probabilities, by contrast, should be chosen by a speaker who wants to indicate that the target event is less than certain, or more generally when its probability is compared and contrasted with a higher one. Comparisons may occur in a variety of contexts. A target probability may be contrasted with a previous probability estimate for the same event, akin to McKenzie and Nelson’s (2003) Glass Speaker Study where the current content state of a glass was contrasted with its previous state. Alternatively, a speaker’s probability estimate may be contrasted with another speaker’s estimate for the same event. Finally, contrast effects may also occur when comparisons are made between options. For example, Windschitl and Wells (1998) showed that perceptions of a target event’s probability can be affected by a comparison between the target probability and the probability of the most likely alternative outcome. In all these contexts of comparison, the target probability may follow from an upward trend (when the reference probability is lower) or from a downward trend (when the reference probability is higher). In the following three experiments, we asked people to choose expressions to describe probabilities of a given magnitude. The task was set in a legal context, where a speaker taking the role of a profiler had to find an appropriate way of characterizing the probability of a suspect’s potential guilt. In the first experiment, the suspect’s probability of being guilty had either increased or decreased compared to an earlier assessment, following the emergence of new evidence. We Is guilt ‘likely’ or ‘not certain’? 9 hypothesized that the same final probability of guilt would be more often described with positive verbal terms when it resulted from an upward trend as opposed to a downward trend. More specifically, we assumed that the original level of probability would be used as the reference point, creating opposite (complementary) frames, as in McKenzie and Nelson’s (2003) Glass Speaker Study. The second experiment introduced two speakers. The second speaker’s opinion about the suspect’s guilt probability deviated from that of the first speaker. Here again, we assumed that the probability expressed by the first speaker would be taken as a reference point, suggesting that the second speaker would prefer choosing a positive term, if he believed more strongly that the suspect was guilty, and a negative term, if he was less convinced about the suspect’s guilt than his colleague. In the third experiment, the probabilities applied to two different suspects, where one was more suspicious than the other. The issue was whether the directionality of the verbal phrase chosen to characterize the target suspect’s guilt probability would be affected by the higher or lower guilt probability of the alternative suspect. This would in turn demonstrate that the alternative outcome effect not only affects the verbal probability chosen (Windschitl & Wells, 1998) but also its directionality. The verbal probability expressions used in these experiments were selected on the basis of results from a study of probability terms by Juanchich, Villejoubert and Mullet (2008). In this study, 42 participants were asked to provide numeric “translations” (in percentages) of 15 French probability phrases. Another group of 51 participants evaluated the directionality of the same phrases, by being directly asked whether the phrase directed their attention towards the potential occurrence or the non-occurrence of the target outcome. These data allowed us to select pairs of positive and negative phrases, which could be used to describe the same numeric probabilities. Is guilt ‘likely’ or ‘not certain’? 10 2. Experiment 1 Much research has been devoted to the study of how people update their probabilities as a function of incoming evidence. A long-standing issue in this debate is whether or not people’s reasoning adheres to Bayesian principles (e.g., Fischhoff & Beyth-Marom, 1983; Gigerenzer & Hoffrage, 1995; Phillips & Edwards, 1966; Villejoubert & Mandel, 2002). What has received much less attention is how people choose to report their revised beliefs. Rapoport, Wallsten, Erev, and Cohen (1990) compared revision of opinion with verbally and numerically expressed uncertainties, but did not examine the effect of the direction of the revision on choices of positive and negative verbal phrases. Thus we lack evidence showing whether choices of phrase directionality are affected by belief updating. In this and the following studies, participants were told to take the role of a profiler asked to describe a suspect’s numeric probability of guilt in verbal terms. The numeric probability was said to have been obtained by feeding case information and the suspect’s details into a computer program, which then calculated a probability of guilt on the basis of the information provided. Note that, although actual profilers seldom have to express the probability of a suspect’s guilt, they often have to choose verbal probabilities to communicate uncertainty about suspects’ characteristics in their reports (Collins & Alison, 2002; Villejoubert, Almond, & Alison, 2008). Consequently, an important issue consists in identifying which verbal phrase will be selected when communicating uncertainty with an audience. In line with the contrast and comparison account of verbal probabilities’ directionality choice outlined above, we predicted that the same probability magnitude will be preferably communicated with positive expressions when it results from an upward revision (upward trend), whereas it will be preferably described using a negative expression when it results from a downward revision (downward trend). Is guilt ‘likely’ or ‘not certain’? 11 2. 1. Method 2. 1. 1. Participants and Design. Participants were 123 Human Science students from the University of Toulouse (95 women; 28 men, mean age 24.45 years, SD = 9.93). Participation was voluntary and unpaid. Participants were randomly allocated to one of four experimental conditions. Half the participants were told the final probability of guilt was 40% (Low p-magnitude) and the remaining half were told it was 60% (High p-magnitude). Half the participants in the Low p-magnitude group were informed it was originally estimated to be 10% (upward trend) whereas the remaining half were told the original estimate was 70% (downward trend). Similarly, half the participants in the High p-magnitude group were told it was originally 30% (upward trend) and the remaining half were told it used to be 90% (downward trend). The experiment thus relied on a 2 × 2 between-subject design, with Focal Probability Magnitude (Low vs. High p-magnitude) and Trend (Upward vs. Downward trend) as two orthogonal factors (See Table 1 for an overview of the design). <Insert Table 1 about here> 2. 1. 2. Material and Procedure. All participants received a 2-page questionnaire. The study was presented as aiming to understand how people communicate uncertainty. Participants were informed answers were anonymous and confidential, and that minimum age for participation was 18 years. They were instructed to read and answer the questions in order. They were then introduced to the following scenario (translated from French): Imagine that you are a profiler. Your work consists in evaluating to what extent a suspect could be guilty of a given offense. You use a very reliable computer program, which analyses all the evidence you have and which gives you the result in the form of numerical probability of guilt. A serious hold-up has been committed; the police have Is guilt ‘likely’ or ‘not certain’? 12 a suspect, but no definitive proof of his guilt or his innocence. After a week of investigation, they ask for your help and provide you with all the pieces of evidence they have collected. After working on this case, you conclude that, based on the available evidence, there is a [p1] probability of guilt. You present the result of your analysis to the police. Which of the following expressions will you prefer to use? [Verbal probability selection task 1] A week later, the police find new pieces of evidence. These new pieces of information lead to an increase/decrease of the probability to be guilty from p1 to p2. The suspect has now a [p2] probability of being guilty. Which of the following expressions will you prefer to use? [Verbal probability selection task 2] Both verbal probability selection tasks required participants to imagine that the probabilities should be communicated in an internal meeting of police officers. In both tasks, participants were asked to choose between a positive and a negative probability phrase. Each pair of phrases were culled from a pre-tested list of verbal probability expressions (Juanchich et al., 2008) as typically communicating a given probability magnitude. Table 2 provides an overview of the pairs of phrases used to describe each level of probability (the first three pairs were given to participants in the low p condition, to characterize an upward or a downward trend, respectively, whereas the last three pairs were presented to participants in the high p condition). Finally, participants’ subjective degree of belief in the suspect’s guilt was measured. They were asked to rate the extent to which they were convinced the suspect was guilty on a 6-point scale ranging from 0 (not at all convinced) to 5 (absolutely convinced). <Insert Table 2 about here> Is guilt ‘likely’ or ‘not certain’? 13 2. 2. Results and Discussion 2. 2. 1. First Choice of Phrase Directionality. Preferences for positive and negative phrases to describe the initial probabilities (p1) are presented in the left half of Table 3. A large majority (71.5%) of participants chose a positive expression rather than a negative one. Moreover, this preference was not related to the magnitude of the numeric probability; χ2 (3, N = 123) = 2.20, p = .53. Thus, people preferred to use a positive term, whether the initial probability was .10, .30, .70 or .90. These results corroborate the general predominance of positive phrases found in other studies of verbal probabilities (Teigen & Brun, 1995), but stand in opposition to the view that positive phrases are associated with high numeric probability values, whereas negative phrases predominantly describe low values (Budescu et al., 2003). They are more compatible with the view that directionality choice is determined by the speaker’s preferred focus of attention. Participants were asked to communicate the probability that the suspect was guilty so the target event was the suspect’s degree of guilt, not his degree of innocence. Recall that within each pair, both verbal phrases presumably conveyed the same probability magnitude at the group level, so choosing a negative phrase was, in principle, as felicitous as choosing a positive one. Speakers’ marked preference for using positive expressions therefore suggests that their default preference will be to focus listeners’ attention on the target event rather than on its complement. <Insert Table 3 about here> 2. 2. 2. Second Choice of Phrase Directionality. Choices of positive and negative probability terms to describe the revised probability (p2) are displayed in Table 4. Contrary to results for the first choice of phrases, the magnitude of the numeric probability communicated had a significant impact on preferences for positive vs. negative directionalities; χ2(1, N = Is guilt ‘likely’ or ‘not certain’? 14 123) = 16.75, p < .001, c = .35, cmax = .87. Overall, positive phrases were largely preferred when the probability to be communicated was .40 (72.3% participants chose a positive phrase) compared to when the probability to be communicated was .60 (45.1%). In other words, people preferred a positive expression when the probability was below .50, but not when the probability was above .50. This pattern of choices goes against the view that negative phrases are mainly used to characterize low probabilities, and shows that a negative phrase (in this case “it is not certain”) can, at least under some circumstances, be preferred to a positive phrase (“it is probable”) for describing a p value above .50. We predicted that phrases selected to describe the revised probabilities would be influenced by the trend they formed, rather than by their absolute magnitude. When p2 was higher than p1 (upward trend), we expected a higher proportion of positive phrases chosen. By contrast, when p2 was lower than p1 (downward trend), we expected higher proportions of negative phrases selection. The pattern of choices observed confirmed these predictions, as Table 4 shows. Though the majority of participants preferred to use a positive phrase to convey p2 when it was set at .40, the proportion of negative phrases choices to describe this probability was significantly higher when it resulted from a decrease in probability (.70 → .40 trend) compared to when it resulted from an increase in probability (.10→ .40 trend); χ2(1, N = 62) = 4.31, p < .05, c = .25. Results were even clearer when p2 was set at .60 as illustrated by the bottom rows of Table 4. In this instance, opposing trends led to a preference reversal: whereas the majority of participants preferred to describe .60 with a positive phrase when it resulted from an upward trend (.30 → .60 trend), most participants preferred to use a negative phrase to describe this same numerical probability when it resulted from a downward trend (.90→ .60 trend);χ2(1, N = 61) = 7.42, p < .01, c = .33. Finally, choices of verbal phrases to describe the revised probability p2 were independent of the phrase selected to describe the original probability p1; χ2(1, N = 123) = 0.79, ns, c = .08. This suggests that expressions Is guilt ‘likely’ or ‘not certain’? 15 chosen for the second probability were determined by the magnitude of the first one, rather than by individual preferences for positive or negative expressions. Overall, 71.9% of the participants chose a positive phrase to describe an increased probability, whereas 56.5% of the participants chose a negative phrase to described a decreased probability. <Insert Table 4 about here> 2. 2. 3. Belief Ratings. After the second verbal probability selection task, participants were asked to rate the extent to which they were convinced that the suspect was guilty. This measure enabled us to test for the possibility that individuals who chose a negative probability term did so because their subjective degree of belief in the suspect’s guilt was lower compared to those who chose a positive term. In fact, as can be observed from Table 4, participants who chose a positive term to describe the final probability held almost identical degrees of belief in the suspect’s guilt as participants who chose a negative term. MannWhitney tests comparing subjective degrees of belief in guilt as a function of the directionality of the term chosen by participants revealed no statistically difference between ratings in any of the experimental conditions (largest z = -1.11). In summary, downward revisions of probabilities reduced the general predominance of positive term choices when p2 was .40, and completely overruled this preference when p2 was .60. Participants who chose a negative probability term were not less convinced that the suspect was guilty than those who chose a positive term. These results suggest that choices of verbal probability terms do not simply mirror participants’ subjective probabilities, but are more in line with McKenzie and Nelson’s (2003) finding that people choose frames to indicate a change relative to an initial reference point. As such, these results reveal that Is guilt ‘likely’ or ‘not certain’? 16 framing effects not only occur when speakers describe quantities but also when they communicate uncertainty. 3. Experiment 2 In Experiment 1, participants were asked to choose a verbal probability phrase to describe an objective outcome probability that had either increased or decreased. Results showed that trend (upward or downward) had an effect on the verbal probability terms chosen. In Experiment 2, we sought to extend these results to a context where two conversational partners have different subjective outcome probabilities in mind. The issue addressed here is therefore whether the probability term chosen to communicate the probability expressed by the second speaker will be influenced by the first speaker’s subjective probability. We hypothesized that when the numerical probability enunciated by the second speaker is higher than that previously proposed by his or her colleague; participants will chose a positive phrase to characterize the second speaker’s estimate. When, however, the second speaker replies by asserting a lower subjective probability, participants should choose a negative phrase to characterize this estimate. In other words, we assume that the probability expressed by the first speaker will be taken as a reference value that is corrected by the second speaker. Accordingly, the probability term chosen to express the second speaker’s opinion will aim to accentuate or weaken the possibility that the outcome will occur (or is true) originally implied by the first speaker’s estimate. 3. 1. Method 3. 1. 1. Participants and Design. A total of 116 Human Science students from the University of Toulouse (95 women; 21 men, mean age 22.32 years, SD = 5.13) were randomly allocated to four groups. Participation was voluntary and unpaid. The experimental design was identical to Experiment 1. Is guilt ‘likely’ or ‘not certain’? 17 3. 1. 2. Material and Procedure. Participants received a 2-page questionnaire, similar to that used in Experiment 1, except from the following changes in the cover scenario (translated from French): Some pieces of evidence can be considered as subjective, so it happens that two profilers working on the same inquiry and using the same program arrive at different conclusions. Consequently, the Police often consult two profilers to work on the same crime. The Police required the profilers’ assistance on the following case: A serious hold-up has been committed, the police have a suspect but they have no definitive evidence about his guilt or about his innocence. After a week of investigation, they ask help from Tom and David and provide them all the pieces of evidence they collected. Tom and David are discussing the potential guilt of the suspect before giving their results to the police officer in charge of the inquiry. Your task is to select the sentence you would expect the speakers to use. Tom, who found that the suspect has a [p1] probability to be guilty, says to David: “According to my analysis …” [Verbal probability selection task 1] David, who found that the suspect has a higher [lower] probability of guilt: [p2], responds to Tom and says: “According to my analysis...” [Verbal probability selection task 2] In both selection tasks, participants were asked to choose between the same pairs of positive and negative phrases used in Experiment 1 (see Table 2). Finally, participants’ subjective degree of belief in the suspect’s guilt was assessed with the same scale that was used in Experiment 1. 3. 2. Results and Discussion Is guilt ‘likely’ or ‘not certain’? 18 3. 2. 1. First Choice of Phrase Directionality. The right half of Table 3 shows preferences for positive and negative phrases to describe the initial probabilities (p1). As in Experiment 1, positive phrases were consistently preferred to negative ones. This preference, however, was no longer independent of the magnitude of the probability characterized by the chosen term; χ2(3, N = 116) = 9.99, p < .05. Participants preferred to use a positive term to describe probabilities of .10, .70 and .90; χ2(1, N = 29) = 9.97, p < .01; χ2(1, N = 31) = 3.90, p < .05), and χ2(1, N = 28) = 17.29, p < .001, respectively. They seem, however, in two minds when describing .30; χ2(1, N = 28) = 0.14, p = .71. It is not clear why such a discrepancy would occur. It seems, in hindsight, that the preference for positive terms was stronger when the probabilities communicated were more extreme: 83% chose a positive probability term to communicate .90 or .10 whereas only 61% did so to communicate .30 or .70. This finding suggests that negative terms may not necessarily always be associated with low numerical probabilities but may instead be selected more often to communicate middle-range probabilities that are distant from either 0 or 1. Still, similarly to Experiment 1, Experiment 2 provided no clear-cut evidence showing that participants would more readily describe smaller probabilities with negative probability terms. 3. 2. 2. Second Choice of Phrase Directionality. Table 5 presents the percentages of positive and negative probability terms chosen in each experimental condition. When the probability announced by the second speaker (Tom) was higher than that of the first speaker (David), most of the participants (82.4%) believed Tom would direct David’s attention towards the suspect’s guilt and chose a positive verbal term to characterize his degree of belief. However, when Tom’s degree of belief in the suspect’s guilt was lower than David’s, most participants (59.7%) believed Tom would communicate his degree of belief verbally with a negative probability term. This reversal of preference for negative terms was significant when p2 was .40, χ2(1, N = 60) = 11.79, p < .01, c = .40, as well as when it was Is guilt ‘likely’ or ‘not certain’? 19 .60, χ² (1, N = 56) = 10.34, p < .01, c = .39. Moreover, we found no relation between the directionality of the term chosen to express the first speaker’s degree of belief and that chosen to express the degree of belief of the second speaker; χ2(1, N = 116) = .06, p = .48, c = .02. <Insert Table 5 about here> 3. 2. 3. Belief Ratings. As in Experiment 1, participants were asked to rate the extent to which they were convinced the suspect was guilty after the second verbal probability selection task. Table 5 shows that participants who chose a positive term held similar beliefs to those who chose a negative term, with the exception of those told that the first speaker believed the suspect’s probability of guilt was .90 whereas the second speaker believed it was .60 (.90 → .60 trend). Within that condition, participants who chose a positive term also believed that the suspect was more likely to be guilty (Mean rank = 22.44) than those who chose a negative term (Mean rank = 10.74). This was the only significant difference in belief ratings observed (U = 14, z = -3.67, p < .001; all other z < -0.22). So participants who were not influenced by the downward comparison (and hence persisted in using a positive term to describe .60 in the decreasing trend) were also those who were almost certain that the suspect was guilty. This suggests interesting individual differences whereby some individuals may be more sensitive to pragmatic cues such as the decreasing trend in the conversation and adjust their choice of term and their subjective degree of belief accordingly. Others, by contrast, may anchor their degree of belief in guilt on the first piece of information provided and interpret the second probability as confirming their initial belief. Overall, these results therefore replicated the findings of Experiment 1 in a conversational setting: once again, the choice of directionality of the second probability term was not determined by the absolute magnitude of the probability it meant to communicate. Is guilt ‘likely’ or ‘not certain’? 20 Instead it depended on the contrast between this magnitude and that of a probability previously expressed by another speaker. In addition, the data collected did not clearly support the proposition that directionality choices are determined by participants’ subjective degrees of belief. Rather, the present finding suggests that conversational partners choose their expressions to complement or reinforce each other’s opinions. As such, they support the view that the directionality of verbal probabilities serves a pragmatic and conversational function (Teigen & Brun, 1999), which improves cooperation (Hilton, 2008). 4. Experiment 3 The consecutive numerical probabilities, p1 and p2, used in the first two experiments were attached to the same event, namely the guilt of one single suspect. They differed either because of a probability revision from one point in time to another (Experiment 1), or because of a difference in opinion between two speakers (Experiment 2). In Experiment 3, we sought to examine whether the framing effects observed in the first two experiments would generalize to situations where the two probabilities compared are attached to a focal event and its complementary alternative event. Thus, our scenario introduced two suspects with different probabilities of having committed a given offense. In this situation, p1 denoted the guilt probability of the first suspect and p2, that of the second suspect. The issue remained to ascertain whether the magnitude of the guilt probability for one suspect would have an impact on the probability term chosen to describe the second suspect’s probability of guilt. Previous research has established that joint evaluations of items can differ quite dramatically from evaluations of the same items presented separately (Hsee, 1996; Schwarz & Hippler, 1995). In addition, previous research has shown that when a focal probability is higher than any of the probabilities for the alternative outcomes, individuals will report higher levels of verbal certainty for the occurrence of the focal outcome compared to the situation where the same focal probability is lower than any of the probabilities for the Is guilt ‘likely’ or ‘not certain’? 21 alternative outcomes (Windschitl & Wells, 1998). Expanding upon these results, one could therefore anticipate that the same guilt probability for a given focal suspect would appear lower when compared with a higher probability for an alternative suspect (pf < pa, downward comparison). Conversely, the guilt probability for the focal suspect should appear larger when contrasted to a lower probability of guilt for an alternative suspect (pf > pa, upward comparison). If directionality of verbal terms depends on the underlying degree of belief, , then differences in subjective belief elicited by the alternative outcome should, in turn, affect individuals’ preferences for probability terms. Thus, in a downward comparison, participants should be more likely to prefer negative words to describe the lower pf. Instead, in an upward comparison, participants should be more likely to prefer positive words to describe the higher pf. Such an account, however, presupposes that choices of positive or negative probability terms primarily reflect the perceived magnitude of a probability. Yet, the two previous experiments found little evidence for that claim. By contrast to the above predictions, a conversational account of directionality choice for probability terms would assume that directionality is not chosen on the basis of the perceived relative magnitude of pf compared to pa but rather will reflect the communicative intentions of the speaker. From this perspective, whereas the revision of an initial probability or a difference of opinions between two speakers would call for the use of a linguistic marker to emphasize the change, a situation where two alternative suspects are described may not necessarily call for the same interpretation. 4. 1. Method 4. 1. 1. Participants and Design. Participants were 137 Human Science students from the University of Toulouse (124 women; 13 men, mean age 20.86 years, SD = 4.40). Participation was voluntary and unpaid. Participants were randomly allocated to two Control and two Comparison conditions. Control participants were told about one single suspect who Is guilt ‘likely’ or ‘not certain’? 22 had either a .40 probability of being guilty (Low p-magnitude) or .60 (High p-magnitude). Participants in the two comparison conditions were told about two suspects, one with a .40 probability of being guilty and the other with a .60 guilt probability. Half of them were introduced to the two suspects in increasing order, with p1 = .40 and p2 = .60, the other half in decreasing order, with p1 = .60 and p2 = .40. 4. 1. 2. Material and Procedure. Participants received a 2-page questionnaire, similar to that used in Experiment 1, with the exception of a few changes detailed below. Participants in the Low-p (High-p) control conditions received information about only one suspect and were told that, based on the available evidence, the suspect’s probability of guilt was .40 (.60). Their task was to choose whether to communicate this probability to the Police with a positive or a negative verbal term (see Table 2 for a description of the terms used) as well as to rate their subjective degree of belief in the suspect’s guilt on a 6-point scale. In the comparison conditions, participants were told that two suspects had been caught and that it was certain that one of them was the perpetrator of the crime. The probability of the first suspect, Mr X., was said to be .60 (.40), and the probability of the second suspect, Mr Y., was said to be .40 (.60). The cover story for the comparison conditions read as follows (translated from French): A serious hold-up has been committed and the Police have two suspects: Mr. X. and Mr. Y. We know for sure that one of them committed the crime but we don’t know which. The Police officers’ investigation did not lead to a definitive decision. After a week of investigation, they ask for your help and provide you with all the pieces of evidence they collected. After each presentation of a suspect’s probability of guilt, participants were asked to choose whether they would prefer to use a positive and negative probability term to Is guilt ‘likely’ or ‘not certain’? 23 communicate that probability verbally to the Police. Finally, they were asked to rate the extent to which they were convinced each suspect was the guilty one on a 6-point scale. 4. 2. Results 4. 2. 1. Choice of Phrase Directionality. Preferences for positive and negative phrases to describe focal probabilities of either .40 or .60 as a function of comparison trend are presented in Table 6, alongside preferences observed in the corresponding control conditions where no comparison was available. As in previous studies, there was a clear preference for using positive phrases: overall, 68% of choices favored the positive term. This preference was independent of the magnitude of the probability whether choices were made in a separate context (control conditions; χ2(1, N = 68) = 2.06, p = .15) or in a conjoint evaluation context for a first suspect (χ2(1, N = 69) = 1.08, p = .30) or for the second suspect (χ2(1, N = 69) = 0.81, p = .37). The pattern of preferences observed thus once more confirmed the pervasive preference for using positive probability terms, independently of the magnitude of the numerical probability communicated. Expanding upon the alternative outcomes account (Windschitl & Wells, 1998), we expected that the same guilt probability for a given focal suspect would appear lower when compared with a higher probability for an alternative suspect (pf = .40 < pa = .60, downward comparison). Consequently, choices of negative terms were expected to be more frequent in those comparison conditions compared to a control condition where the focal suspect was presented alone. This hypothesis, however, was not supported by the results. As the first three data row of Table 6 show, the frequency of negative terms chosen to describe the lower guilt probability of the second suspect was not influenced by the presence of a first suspect with a higher probability of guilt (.60 → .40 trend, pf = .40). Instead, we observed a significant Is guilt ‘likely’ or ‘not certain’? 24 decrease in preference for negative terms compared to the control condition; χ2(1, N = 70) = 5.19, p < .05. Similarly, when the lower guilt probability of the first suspect could be compared with the higher guilt probability for the second suspect (.40 → .60 trend, pf = .40), preferences for negative terms were almost identical to those observed in the control condition; χ2(1, N = 69) = 0.03; p = .87. Windschitl and Wells’s (1998) alternative outcomes account also entailed that a guilt probability of .60 should have appeared larger contrasted to a lower probability of guilt for an alternative suspect . If directionality reflected subjective probability magnitudes, one would predict a decrease in preference for negative terms when a focal probability of .60 is contrasted to a lower alternative probability of .40 compared to a situation where no comparison is possible (control condition). This prediction was partially supported by the results. When the probability of the first suspect could be compared with a lower probability for the second suspect (.60 → .40 trend, pf = .60), we observed a significant decrease in preference for negative terms to describe pf = .60; χ2(1, N = 67) = 6.97, p < .01. However, when the probability of the second suspect could be compared with a lower probability for the first suspect (.40 → .60 trend, pf = .60), preferences for negative terms did not differ from the control condition; χ2(1, N = 68) = 0.51; p = .48. <Insert Table 6 about here> 4. 2. 2. Belief Ratings. As in the two previous experiments, participants were asked to report their subjective belief of guilt. The ratings reported in Table 6 reveal that these judgments did not consistently predict directionality choices. When no comparison was possible, participants who had chosen a negative term to describe a .40 objective probability of guilt tended to be less convinced that the suspect was guilty compared to those who had Is guilt ‘likely’ or ‘not certain’? 25 chosen a positive term; U = 73, z = -2.55, p = .01, one-tailed. In comparison contexts, however, this result no longer held. Choices of negative terms were not associated with lower degrees of belief in the suspect’s guilt for either p1 = .40 or p2 = .40; U = 60, z = -0.12, p = .47, one-tailed and U = 116, z = -0.43, p = .36, one-tailed, respectively. When the objective probability of guilt was .60 and no comparison was possible, those who chose a positive term to describe this probability only held marginally stronger beliefs about the suspect’s guilt; U = 96, z = -1.57, p = .08, one-tailed. When p1 or p2 were .60, however, choices of negative terms were reliably associated with lower subjective degrees of guilt; U = 54, z = -1.84, p < .05 and U = 90.50, z = -2.17, p = .02, one-tailed. Results from the present study thus show that the presence of an alternative outcome (i.e., here, an alternative suspect) can affect preferences for negative and positive probability terms to communicate an objective probability value (i.e., the guilt probability of the suspect). The effects observed, however, differed from those obtained in the previous two experiments. Upward comparisons where a focal suspect with a lower probability of guilt could be compared to an alternative suspect with a higher probability of guilt did not increase the proportion of negative terms chosen to describe the focal suspect’s likelihood of being guilty. Downward comparisons where a focal suspect with a higher probability of guilt could be compared to an alternative suspect with a lower guilt probability only decreased the proportion of negative terms chosen to describe the focal suspect’s probability of guilt when this focal suspect was introduced first. These results are, however, consistent with the conversational (pragmatic) perspective, according to which negative phrases will be selected when speakers are motivated to focus attention on a different aspect of the situation. The present results suggest that a difference in the objective probability of guilt of a second suspect compared to a first one does not call for a change of focus whereas a change of opinion (Experiment 1) or a difference of opinions (Experiment 2) did. Is guilt ‘likely’ or ‘not certain’? 26 Such explicit comparisons, however, decreased the proportion of negative terms chosen to describe p1 both in downward comparisons where p1 (.60) was contrasted with a lower p2 (.40) and in upward comparisons where p1 (.40) was contrasted with a higher p2 (.60). Whereas the first result was predicted by the alternative outcome effect, the second was in direct opposition with the predictions of this account. These results also suggest that participants will implicitly consider the first outcome encountered to be the focal outcome but not the second. It is unclear why more participants would prefer to say that “there is a small possibility” that the first suspect is guilty when a first suspect said to have a .40 objective probability of guilt is compared to a second suspect said to have a .60 probability of guilt. It is possible that the comparison increases the salience of a possible miss error (i.e., suggesting that a suspect is innocent when he is in fact guilty), thereby encouraging participants to focus on the possibility of guilt for both suspects. Future research could examine the effect of manipulating the subjective probability of miss errors by using more extreme probabilities (e.g., .20 vs. .80) or by contrasting a focal suspect with more alternative suspects (e.g., .40 vs. .10, .10, .10, .10, .10, .10). Finally, concerning the role of subjective degrees of beliefs in determining choice of term directionality, results were once more inconsistent, casting further doubt on the possibility that people consistently rely on subjective degrees of beliefs to chose a verbal probability term. 5. General Discussion Speakers asked to describe probabilities in words, are faced with two decisions. The first concerns the selection of an expression that corresponds to the level of probability one has in mind. For example, speakers will need to decide whether they should argue that it is probable or else that there is merely a small possibility a suspect is guilty. The second decision concerns directionality. Supposing the suspect’s guilt is judged to be likely, should guilt be described as probable or not certain? Previous studies of how probabilities are (or Is guilt ‘likely’ or ‘not certain’? 27 should be) communicated have almost exclusively focused on the former question. The three studies reported in this article, by contrast, focused on the determinants of directionality. We eluded the question of level by using pre-tested phrases to communicate probabilities of different magnitudes. Thus participants were only offered a choice between one positive and one negative way of communicating the same level of guilt. The central findings of the present studies can be subsumed under two general headings: a positivity bias and a trend effect. 5. 1. Positivity bias In all three studies, participants were initially asked to choose a phrase to describe probability values ranging from .1 to .9. In 11 out of 12 conditions (four different p1 values in each experiment), the majority preferred a positive phrase. Overall preferences for positive phrases to describe p1 were 71.5%, 72.5%, and 71.0% in Experiments 1, 2, and 3, respectively. These results are in line with those observed in previous studies where speakers have produced their own phrases, as well as those where lists of phrases were prepared by investigators. In those previous studies, positive phrases were up to four times more frequent than negative ones (see Teigen & Brun, 1995). So overall, it is more natural to describe events in terms of their occurrence rather than their non-occurrence. Affirmations are logically prior to negations, and believing is simpler than doubting (Gilbert, 1991; Horn, 1989). Furthermore, this result fits very well with the prevalence of unmarked over marked adverbs or adjectives (e.g., probable vs. improbable) found in the psycholinguistics literature (Clark & Clark, 1977). In previous studies, negative phrases have typically been shown to be used for describing low probabilities (e.g., Budescu et al., 2003). One would therefore expect a marked preference for negative phrases to describe lower levels of probability. No such pattern could be detected, however. In all three experiments, most participants chose positive phrases, even Is guilt ‘likely’ or ‘not certain’? 28 for small probabilities. And conversely, negative phrases occurred with equal frequency for high and low probabilities. Two possible explanations can account for this apparent lack of relationship between directionality and probability magnitude. One has to do with the legal context, which formed the basis for the scenarios used. The probabilities referred in all cases to the guilt of a person under investigation. The main focus was therefore on the suspect’s degree of guilt, however small, rather than upon the complementary probability (i.e., his chances of being innocent). A second, and perhaps more plausible explanation, is methodological. Previous studies have confounded the issues of probability magnitude and directionality by not studying them in separate designs. The present experiment differs by allowing participants to make a choice between positive and negative phrases at each magnitude level. This calls attention to the existence of alternative phrases both for high and low probabilities, and reminds the speaker that there is actually a choice to be made. Thus, the presence of a negative phrase makes the negative frame available even for high probabilities, and conversely, a suggested positive phrase for small probabilities makes participants aware that even a probability of .10 can be described positively with a phrase such as “there is a tiny probability.” 5. 2. The Trend Effect Our main focus of interest in these studies was not p1, but p2, the second probability to be communicated. We hypothesized that choice of verbal expression is determined by conversational concerns. More specifically, we expected that in conversational contexts the comparison of different levels of probability would have an impact on the choice of phrase. This was strongly confirmed by the results. In Experiment 1 and 2, the first probability turned out to have a strong influence on the second. If initial expectations, or probabilities voiced by the first speaker had to be modified upwards, positive phrases would be chosen, when probabilities were modified in a downward direction, negative phrases became strongly Is guilt ‘likely’ or ‘not certain’? 29 preferred. We have thus established evidence for a trend effect. In these cases, choice of phrase is determined by the relative and not by the absolute magnitudes of the probabilities communicated. The equivalence between the positive and negative phrase in individual pairs could be disputed. For example, the preference for a positive phrase could be explained by other factors than its directionality, such as its usualness, the extent to which it belongs to the respondent’s “lexicon” of preferred phrases (Karelitz & Budescu, 2004), is easy to pronounce, or else how well it corresponds to the target probability compared to its negative counterpart. However, the fact that a similar pattern of preference was obtained across four or more pairs of phrases, and also that pattern of preferences for positive and negative terms were reversed as a function of trend all tend to confirm that choices were determined by conversational context rather than by intrinsic features of the terms presented. The finding that trend can overturn directionality preferences, might seem difficult to reconcile with the fuzzy interpretation of the meaning of verbal terms, advanced by Budescu et al., 2003). Moreover, we found inconsistent evidence for the proposition that choices of negative terms would be determined by lower subjective degrees of belief. However, the fuzzy concept model does not claim to explain why phrases differ in directionality, and why the membership function of a phrase is characterized by a particular shape. One reason for the apparent vagueness or “spread” of a given term could be due to the fact that different respondents imagine different conversational contexts for terms they have been asked to assess. Thus our results suggest that the fuzzy account and the pragmatic account are complementary rather than mutually exclusive. More research is needed, however, to distinguish the conditions under which individuals will chose a negative probability term because they hold lower degrees of beliefs from those under which they do so for pragmatic reasons. Is guilt ‘likely’ or ‘not certain’? 30 The present findings are clearly in line with a linguistic, qualitative perspective on quantifiers proposed by Moxey and Sanford (2000). The trend effect based on past probabilities (as in Experiment 1) is also in agreement with McKenzie and Nelson’s (2003) Glass study, which showed that description of frames depended on reference points. In the present studies we have introduced, metaphorically speaking, a “probability glass,” whose content is described with positive phrases when the probability level has increased and with negative phrases when the level has decreased. Similar trend effects can also be observed in other domains, where the same quantity can be given complementary descriptions. For instance quantities that fall within an uncertainty interval can alternatively be described positively as “more than X” or negatively as “less than Y”. The choice between such lower bound and upper bound statements can also be determined by trend. For example, if the temperature is 22 degrees centigrade and someone says: “Today it is more than 20 degrees,” a listener may infer increasing temperatures, and that yesterday was colder. If the speaker had said “today it is less than 25 degrees,” a listener would think that the day before was quite hot (Teigen, 2008). According to the pragmatic view (Grice, 1989; Levinson, 2000), speakers select the phrases that allow them to be as relevant and informative as possible. According to Sperber and Wilson’s (1995) relevance theory, relevance can be defined as an input, which improves the recipient’s knowledge based on previous assumptions. Positive phrases will be chosen to communicate agreement and to confirm or strengthen a previous opinion, whereas negative phrases can be seen as a correction, or at least an attempt to reorganize previous knowledge. Positive and negative phrases are thus not completely symmetrical. In our research, negative phrases were chosen mainly in cases where the first probability was judged to be too high. This represents further evidence for the “shortfall” or “presupposition denial” hypothesis proposed by Moxey and colleagues (Moxey, 2006; Moxey & Sanford, 1987; Moxey et al., Is guilt ‘likely’ or ‘not certain’? 31 2001), which postulates that quantifiers with negative polarity can be viewed as negations of an expected quantity. Results from Experiment 3 indicate that the trend effect is not simply a matter of contrast evoked by upward and downward comparisons. In this experiment, the higher or lower probability of one candidate did not always have corresponding effects on the phrases chosen to describe another, as could have been expected from the “alternative outcomes effect” (Windschitl & Wells, 1998; Windschitl & Young, 2001). This design differed from Experiment 1 and 2 by not requiring an upward or downward adjustment of the same probability. Moreover, results from this experiment suggested an order effect, whereby the first probability was more often described by positive phrases than the second, regardless of p magnitude (lower or higher than .50). This result was unexpected for upward comparisons (when a lower probability is compared to a higher one). Perhaps positive phrases are also the default, more natural starting point for a more complex sequence of communications. 5. 3. How Verbal Probabilities are Understood In cases where it is difficult to agree on the exact meaning of a verbal term, it has been commonplace to assume that the meaning “depends upon context”. However, attempts to study the meaning of verbal terms “in context” have not always been successful. BeythMarom (1982) found that verbal terms in context were given even more different interpretations than isolated phrases. Brun and Teigen (1988) reached the same conclusion. These studies focused on the numerical meanings of verbal terms embedded in textual fragments or clips from newscasts. In the present study, we have instead placed phrases in conversational contexts. This revealed that people have strong intuitions about which phrases are appropriate to express higher or lower probabilities in conversations when one utterance is intended to correct or elaborate on another. In these cases, it was possible to predict choice of verbal phrase based on the context in which the phrase was uttered. Is guilt ‘likely’ or ‘not certain’? 32 Agreement about which phrase will be chosen does not, however, entail agreement about its interpretation. Listeners who hear a statement about guilt being “not certain” may not be able to back-translate this into a probability of .60. Perhaps listeners or readers would be able to guess that this phrase presupposes a stronger belief that had to be modified, but without any exact notion of the magnitude of this revision. They may also perceive it as a recommendation to start looking for other suspects, even when the original intention was just to describe a probability and not to recommend a particular course of action. Further research might show whether different choice of phrases for describing guilt will lead to different decisions (see Teigen & Brun, 1999). Phrases that are selected to fit a particular communicative context may be especially vulnerable for misunderstandings when taken out of these contexts. For instance, newspaper headlines often report that a previously held belief is claimed by some expert to be “uncertain” (e.g., “uncertainty about global warming”). Here the probability corresponding to “uncertainty” is ambiguous as long as we do not know which probability the expert is trying to reduce. All we can tell is that there is some disagreement between experts in this field. To sum up, in the present study, trends were shown to operate in two ways: As probability revisions (of the same speaker) and as different opinions held by first and second speaker in a dialogue. Both kinds of trends had similar effects on the choice of probability terms, but only the first one influenced the listeners’ (or readers’) beliefs, setting it apart from a simple recency effect. Thus, the use of trend effects to manipulate the listener’s conviction seems to require the construction of a narrative where probabilities develop over time. 5. 4. Implications for Further Research Traditional verbal probability scales place negative expressions to the left (or at the bottom) to describe probabilities below .50 (e.g., p = .10 is “translated” to mean extremely unlikely), whereas high probabilities are placed to the right, to describe medium to high Is guilt ‘likely’ or ‘not certain’? 33 probabilities (e.g., p = .80 is described as “very likely”). Verbal probability scales have proposed as means to address uncertainty in different critical domains such as medicine (Witteman, Renoojj, & Koele, 2007) or climate change (Budescu, Broomell, & Por, 2009). Those scales, however, could be further improved by distinguishing two variables: the probability magnitude and the focus of attention. For example, the Intergovernmental Panel on Climate Change (2007) proposed to use positive and negative verbal terms (e.g., likely and unlikely) to communicate the probability of occurrence of various phenomena related to climate change (e.g., the increase in frequency of hot days and nights). Budescu, Broomell and Por (2009) showed that recipients of such uncertain messages were likely to misinterpret the magnitude of probability communicated by those terms and proposed simple recommendations to address this. The present research points to an additional issue concerning the use of both positive and negative terms to communicate uncertainty. Reporting that global warming is very unlikely to be more than 4.5°C may not only bring about reasons against global warming in recipients’ minds, it may also indicate that the current probability of occurrence is less than it used to be. This latter issue could be addressed by using two scales, thus resulting in a more coherent set of descriptions: One set of positive probability phrases, from the tiniest chance to full certainty, and one set of expressions for uncertainties and doubts, from small uncertainties to serious doubts. As suggested by linguists working on epistemic predicates (possible, likely, and not certain), verbal terms are not to be arranged on a single dimension, but along two parallel sides of a square, forming pairs of “contraries” (polar opposites, like certain vs. impossible), “contradictories” (like certain vs. not certain), and “subcontraries” (like possible vs. not certain; for discussions of the linguistic implications of such an arrangement, see Levinson, 2000; Horn, 1989). Is guilt ‘likely’ or ‘not certain’? 34 In the present study, we have attempted to isolate and manipulate only one determinant of verbal probability, namely contrast with (own or other’s) prior opinion. But a positive or a negative probability phrase may be selected for several other reasons as well. Negative phrases may signal cautiousness, by focusing on potential non-occurrence of the target event. Also, people who are not confident in an appraisal can be expected to describe the probability they have in mind with a negative phrase, whereas a confident speaker might prefer the use of a positive phrase. Listeners will probably perceive positive phrases as more informative than negative ones. However, the reserve inherent in negative phrases makes them suited to communicate warnings about an action, and even function as a polite way to convey an upsetting truth (Bonnefon & Villejoubert, 2006). A closer analysis might reveal that the positive set of phrases are better suited to express external, or “aleatory” probabilities, whereas the negative set of phrases more strongly suggest internal, or “epistemic” states of mind (Kahneman & Tversky, 1982). This would be in line with Horn’s suggestion that negations belong to a different order than affirmations: “Negative statements are about positive statements, while affirmatives are directly about the world” (1989, p. 3). Finally, a better understanding of the choices people make when they describe and discuss uncertain outcomes might prevent misunderstandings and enhance the quality of professional communication. The present examples were embedded in a legal context, but similar examples could be drawn from medical settings (e.g., communication to patients), financial advice, political forecasts, auditors’ reports, project planning, and even scientific hypothesis testing. In all these fields, and more, chances and uncertainties are described, not as singular, isolated claims, but in comparison and contrast with previous opinions in an ongoing discourse. John Donne famously remarked that no man is an island; the present study demonstrates that, in addition, no probability term is an island. Is guilt ‘likely’ or ‘not certain’? 35 References Beyth-Marom, R. (1982). How probable is probable? A numerical translation of verbal probability expressions. Journal of Forecasting, 1, 257-269. doi: 10.1002/for.3980010305 Bonnefon, J. F., & Villejoubert, G. (2006). Tactful, or doubtful? Expectations of politeness explain the severity bias in the interpretation of probability phrases. Psychological Science, 17, 747-751. doi: 10.1111/j.1467-9280.2006.01776.x Brun, W., & Teigen, K. H. (1988).Verbal probabilities: Ambiguous, context-dependent, or both? Organizational Behavior and Human Decision Processes, 41, 390-404. doi: 10.1016/0749-5978(88)90036-2 Budescu, D. V., Broomell, S. B., & Por, H. H. (2009). Improving communication of uncertainty in the IPCC reports. Psychological Science, 20, 299-308. Doi: 10.1111/j.1467-9280.2009.02284.x Budescu, D. V., Karelitz, T. M., & Wallsten, T. S. (2003). Predicting the directionality of probability words from their membership functions. Journal of Behavioral Decision Making, 16, 159-180. doi: 10.1002/bdm.440 Budescu, D. V., & Wallsten, T. S. (1995). Processing linguistic probabilities: General principles and empirical evidence. The Psychology of Learning and Motivation, 32, 275-318. Budescu, D. V., Weinberg, S., & Wallsten, T. S. (1988). Decisions based on numerically and verbally expressed uncertainties. Journal of Experimental Psychology: Human Perception and Performance, 14, 281-294. doi: 10.1037/0096-1523.14.2.281 Clark, H. H., & Clark, E. V. (1977). The Psychology of Language: An Introduction to Psycholinguistics. New York: Harcout, Brace. Is guilt ‘likely’ or ‘not certain’? 36 Collins, S., & Alison, L. (2002). How certain are offender profilers about the claims they make? Internal report for the National Crime and Operations Faculty. Hook, Bramshill, UK. Diez, F. J., & Druzdzel, M. J. (in press). Verbal expressions of.probability. Encyclopedia of Medical Decision Making. Los Angeles: Sage Publications. Erev, I. & Cohen, B. L. (1990). Verbal versus numerical probabilities: Efficiency, biases and the preference paradox. Organizational Behavior and Human Decision Processes, 45, 1–18. doi: 10.1016/0749-5978(90)90002-Q Fischhoff, B., & Beyth-Marom, R. (1983). Hypothesis evaluation from a Bayesian perspective. Psychological Review, 90, 239–260. doi: 10.1037/0033-295X.90.3.239 Gigerenzer, G., & Hoffrage, U. (1995). How to improve Bayesian reasoning without instruction: Frequency formats. Psychological Review, 102, 684–704. Gilbert, D. T. (1991). How mental systems believe. American Psychologist, 46, 107-119. Grice, H. P. (1989). Logic and conversation. In H. P. Grice (Eds.), Studies in the way of words (pp. 22-40). Cambridge, MA: Harvard University Press. Halberg, A. M., & Teigen, K. H. (2009). Framing of imprecise quantities: When are lower interval bounds preferred to upper bounds? Journal of Behavioral Decision Making. Advance online publication. doi: 10.1002/bdm.635. Hilton, D. J. (2008). Emotional tone and argumentation in risk communication. Judgment and Decision Making, 3, 100-110. Honda, H., & Yamagishi, K. (2006). Directional verbal probabilities: Inconsistencies between preferential judgments and numerical meanings. Experimental Psychology, 53, 161170. doi: 10.1027/1618-3169.53.3.161 Horn, L. R. (1989). A natural history of negation. Chicago: University of Chicago Press. Is guilt ‘likely’ or ‘not certain’? 37 Hsee, C. K. (1996). The evaluability hypothesis: An explanation for preference reversals between joint and separate evaluations of alternatives. Organizational Behavior and Human Decision Processes, 67, 247-257. doi: 10.1006/obhd.1996.0077 Intergovernmental Panel on Climate Change. (2007). Summary for policymakers: Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Retrieved from http://www.ipcc.ch/pdf/assessment-report/ar4/wg1/ar4-wg1-spm.pdf Juanchich, M., Villejoubert, G., & Mullet, E. (2008, May). What does directionality mean? Paper presented at the European Group for Process Tracing Studies Conference, Bergen, Norway. Kahneman, D., & Tversky. A. (1982). Variants of uncertainty. Cognition, 11, 143-157. Karelitz, T.M., & Budescu, D.V. (2004). You say probable and I say likely: Improving interpersonal communication with verbal probability phrases. Journal of Experimental Psychology: Applied, 10, 25-41. Levinson, S. C. (2000). Presumptive meanings: The theory of generalized conversational implicature. Cambridge, Mass: MITPress. Mandel, D. R. (2008). Violations of coherence in subjective probability: A representational and assessment processes account. Cognition, 106, 130-156. doi: 10.1016/j.cognition.2007.01.001 McGuire, W. J., & McGuire, C. V. (1992). Cognitive-versus-affective positivity asymmetries in thought systems. European Journal of Social Psychology, 22, 571-591. doi: 10.1002/ejsp.2420220605 McKenzie, C. R., & Nelson, J. D. (2003). What a speaker’s choice of frame reveals: Reference points, frame selection, and framing effects. Psychonomic Bulletin and Review, 10, 596-602. Is guilt ‘likely’ or ‘not certain’? 38 McNeil, B. J., Pauker, S. G., Sox, H. C., & Tversky, A. (1982). On the elicitation of preferences for alternative therapies. New England Journal of Medicine, 306, 12591261. Moxey, L. M. (2006). Effects of what is expected on the focusing properties of quantifiers: A test of the presupposition-denial account. Journal of Memory and Language, 55, 422439. doi: 10.1016/j.jml.2006.05.006 Moxey, L. M., & Sanford, A. J. (1987). Quantifiers and focus. Journal of Semantics, 5, 189206. doi:10.1093/jos/5.3.189 Moxey, L. M., & Sanford, A. J. (2000). Communicating quantities: A review of psycholinguistic evidence of how expressions determine perspectives. Applied Cognitive Psychology, 14, 237-255. Moxey, L. M., Sanford, A. J., & Dawydiak, E. J. (2001). Denials as controllers of negative quantifier focus. Journal of Memory and Language, 44, 427-442. doi:10.1006/jmla.2000.2736 Peeters, G. (1971). The positive-negative asymmetry: On cognitive consistency and positivity bias. European Journal of Social Psychology, 1, 455-474. Piercey, M. D. (2009). Motivated reasoning and verbal vs. numerical probability assessment: Evidence from an accounting context. Organizational Behavior and Human Decision Processes, 108, 330-341. Phillips, L. D., & Edwards, W. (1966). Conservatism in a simple probability inference task. Journal of Experimental Psychology, 72, 346-354. Rapoport, A., Wallsten, T. S., Erev, I. & Cohen, B. L. (1990). Revision of opinion with verbally and numerically expressed uncertainties. Acta Psychologica, 74, 61-79. Schwarz, N., & Hippler, H.-J. (1995). Subsequent questions may influence answers to preceding questions in mail surveys. Public Opinion Quarterly, 59, 93-97. Is guilt ‘likely’ or ‘not certain’? 39 Sperber, D., & Wilson, D. (1995). Relevance: Communication and Cognition. Oxford: Blackwell. Teigen, K. H. (1988a). When are low-probability events judged to be probable? Effects of outcome-set characteristics on verbal probability estimates. Acta Psychologica, 67, 157-174. doi: 10.1016/0001-6918(88)90011-X Teigen, K. H. (1988b). The language of uncertainty. Acta Psychologica, 68, 27-38. doi: 10.1016/0001-6918(88)90043-1 Teigen, K. H. (2008). More than X is a lot: Pragmatic implicatures of one-sided intervals. Social Cognition, 26, 379-400. doi: 10.1521/soco.2008.26.4.379 Teigen, K. H., & Brun, W. (1995). Yes, but it is uncertain: Direction and communicative intention of verbal probabilistic terms. Acta Psychologica, 88, 233-258. doi: 10.1016/0001-6918(93)E0071-9 Teigen, K. H., & Brun, W. (1999). The directionality of verbal probability expressions: Effects on decisions, predictions, and probabilistic reasoning. Organizational Behavior and Human Decision Processes, 80, 155-190. doi: 10.1006/obhd.1999.2857 Teigen, K. H., & Brun, W. (2003a). Verbal expressions of probability and uncertainty. In D. Hardman & L. Macchi (Eds.), Thinking: Psychological perspectives on reasoning, judgment, and decision making (pp. 125-145). Chichester: Wiley. Teigen, K. H., & Brun, W. (2003b). Verbal probabilities: A question of frame? Journal of Behavioral Decision Making, 16, 53-72. doi: 10.1002/bdm.432 Teigen, K. H., & Karevold, K. I. (2005). Looking back versus looking ahead: Framing of time and work at different stages of a project. Journal of Behavioral Decision Making, 18, 229-246. doi: 10.1002/bdm.502 Is guilt ‘likely’ or ‘not certain’? 40 Theil, M. (2002).The role of translations of verbal into numerical probability expressions in risk management: a meta-analysis. Journal of Risk Research, 5, 177–186. doi: 10.1080/13669870110038179 Villejoubert, G., & Mandel, D. R. (2002). The inverse fallacy: An account of deviations from Bayes’s theorem and the additivity principle. Memory & Cognition, 30, 171-178. Villejoubert, G., Almond, L., & Alison, L. (2008). Interpreting claims in offender profiles: The role of probability phrases, base-rates and perceived dangerousness. Applied Cognitive Psychology, 22, 1-19. doi:10.1002/acp.1438 Wallsten, T. S., Budescu, D. V., Zwick, R., & Kemp, S. M. (1993). Preference and reasons for communicating probabilistic information in numerical or verbal terms. Bulletin of the Psychonomic Society, 31, 135-138. Windschitl, P. D., & Wells, G. L. (1998). The alternative-outcomes effect. Journal of Personality and Social Psychology, 75, 1411-1423. doi: 10.1037/0022-3514.75.6.1411 Windschitl, P. D., & Young, M. E. (2001). The influence of alternative outcomes on gut-level perceptions of certainty. Organizational Behavior and Human Decision Processes, 85, 109-134. doi: 10.1006/obhd.2000.2934 Is guilt ‘likely’ or ‘not certain’? 41 Table 1 Overview of the experimental design used in Experiments 1 and 2 Final p-magnitude (p2) Trend Upward (p1 < p2) Downward (p1 > p2) Low .10 → .40 .70 → .40 High .30 → .60 .90 → .60 Note. In Experiment 1, p1 and p2 refer to the initial and the revised probabilities, respectively. In Experiment 2, p1 is the probability expressed by the first speaker and p2 is the probability expressed by the second speaker. Is guilt ‘likely’ or ‘not certain’? 42 Table 2 Positive and negative verbal terms proposed to communicate the probability magnitudes used in the experiments (French terms in parentheses) Verbal terms Probability magnitude p1 = 10% (Il y a une mince probabilité) It is probable p1 = 70% (Il est probable) There is a small possibility p2 = 40% (Il y a une petite possibilité) There is a small possibility p1 = 30% (Il y a une petite possibilité) There is a very high probability p1 = 90% (Il y a une très forte probabilité) It is probable p2 = 60% (Il est probable) (Il n’est pas certain) Note. The same verbal terms are proposed for p = .30 as for p = .40, and also the same verbal terms are used to describe p = .60 and p = .70, owing to the fact that these phrases cover a range of numerical meanings that are equally applicable to both sets of p values. In Experiment 3, only terms for communicating .40 and .60 were used. (Il n’est pas tout à fait sur) It is not certain (Il est assez peu probable) It is not completely sure (Il est assez peu probable) It is relatively unlikely (Il n’est pas certain) It is relatively unlikely (Il est très peu probable) It is not certain Positive There is a slight probability Negative It is highly unlikely Is guilt ‘likely’ or ‘not certain’? 43 Table 3 Percentages of choices of negative and positive verbal phrases to describe the initial probabilities of guilt (p1) in each experimental condition of Experiments 1 and 2 Experiment 1 p1 .10 .30 .70 .90 a Experiment 2 pa .01 .005 n.s. .01 N 29 28 31 28 Negative Positive 20.7% 46.4% 32.3% 10.7% 79.3% 53.6% 67.7% 89.3% pa .002 n.s. .07 <.001 N 31 30 31 31 Negative Positive 25.8% 23.3% 38.7% 25.8% 74.2% 76.7% 61.3% 74.2% Binomial tests of choice proportions. Is guilt ‘likely’ or ‘not certain’? 44 Table 4 Percentages of negative and positive terms chosen to describe revised probabilities (p2) of .40 and .60 as a function of trend (upward trend, p1 < p2 vs. downward trend, p1 > p2) and their associated mean subjective belief in the suspect’s guilt, Experiment 1. Choice of terms Trend .10 → .40 .70 → .40 .30 → .60 .90 → .60 Negative Positive 12.9% 35.5% 43.3% 77.4% 87.1% 64.5% 56.7% 22.6% pa <.001 n.s. n.s. .003 Subjective beliefs Negative 2.50 (0.58) 1.55 (0.69) 2.77 (0.44) 1.96 (1.16) Positive 2.15 (0.82) 1.85 (0.75) 2.71 (0.47) 2.57 (0.53) pb n.s. n.s. n.s n.s Note. Standard deviations for subjective beliefs are in parentheses. a Binomial tests of choice proportions. bMann-Whitney tests of belief ratings for positive vs. negative terms. Is guilt ‘likely’ or ‘not certain’? 45 Table 5 Percentages of negative and positive terms chosen to describe the second speaker’s probabilities (p2) of .40 and .60 as a function of trend (upward trend, p1 < p2 vs. downward trend, p1 > p2) and their associated mean subjective belief in the suspect’s guilt, Experiment 2. Choice of terms Trend .10 → .40 .70 → .40 .30 → .60 .90 → .60 Negative Positive 10.3% 51.6% 25.0% 67.9% 89.7% 48.4% 75.0% 32.1% pa <.001 n.s. .01 .09 Subjective beliefs Negative 2.67 (1.15) 2.69 (0.95) 2.71 (1.11) 3.00 (1.00) Positive 2.04 (0.82) 2.47 (1.64) 2.86 (0.91) pb n.s. n.s. n.s 4.56 (0.53) .001 Note. Standard deviations for subjective beliefs are in parentheses. a Binomial tests of choice proportions. bMann-Whitney tests of belief ratings for positive vs. negative terms. Is guilt ‘likely’ or ‘not certain’? 46 Table 6 Percentages of negative and positive terms chosen to describe two suspects’ guilt probabilities (p = .40 and p = .60, respectively) as a function of trend (upward trend, p1 < p2 vs. downward trend, p1 > p2) and their associated mean subjective belief in the suspect’s guilt, Experiment 3. Choice of terms Trend Negative Positive pa pf = .40 .40 → .60 .60 → .40 Control 11.4% 27.6% 34.3% 88.6% 72.4% 65.7% <.001 .02 .09 pf = .60 .40 → .60 .60 → .40 Control 26.0% 42.9% 54.2% 89.7% 57.1% 45.8% .002 n.s. n.s. 2.71 (1.50) 3.78 (0.85) 2.87 (1.30) 3.75 (1.64) 2.85 (2.76) 3.25 (0.68) .05 .02 .08 2.00 (0.82) 2.00 (0.86) n.s. 2.36 (0.81) 2.43 (0.84) n.s. 1.75 (0.62) 2.35 (0.57) .01 Subjective beliefs Negative Positive pb Note. Standard deviations for subjective beliefs are in parentheses. a Binomial tests of choice proportions. bMann-Whitney tests of belief ratings for positive vs. negative terms.