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

Context Matters: Emotional Sensitivity to Probabilities and the Bias for Action in Cancer Treatment Decisions

BACKGROUND

Past studies have shown a commission bias for cancer treatment, a tendency to choose active treatment even when watchful waiting is less risky. This bias suggests motivations for action beyond mortality statistics, but recent evidence suggests that individuals differ in their emotional sensitivity to probabilities (ESP), the tendency to calibrate emotional reactions to probability. The current study aims to examine the role of ESP in the commission bias, specifically whether those higher in ESP are more likely to choose watchful waiting when risk probabilities align with that choice.

METHODS

Participants (N = 1,055) read a scenario describing a hypothetical cancer diagnosis and chose between surgery and watchful waiting, with random assignment between versions where the mortality rate was either lower for surgery or for watchful waiting. We modeled choice using the Possibility Probability Questionnaire (PPQ), a measure of ESP, and several other individual differences in a logistic regression.

RESULTS

We observed a commission bias as in past studies with most participants choosing surgery both when surgery was optimal (71%) and when watchful waiting was optimal (58%). An ESP × Condition interaction indicated that the predictive role of ESP depended on condition. Those higher in ESP were more likely to choose surgery when probabilities favored surgery, β = 0.57, P < 0.001, but when probabilities favored watchful waiting, ESP had a near-zero relationship with choice, β = 0.05, P < 0.99.

CONCLUSIONS

The role of ESP in decision making is context specific. Higher levels of ESP predict choosing action when that action is warranted but do not predict a shift away from surgery when watchful waiting offers better chances of survival. ESP does not overcome the commission bias.

HIGHLIGHTS

Past studies have identified a "commission bias," a tendency to choose active treatment over watchful waiting, even when mortality rate is lower for waiting.Evaluation of risk probabilities is related to individual differences in emotional sensitivity to probabilities (ESP) and has been shown to predict reactions to and decisions about health risk situations.ESP appears to be selectively factored into decision making. ESP was a robust predictor of choosing surgery when probability information supported surgery but did not predict decisions when probability information supported watchful waiting.Those who are most emotionally attuned to probabilities are just as susceptible to the commission bias as those who are less attuned.

Dimensions of uncertainty communication: What is conveyed by verbal terms and numeric ranges

The paper reviews two strands of research on communication of uncertainty that usually have been investigated separately: (1) Probabilities attached to specific outcomes, and (2) Range judgments. Probabilities are sometimes expressed by verbal phrases ("rain is likely") and at other times in a numeric format ("70% chance of rain"), whereas range judgments describe the potential amounts expected ("1-4 mm of rain"). Examination of previous research shows that both descriptions convey, in addition to the strength of expectations, pragmatic information about the communicative situation. For instance, so-called verbal probability expressions (VPE), as likely, unlikely, a chance, or not certain give some, albeit vague, probabilistic information, but carry in addition an implicit message about the sources of uncertainty, the outcome's valence and severity, along with information about the speakers' attitudes and their communicative intentions. VPEs are directional by drawing attention either to an outcome's occurrence ("it is possible") or to its non-occurrence ("it is doubtful"). In this sense they may be more informative than numbers. Uncertainties about outcomes in a distribution (continuous quantities) are alternatively expressed as interval estimates. The width of such intervals can function as a cue to credibility and expertise. Incomplete, one-sided intervals, where only one boundary is stated, imply directionality. "More than 100 people" suggests a crowd, while "less than 200" implies a shortfall. As with VPEs, directionally positive intervals are more frequent, and perhaps more neutral than negative ones. To convey expectancies and uncertainty in a balanced way, communicators may have to alternate between complementary frames.

Developmental Trajectories in the Understanding of Everyday Uncertainty Terms

Dealing with uncertainty and different degrees of frequency and probability is critical in many everyday activities. However, relevant information does not always come in the form of numerical estimates or direct experiences, but is instead obtained through qualitative, rather vague verbal terms (e.g., "the virus often causes coughing" or "the train is likely to be delayed"). Investigating how people interpret and utilize different natural language expressions of frequency and probability is therefore crucial to understand reasoning and behavior in real-world situations. While there is considerable work exploring how adults understand everyday uncertainty phrases, very little is known about how children interpret them and how their understanding develops with age. We take a developmental and computational perspective to address this issue and examine how 4- to 14-year-old children and adults interpret different terms. Each participant provided numerical estimates for 14 expressions, comprising both frequency and probability phrases. In total we obtained 2856 quantitative judgments, including 2240 judgments from children. Our findings demonstrate that adult-like intuitions about the interpretation of everyday uncertainty terms emerge fairly early in development, with the quantitative estimates of children converging to those of adults from around 9 years on. We also demonstrate how the vagueness of verbal terms can be represented through probability distributions, which provides additional leverage for tracking developmental shifts through cognitive modeling techniques. Taken together, our findings provide key insights into the developmental trajectories underlying the understanding of everyday uncertainty terms, and open up novel methodological pathways to formally model the vagueness of probability and frequency phrases, which are abundant in our everyday life and activities.

Eye-tracking evidence for fixation asymmetries in verbal and numerical quantifier processing

When people are given quantified information (e.g., ‘there is a 60% chance of rain’), the format of quantifiers (i.e., numerical: ‘a 60% chance’ vs. verbal: ‘it is likely’) might affect their decisions. Previous studies with indirect cues of judgements and decisions (e.g., response times, decision outcomes) give inconsistent findings that could support either a more intuitive process for verbal than numerical quantifiers or a greater focus on the context (e.g., rain) for verbal than numerical quantifiers. We used two pre-registered eye-tracking experiments (n(1) = 148, n(2) = 133) to investigate decision-making processes with verbal and numerical quantifiers. Participants evaluated multiple verbally or numerically quantified nutrition labels (Experiment 1) and weather forecasts (Experiment 2) with different context valence (positive or negative), and quantities (‘low’, ‘medium’, or ‘high’ in Experiment 1 and ‘possible’, ‘likely’, or ‘very likely’ in Experiment 2) presented in a fully within-subjects design. Participants looked longer at verbal than numerical quantifiers, and longer at the contextual information with verbal quantifiers. Quantifier format also affected judgements and decisions: in Experiment 1, participants judged positive labels to be better in the verbal compared to the equivalent numerical condition (and to be worse for negative labels). In Experiment 2, participants decided on rain protection more for a verbal forecast of rain than the equivalent numerical forecast. The results fit the explanation that verbal quantifiers put more focus on the informational context than do numerical quantifiers, rather than prompting more intuitive decisions.

Cultivating credibility with probability words and numbers

Recent research suggests that communicating probabilities numerically rather than verbally benefits forecasters’ credibility. In two experiments, we tested the reproducibility of this communication-format effect. The effect was replicated under comparable conditions (low-probability, inaccurate forecasts), but it was reversed for low-probability accurate forecasts and eliminated for high-probability forecasts. Experiment 2 further showed that verbal probabilities convey implicit recommendations more clearly than probability information, whereas numeric probabilities do the opposite. Descriptively, the findings indicate that the effect of probability words versus numbers on credibility depends on how these formats convey directionality differently, how directionality implies recommendations even when none are explicitly given, and how such recommendations correspond with outcomes. Prescriptively, we propose that experts distinguish forecasts from advice, using numeric probabilities for the former and well-reasoned arguments for the latter.

Study on the Relationship between Worker States and Unsafe Behaviours in Coal Mine Accidents Based on a Bayesian Networks Model

Unsafe behaviours, such as violations of rules and procedures, are commonly identified as important causal factors in coal mine accidents. Meanwhile, a recurring conclusion of accident investigations is that worker states, such as mental fatigue, illness, physiological fatigue, etc., are important contributory factors to unsafe behaviour. In this article, we seek to provide a quantitative analysis on the relationship between the worker state and unsafe behaviours in coal mine accidents, based on a case study drawn from Chinese practice. Using Bayesian networks (BN), a graphical structure of the network was designed with the help of three experts from a coal mine safety bureau. In particular, we propose a verbal versus numerical fuzzy probability assessment method to elicit the conditional probability of the Bayesian network. The junction tree algorithm is further employed to accomplish this analysis. According to the BN established by expert knowledge, the results show that when the worker is in a poor state, the most vulnerable unsafe behaviour is violation, followed by decision-making error. Furthermore, insufficient experience may be the most significant contributory factor to unsafe behaviour, and poor fitness for duty may be the principal state that causes unsafe behaviours.

Research participants' preferences for receiving genetic risk information: a discrete choice experiment

PURPOSE

This study aims to determine research participants' preferences for receiving genetic risk information when participating in a scientific study that uses genome sequencing.

METHODS

A discrete choice experiment questionnaire was sent to 650 research participants (response rate 60.5%). Four attributes were selected for the questionnaire: type of disease, disease penetrance probability, preventive opportunity, and effectiveness of the preventive measure. Panel mixed logit models were used to determine attribute level estimates and the heterogeneity in preferences. Relative importance of the attribute and the predicted uptake for different information scenarios were calculated from the estimates. In addition, this study estimates predicted uptake for receiving genetic risk information in different scenarios.

RESULTS

All characteristics influenced research participants' willingness to receive genetic risk information. The most important characteristic was the effectiveness of the preventive opportunity. Predicted uptake ranged between 28% and 98% depending on what preventive opportunities and levels of effectiveness were presented.

CONCLUSION

Information about an effective preventive measure was most important for participants. They valued that attribute twice as much as the other attributes. Therefore, when there is an effective preventive measure, risk communication can be less concerned with the magnitude of the probability of developing disease.

Communicative Functions of Directional Verbal Probabilities: Speaker's Choice, Listener's Inference, and Reference Points

Verbal probabilities have directional communicative functions, and most can be categorized as positive (e.g., “it is likely”) or negative (e.g., “it is doubtful”). We examined the communicative functions of verbal probabilities based on the reference point hypothesis According to this hypothesis, listeners are sensitive to and can infer a speaker's reference points based on the speaker's selected directionality. In four experiments (two of which examined speakers’ choice of directionality and two of which examined listeners’ inferences about a speaker's reference point), we found that listeners could make inferences about speakers’ reference points based on the stated directionality of verbal probability. Thus, the directionality of verbal probabilities serves the communicative function of conveying information about a speaker's reference point.

Seeing What You Want to See: How Imprecise Uncertainty Ranges Enhance Motivated Reasoning

In this article, we consider a novel criterion for evaluating representations of uncertainty ranges, namely, the extent to which a representation enhances motivated reasoning. In two studies, we show that perceptions of the distribution underlying ambiguous numerical ranges are affected by the motivations and worldviews of end users. This motivated reasoning effect remained after controlling for objective numeracy and fluid intelligence but was attenuated when the correct interpretation was made clear. We suggest that analysts and communicators explicitly consider the potential for motivated evaluation when evaluating uncertainty displays.

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.

To what extent do politeness expectations shape risk perception? Even numerical probabilities are under their spell!

Politeness theory posits that uncertainty quantifiers can be interpreted as hedging strategies and thus be perceived as communicating greater certainty than when they are interpreted as likelihood-communication devices. This has only been tested with verbal probabilities (e.g., it is possible). The present paper aims to test whether numerical probabilities can also be interpreted as face-management devices and to investigate the effect of such an interpretation on risk perception. Four experiments focused on the effect of interpretations of numerical probabilities in negative outcome predictions on risk perception (e.g., there is a 50% probability that your stocks will lose their value). Politeness expectation was manipulated by the personality of the speaker (i.e., blunt vs. tactful, Experiments 1 and 2) and according to the conversational partners' need for politeness (Experiments 3 and 4). Results show that numerical probabilities, like verbal ones, were interpreted as likelihood-communication or face-management devices and that the two interpretations led to different risk perceptions. Findings were replicated with different formats, such as percentage (e.g., 50%) and chance ratio (e.g., 1 chance in 3) and with different degrees of certainty (e.g., .30, .50 and .70). Theoretical and practical implications relevant to risk communication are presented and discussed.

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

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