Affective and Cognitive Factors Influencing Sensitivity to Probabilistic Information
Abstract
In study 1 different groups of female students were randomly assigned to one of four probabilistic information formats. Five different levels of probability of a genetic disease in an unborn child were presented to participants (within-subject factor). After the presentation of the probability level, participants were requested to indicate the acceptable level of pain they would tolerate to avoid the disease (in their unborn child), their subjective evaluation of the disease risk, and their subjective evaluation of being worried by this risk. The results of study 1 confirmed the hypothesis that an experience-based probability format decreases the subjective sense of worry about the disease, thus, presumably, weakening the tendency to overrate the probability of rare events. Study 2 showed that for the emotionally laden stimuli, the experience-based probability format resulted in higher sensitivity to probability variations than other formats of probabilistic information. These advantages of the experience-based probability format are interpreted in terms of two systems of information processing: the rational deliberative versus the affective experiential and the principle of stimulus-response compatibility.
1. INTRODUCTION
In many domains, there is the problem of how to present information on the likelihood of various events against which people have to choose an appropriate (commensurate) level of protection. Examples are informing people about the likelihood of accidents associated with various technologies. In a medical context, there is the question of informing patients about the probability of various diseases, etc. Generally, people who are not trained in statistics and the concepts of probability are not particularly good at understanding and evaluating probabilistic information. In particular, people have serious problems with estimating small probabilities, such as the likelihood of having a child with a genetic disease, power plant accident, etc. These problems concern (1) people's overrating small probabilities, and (2) insensitivity to changes in the magnitude of these probabilities.
There have been a lot of findings about the phenomenon of overrating small probabilities. In the 1950s, Attneave(1) found that the estimations of English letters were highly correlated with actual frequencies of these letters in English. However, his subjects overestimated frequencies of infrequent letters and underestimated frequencies of frequent letters. Similarly, Lichtenstein, Slovic, Fischhoff, Layman, and Combs(2) in their study on judgments of frequency of various causes of death found that rare causes of death were overestimated and common causes were underestimated. Finally, as shown in Fig. 1, one of the central assumptions of prospect theory is that in risky situations people underweight moderate and large probabilities but overweight rare events. Several empirical studies(3-5) confirmed these properties of the prospect theory probability weighting function. Most likely, such a probability weighting function is related to people's overrating small probabilities.
Hypothetical probability weighting function.
The problem of insensitivity to changes in magnitude of small probabilities was extensively studied by Kunreuther et al.(6) They tried various ways to improve people's sensitivity to very low probabilities (e.g., of hypothetical discharge of toxic chemicals by a plant). The authors found that the best way of communicating probabilities to ordinary people is to make available comparison stories (scenarios), which allow them to judge differences between probabilities.
A somewhat similar result was obtained by Siegrist et al.(7) They compared the effectiveness of four different formats (both graphical and numerical) of risk communication. The authors found that only the paling perspective scale resulted in the subject discriminating between two different levels of risk of having a newborn with Down's syndrome. In this format (similar to that used by Kunreuther(6)), the subject could compare communicated risk with other risks, such as any chromosomal anomaly or major congenital anomaly. Thus, again the availability of comparisons allowed one to judge differences between probabilities. Still, as shown by Ancker, Weber, and Kukafka,(8) even different arrangement of stick figures representing health risks may have an impact on perception of the risk.
In the present article, we focus on how to improve judgments of low probabilities in the context of medical diagnosis. More specifically, we deal with the question of how to improve in communicating information about the probability of Down's syndrome—a genetic condition caused by extra genes from the 21st chromosome that result in certain characteristics including some degree of mental retardation, or cognitive disability, and other developmental delays. Two types of factors that potentially improve differentiation between low probabilities are considered cognitive and affective factors.
There is evidence that different ways of communicating the same information about probability can change its perception. Gigerenzer and his collaborators(9,10) claim that frequencies are better understood by people than probabilities or percentages. For example, people can easily understand the meaning of the statement that 3 people in 100 have a certain disease, while some may have problems with adequately understanding the statement that 3% of persons have this disease. Gigerenzer and his collaborators,(9,10) as well as Cosmides and Tooby,(11) claim that in the natural environment, people encounter frequencies of actual events and that they store and operate on this information.
However, Denes-Raj and Epstein(12) showed that when offered a choice between two bowls with one containing 9 in 100 winning beans and another one containing 1 winner in 10, many participants preferred the first bowl. Thus, participants preferred a greater absolute number rather than a better proportion of winning beans. Similarly, when Yamagishi(13) asked respondents to evaluate a risk of death in the population due to different causes, he found that the judged degree of riskiness was affected by the number of deaths but not by the proportion of fatal cases caused by a given disease. It turned out that people perceived the risk as higher when a given number of fatal cases was greater, irrespective of the total number possible. For example, the judged degree of riskiness was perceived higher when the proportion of fatal cases was given in reference to 10,000 (e.g., 1,286 cases out of 10,000) than in reference to 100 (e.g., 12.86 cases out of 100). Thus, frequencies can be misperceived as well.
It is interesting that both proponents of “natural” frequencies(9) as well as proponents of comparison stories(6) used numbers when presenting people information about the probability (or frequency), and also when asking them to evaluate the risk. Contrary to this, and in line with Cosmides and Tooby,(11) one can think that during their evolution, humans made their decisions using no numbers at all, but based on frequencies encoded and stored in memory from their trial-by-trial experience.
As already mentioned, there is a somewhat forgotten series of experiments started in the 1950s (see, e.g., Attneave(1)) that shows that when people are presented with sequential displays of binary events (such as letters, words, lights, etc.), without mentioning any numbers, their estimations of frequency of occurrence are remarkably accurate. For example, Hintzman(14) presented to his subjects a list of short words in which some words were repeated. Following the presentation, subjects were tested to estimate frequencies of occurrence of different words. The respondents turned out to be very sensitive to actual frequencies of occurrence of the words (for an overview of some early research, see Peterson and Beach(15)).
Most recently Hertwig, Barron et al.(16) made a differentiation between decisions from descriptions and decisions from experience. People make decisions from descriptions when the outcome of each option and the probabilities of this outcome are provided, and the information is conveyed visually (e.g., using a pie chart or frequency distribution). People make decisions from experience when they rely on personal experience, without a description of possible outcomes (e.g., whether to back up a computer's hard drive, cross a busy street, or go out on a date). Hertwig et al.(16) claim that decisions from experience and decisions from description can lead to dramatically different choice behavior. In the case of decisions from description, people make choices as if they overrated the probability of rare events, as described by prospect theory. On the other hand, in the case of decisions from experience, people make decisions as if they underrated the probability of rare events.
From the above findings and the claim of Cosmides and Tooby(11) that in their natural environment humans are accustomed to making decisions based upon experience, i.e., on naturally encountered frequencies, one could suppose, that with the experience-based probability format, people would be more accurate in their assessments than with any numerical format. On the basis of this general assumption, we formulated two hypotheses.
Hypothesis 1 is based on the following reasoning: with a numerical format, people tend to overrate the probabilities of rare events. On the other hand, with the experience-based probability format, people should be more accurate in evaluating the probability of rare events than with numerical formats. Assuming that the evaluation of riskiness is based on the perceived probability of the events, we predict the following:
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Hypothesis 1: Under the experience-based probability format, evaluations of riskiness associated with rare events will be lower than those under other formats of probabilistic information (e.g., percentages, frequency).
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Hypothesis 2: Compared to other formats of probabilistic information (e.g., percentages, frequency), in their perception, people will be most sensitive to probability variations when observing a sequence of events (experience-based probability).
Recent research shows that when outcomes of risky choices are heavily emotionally laden, subjects become insensitive to probability variations. Indeed, Hsee and Rottenstreich(17) showed that the shape of prospect theory's S-shaped weighting function changes, depending on the affective reactions associated with the potential outcomes of risky choices. They demonstrated that affect-rich outcomes (those evoking strong emotional reactions), as opposed to affect-poor ones, resulted in lower sensitivity to intermediate probability variations. In other words, the S-shaped weighting function becomes flatter for affect-rich outcomes (see Fig. 2).
Hypothetical S-shape probability weighting function for affect-poor and affect-rich stimuli.
In line with such findings, Loewenstein et al.(18) proposed the “risk-as-feelings” model, according to which, affect, experienced at the moment of decision making, influences risk assessments. Following this line of research, we decided to test whether the insensitivity to probability variations for emotionally laden stimuli concerns not only the weighting function, but also the perception (estimation) of probability. We formulated the following hypothesis:
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Hypothesis 3: In their perception of risk, people are more sensitive to probability variations when the event is less emotionally laden.
2. STUDY 1
2.1. Method
2.1.1. Participants and Procedure
Female students (N = 161) enrolled at Warsaw Agricultural University participated in the study. The women's age ranged between 20 and 25 years.1 Participants were requested to read the following instruction:
“Please imagine, that you plan to have a child. You go for genetic consulting and during the visit the doctor informs you that there is a risk of a genetic disease in your child.”
After that, participants were given probabilistic information of a genetic disease in a newborn child. Depending on experimental conditions, probabilistic information was communicated via different formats.
As one can see in Table I, the participants were randomly assigned to one of five experimental conditions. Conditions differed in respect to the format in which the probabilistic information was presented. In conditions 1 and 2, we used the same communication format. The only difference between them was the photo of a child with a genetic disease. In addition to mental retardation and other developmental delays, some common physical traits of Down's syndrome are an upward slant of the eyes, flattened bridge of the nose, and decreased muscle tone. Consequently, our two photos of a child with Down's syndrome differed with respect to some of these physical traits. In condition 1 the moderate form of genetic disease was presented (in this way evoking low affective stimuli), whereas in condition 2 the severe one was presented (in this way evoking high affective stimuli). The outcomes of the events were randomized for each of the five probability levels. Photographs were presented repeatedly for 0.7 seconds each, with 0.2 seconds interval between them. Thus, the total presentation lasted less than two minutes.
| Condition | Communication Format (Between Subjects) | Specification | Five Probability Levels (Within Subjects) |
|---|---|---|---|
| 1 | Experience based with weaker affective stimuli | A sequence of 100 binary events represented by two photos—one of a healthy child and the other of a child with a moderate form of Down's syndrome | 0.01 |
| 2 | Experience based with stronger affective stimuli | A sequence of 100 binary events represented by two photos—one of a healthy child and the other of a child with a severe form of Down's syndrome | 0.03 |
| 3 | Frequency | Explicitly expressed frequency (e.g., three in one hundred) | 0.06 |
| 4 | Scenario | “Balls in the urn” scenario (e.g., 3 black balls and 97 white balls) | 0.12 |
| 5 | Graphical representation | A chart with 100 (graphic) images, representing the proportion of healthy to unhealthy children | 0.20 |
In the frequency format, the number of occurrences of a child with Down's syndrome out of 100 was presented. In the scenario format, the number of black balls (representing a child with Down's syndrome) in the urn containing 100 balls was presented. In the graphical representation format, a chart with 100 (graphic) images—some of which were red and some of which were green—representing the proportion of healthy to unhealthy children was presented.
Using the formats five different types of probabilistic information were communicated. After each one, participants were requested to indicate in the specially created questionnaire: (1) the acceptable level of pain they would tolerate to avoid the disease,2 (2) subjective evaluation of the disease risk, and (3) subjective evaluation of being worried by this risk. Participants answered on a visual analog scale. As for the declared acceptable level of pain, participants indicated the most intense pain level they would tolerate suffering as mothers to prevent a given risk of the genetic disease in their child. Similarly, subjective evaluation of the risk that the disease will occur was measured on a visual analog scale ranging from “complete lack of risk” to “extremely high risk.” Finally, subjective evaluation of being worried by the possibility of the disease was also measured on a visual analog scale ranging from “extremely calm” to “extremely anxious.”
Between each evaluation of probability, participants had a three-minute break during which they were listening to a fragment of a poem (as an experimental filler).
2.2. Results
We did not find any differences between less and more affectively laden groups under the experience-based probability format. Therefore, in the analyses below we put together the data from these two groups. Since one of our three dependent measures, that of subjective evaluation of riskiness, revealed a different pattern of results than the two other measures, first we present analyses on the scale of pain and the scale of worry, and separately for the evaluation of riskiness. Figs. 3 and 4 represent average evaluations of the five risk levels on the scales of pain and worry in the four probability formats. As can be seen, in comparison with other communication formats, under the experience-based probability format, participants were less worried by the risk of the disease, and accepted a lower level of pain that they would tolerate to avoid the disease. One-way ANOVA for four information formats, with five risk levels as a repeated factor performed on evaluations on the scale of pain and worry, revealed significant effects of both level of risk (F[4;157]= 25.71; p < 0.001 for the scale of pain, and F[4;157]= 73.28; p < 0.001 for the scale of worry) and information format (F[3;157]= 5.24; p < 0.01 for the scale of pain, and F[3;157]= 3.98; p < 0.01 for the scale of worry).
Average evaluations of the five risk levels on the scale of pain in the four formats of communicating probabilistic information.
Average evaluations of the five risk levels on the scale of worry in the four formats of communicating probabilistic information.
Thus, our results confirm hypothesis 1 that under the experience-based probability format evaluations of riskiness associated with rare events were lower than under any other format of probabilistic information. Assuming that evaluations on both scales are based on perceived probability of the disease, our results imply that under the experience-based probability format, people's evaluations of rare events were less overrated than under any other format of probabilistic information.
Regarding the evaluation of riskiness, the one-way ANOVA for four information formats, with five risk levels as a repeated factor, revealed significant effects of information format (F[3;157]= 3.08; p < 0.05). However, in this case evaluations of riskiness associated with rare events were lowest for the frequency format of probability. As we will see in study 2, this effect was not replicated; therefore, we tend to attribute this to the vagueness of the notion of “risk” in ordinary people's cognition.
In accordance with our hypothesis 2, one should also expect an interaction effect of the information format and the level of risk. However, one-way ANOVA for four information formats, with five risk levels as a repeated factor, performed on evaluations on the scale of pain and worry, revealed no significant interaction effects. Thus, the data did not support hypothesis 2 that, compared to other formats of probabilistic information (e.g., percentages, frequency), in their perception people will be most sensitive to probability variations when they observe a sequence of events (experience-based probability).
As already mentioned, we also did not confirm hypothesis 3 that under the experience-based probability format, people are more sensitive to probabilistic information when it is less affectively laden.
2.3. Discussion
We confirmed the hypothesis that under the experience-based probability format, evaluation of worry and other reactions to riskiness associated with rare events were lower than under numerical formats of probabilistic information. This may imply that under the experience-based probability format, people's evaluations of small probabilities were less overrated than under any other format. However, our procedure did not allow us to directly test this claim. Still, our result is in agreement with findings by Hertwig et al.,(16) who showed that people overestimated the probabilities of rare events when they were taken from descriptions and underestimated these probabilities when they came from participants’ direct experience. Although we did not study how people weigh the probability of rare events in making decisions, and instead studied subjectively perceived probabilities, we think that our finding is pertinent to the problem raised by Hertwig et al.(16) These authors explain the underweighting of rare events probability learned from experience by the fact that respondents tended to draw too few samples (median draws per problem = 15), which led to skewed distributions and to less frequent occurrences of the rare event than in reality. Our results demonstrate that Hertwig's(16) explanation is not sufficient. In our study, participants did not choose how many draws they would take to learn the distribution; instead, each participant experienced the same sequence of 100 events with a specified number of minority events (1%, 3%, etc.).
Thus, people's underweighting of a rare event probability under its numerical format must be an effect of more basic cognitive processes than limited search effort and the resulting skewed observed distributions. We believe it may be related to how probabilistic information expressed in different formats is processed. As is well known, human cognition works through two distinct processes: system 1, which corresponds to intuitive thought, and system 2, which corresponds to rational thought.(18-21) In Kahneman's(20) words: The operations of system 1 are fast, automatic, effortless, associative, and often emotionally charged … The operations of system 2 are slower, serial, effortful, and deliberately controlled … .
Following this distinction, we can assume that when the experience-based format (where no numbers are involved) is used, it originates in operations of system 1, which generates automatic, effortless impressions. On the other hand, processing of numbers concerns the deliberative mode of thinking. It requires the individual to have specific knowledge and abilities. Indeed, as shown by Peters et al.,(15) in these type of tasks high-numeracy people have an advantage over those with low numeracy. Still, both groups of people have problems with mental arithmetic.(22)
Now, the question remains which of the two systems facilitates processing of probabilistic information? As research shows, information processing is strongly affected by stimulus-response compatibility.(23,24) As shown by Fischer and Hawkins(25) one of the categories of compatibility is scale compatibility (see also Hawkins(26)), i.e., the similarity between input and output. Generally speaking, stimulus-response compatibility facilitates performance (in both judgments and decision making).
One can assume that in our case, where individuals were faced with the tasks of assessment regarding being worried by the possibility of the disease, or accepting pain to avoid the child's possible disease, system 1 is activated. Thus, we can expect the experience-based format of probability to be more compatible with such output, compared to numerical formats of probability presentation. This input-output compatibility should result in more accurate evaluations.
Naturally, when looking at participants’ levels of worry and willingness to tolerate pain, there is no way to directly assess the accuracy of the evaluation of risk levels. Neither are we able to directly test whether people's evaluations of rare events were over- or underrated. However, we found that when the experience-based format was used, people's assessments of worry, etc. were lower than when numerical formats were used. From earlier research, we know that when using numerical formats people tend to overrate the probabilities of rare events. From this we can infer that people's evaluations of the probabilities of rare events when using the experience-based format are perhaps less overrated than when using numerical formats. In this sense one can claim that when using the experience-based probability format, people's evaluations of risk levels are more accurate than when using numerical formats.
However, our study did not support the hypothesis that people would be more sensitive to probabilistic information with the experience-based probability format, as compared to the numerical formats of probabilistic information. Neither did we find that people were less sensitive to probabilistic information when the stimulus was affectively laden.
The question remains how probabilistic information is represented under graphical representation. On the one hand, in this format, probabilities are not expressed in numbers. Yet on the other hand, upon seeing a graphical representation consisting of two kinds of elements, the observer can easily translate the observed proportions into numbers. In any case, this format is not the equivalent to sequentially learned experienced frequencies. Our results suggest that the graphical representation format is closer to the numerical formats than to the experience-based format.
Of course, it is possible that the strength of our experimental manipulation was inadequate. The two photos of a child with a genetic disease possibly did not differ enough to evoke lower versus higher affective reactions. However, the lack of a difference in sensitivity to probability variations between groups, in response to more versus less emotionally loaded stimuli, could be characteristic of the experience-based probability format, whereas not of the other formats. We decided to test this conjecture in the next experiment.
3. STUDY 2
The purpose of study 2 was to test the difference in sensitivity to probability variations, under different probability formats, for emotionally laden stimuli. It is well known that emotionally loaded stimuli often deteriorate performance. Indeed, Hsee and Rottenstreich(17) showed that when stimuli were strongly emotionally loaded, individuals were insensitive to probability variations. Moreover, one can speculate that emotionally loaded stimuli deteriorate performance when they require a sufficiently substantial cognitive effort, while they need not deteriorate performance if the task does not require such an effort. For this very reason, in some judgmental tasks, stimulus-response compatibility facilitates performance, while in other tasks it does not. It does so when the task requires substantial cognitive effort. In such tasks, the stimulus-response compatibility simply reduces cognitive effort.
Similarly, stimulus-response compatibility may be an important factor in the assessment of worry, or other feelings of riskiness. The assessment of worry seems to be more compatible with the direct experience of the frequency of dangerous events in system 1, than with deliberate reasoning about the probability of dangerous events when this is presented in a numerical format in system 2. Therefore, the assessment of worry, etc. when it originates in system 1 should be less affected by emotional distortion than assessment of worry when it originates in system 2. In line with the above reasoning, we formulated the following hypothesis:
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Hypothesis 4: For the emotionally laden stimuli, the experience-based probability format will result in higher sensitivity to probability variations than other formats of probabilistic information.
3.1. Method
3.1.1. Participants and Procedure
Female students (N = 176) enrolled at two Warsaw universities were randomly assigned to one of the six experimental conditions. The instruction and procedure of study 2 were similar to those of study 1. However, three formats of communicating probabilistic information (experienced-based, frequency, scenario) were employed, instead of the four in study 1.
Each of the three formats was employed in two variants. In variant 1 participants were informed about the probability without seeing a photo of a child, whereas in variant 2 in addition to information on probability, participants were shown a photo of a child with a severe case of Down's syndrome.
Thus, in the case of the experience-based format, participants were presented with a sequence of 100 labels “healthy child” and “unhealthy child” in variant 1, or a sequence of 100 photos of a child without Down's syndrome and with Down's syndrome in variant 2. In the frequency and in the scenario formats, in the case of the emotionally laden stimuli, a photo of a child with Down's syndrome was presented in addition to the corresponding numerical information.
After learning the probabilistic information about a genetic disease, the participant was asked to fill in a questionnaire—similar to the procedure in the first study. Also, as in the first study, between each evaluation of probability, participants had a three-minute break during which they listened to a fragment of a poem (as an experimental filler).
3.2. Results
5, 6 and 7 represent the mean evaluations of risk levels (averaged over five risk levels) on the scales of pain, worry, and risk in the three probability formats, for the affect-poor (without photo) and affect-rich stimuli (being shown a photo of child with a severe form of Down's syndrome). As is visible, evaluations on pain, worry, and risk are higher for the affect-rich than for the affect-poor stimuli. Performing two-way ANOVA (two levels of emotionally laden stimuli × three formats of communicating probabilistic information, with five risk levels as repeated factor) on the scores on the scale of pain, worry, and risk revealed significant effects of affect for the scale of pain (F[1;170]= 11.27; p < 0.001), for the scale of worry (F[1;170]= 12.00; p < 0.001), and for the scale of risk (F[1;170]= 12.27; p < 0.001). Similarly, the analysis revealed significant effects of format for the scale of pain (F[2;170]= 13.90; p < 0.001), for the scale of worry (F[2;170]= 9.46; p < 0.001), and for the scale of risk (F[2,170]= 6.93; p < 0.001). As can be seen, compared to other communication formats, evaluations of risk are generally lowest under the experience-based probability format. Finally, for both scales, the analysis revealed significant affect–format interaction effects (for the scale of pain F[2;170]= 4.16; p < 0.05, for the scale of worry F[2;170) = 5.67; p < 0.01), and for the scale of risk (F[2,170]= 5.39; p < 0.01). For pain, worry, and risk the differences in evaluations between affect-rich and affect-poor stimuli were higher under both numerical formats than for the experience-based probability format.
Mean evaluation scores (averaged over five risk levels) on the scale of pain in the three formats of communicating probabilistic information for the affect-poor (without picture) and affect-rich stimuli (with picture).
Mean evaluation scores (averaged over five risk levels) on the scale of worry in the three formats of communicating probabilistic information for the affect-poor (without picture) and affect-rich stimuli (with picture).
Mean evaluation scores (averaged over five risk levels) on the scale of risk in the three formats of communicating probabilistic information for the affect-poor (without picture) and affect-rich stimuli (with picture).
To further test the hypothesis concerning people's sensitivity to probability variations, we analyzed the differences between evaluations of the highest (0.20) and lowest (0.01) risk levels, on each of the scales separately. 8, 9, and 10 show these differences. As can be seen, for both numerical probability formats—frequency and scenario—participants were much less sensitive to changes in probability when they were shown a photo of a child with severe Down's syndrome versus not being shown the photo. On the other hand, such a difference was not observed in the case of the experienced probability format. Two-way ANOVA performed on differences between evaluations on the scale of pain (two levels of emotionally laden stimuli × three information formats) revealed a significant affect effect (F[1;170]= 7.20; p < 0,01). At the same time, there was a significant format–affect interaction effect (F[2;170]= 4.46; p < 0.05). Similarly we found a significant affect effect for the scale of worry (F[1;170]= 12.57; p < 0.001) and for the scale of risk (F[1;170]= 8.99; p < 0.001), and significant interaction format–affect effect for the scale of worry (F[2;170]= 9.74; p < 0.001) and for the scale of risk (F[2;170]= 5.78; p < 0.01). Thus, while in the case of less emotionally laden stimuli, sensitivity to probabilistic information did not differ between various formats, in the case of more emotionally laden stimuli, the assessments were more sensitive to probability changes under the experience-based probability format than under the two other formats (frequency and scenario).
The difference between evaluations of the highest (0.20) and lowest (0.01) risk levels on the scale of pain for affect-rich and affect-poor stimuli.
The differences between evaluations of the highest (0.20) and the lowest (0.01) risk levels for the scale of worry for affect-rich and affect-poor stimuli.
The differences between evaluations of the highest (0.20) and the lowest (0.01) risk levels for the scale of risk for affect-rich and affect-poor stimuli.
3.3 Discussion
The results of our second experiment show the advantage of the experienced probability format over other probability formats is particularly prominent when the risk being evaluated is affectively laden. Indeed, it turned out that only with the experience-based probability format, the subjects’ evaluations of risk were not affected by how heavily emotionally laden the stimulus was. Our interpretation of this finding is that when the experience-based format (where no numbers are involved) is used, it originates in operations of system 1, which generates automatic, effortless impressions. On the other hand, when probabilities are presented in a numerical format, it originates in deliberate reasoning in system 2.
Some support for this claim can be found in probability learning experiments. In these tasks, participants are presented with a repeated choice between two responses, one of which has a higher payoff probability than the other (e.g., 70% vs. 30%). The participant is required to predict which of two events will occur in each trial. In these tasks it is commonly observed that participants match their response probabilities to the payoff probabilities. Such a probability matching strategy is obviously suboptimal. (Optimal is a pure strategy to consistently choose the more frequent response.) What is, however, important in the present context is that probability matching implies that subjects learn the stimuli probabilities exceptionally well. What is even more important, probability matching behavior is also observed in experiments with animals.
We further assume that the assessment of worry, or other feelings of riskiness, is more compatible with the experience of frequency of dangerous events in system 1 than with deliberate reasoning about the probability of a dangerous event when this is presented in a numerical format in system 2. Therefore, the assessment of worry, etc. when it originates in experience of frequency is easier than the assessment of worry, etc. when it originates in deliberate reasoning in system 2. As a result, the assessment of worry, etc. when it originates in system 1 is less affected by emotional distortion than the assessment of worry, etc. when it originates in system 2
Therefore, under the experienced probability format, people's evaluations could be sensitive to frequency information, regardless of how emotionally laden the stimulus is, whereas under the numerical formats, evaluations were more affected by emotional distortion, and thus less sensitive to frequency information.
However, it is also possible that under the experience-based probability format, repeated presentation of the same emotionally laden stimulus (photo of a child with Down's syndrome) could result in emotional habituation, thus the difference between evaluating affect-poor and affect-rich stimuli disappeared. The present experiments do not allow us to decide which of the above explanations is correct. Further research is needed to answer this question. Similarly of interest to future research would be the claim that when the individual is required to make a cognitive assessment, the rational system should be better than the experiential system at extracting frequency information from the probability presentations.
4. GENERAL DISCUSSION
Our results show some advantages of using the experience-based format for communicating probabilistic information. Firstly, the experience-based probability format seems to weaken the tendency to overrate the probability of rare events. Secondly, under all but the experience-based probability format, people are less sensitive to probabilistic information when it is affectively laden. These are two important advantages, as people's overrating of small probabilities and their insensitivity to probability variations in the case of emotionally laden stimuli seem to be the two most serious problems concerning communicating probabilities to ordinary people.
Where do these advantages of using the experience-based format for probability information come from? According to Cosmides and Tooby,(11) in the evolutionary process, humans had to develop mechanisms allowing them to utilize frequency information (e.g., when going hunting for game in a given direction, you were successful in 5 out of 20 hunts). In any case, there is much evidence that people easily learn frequencies from their environment and use this when performing various tasks. For example, research on reading shows that the frequency with which words are used strongly influences the speed of reading.(27) Hasher and Zacks(28) showed that even very young (preschool) children encode frequency information accurately. They also found no developmental differences in the accuracy of judgments about frequency. Based on these findings, the authors claim that frequency is automatically encoded and stored in human memory.
Gigerenzer and his collaborators(9,10) claim that the “natural” format for probability information is the frequency (“as actually experienced in a series of events, rather than probabilities or percentages,” p. 5). We certainly agree with this claim. However, we are surprised that in their experiments, these authors did not present “actual series of events” to their subjects, but numbers—although in the format of frequencies rather than probabilities or percentages. Our results show that what really matters is whether one uses numbers (frequencies or probabilities or percentages) or an “actual series of events.” We think that only in the latter case can people fully comprehend the meaning of frequencies. Thus, information on probability should be presented not in the form of numbers, but as a sequential display of events. As our research shows, only this format facilitates the accuracy of evaluating the risk level, as well as sensitivity to probability variations.
Naturally, there are also disadvantages to using an experience-based format. First, using this format to communicate probabilities requires a certain amount of time. Actually, not very much time is needed, as shown in our experiment. The more serious disadvantage for practitioners is the need to prepare material fitting events, the probability of which we want to communicate. More specifically, one has to construct a series of events corresponding to the problem in question. For example, a physician could prepare a series similar to the one used in our experiment (a sequence of pictures of a child with the disease versus a child without the disease), and present this to patients (or parents) interested in knowing the risk of birthing a child with a given disease. Still, such a procedure seems to be superior over the one proposed by Kunreuther, Novemsky, and Kahneman,(6) which requires looking for familiar context information to create appropriate comparison stories (scenarios). Perhaps, the most serious problem with using an experience-based format is that it is not suitable for cases dealing with extremely small probabilities, such as considered by Kunreuther et al.(6) One cannot feasibly produce a series when the event of interest occurs once in a million, etc. So perhaps for such cases, the procedure proposed by Kunreuther et al.(6) is necessary.
Footnotes
ACKNOWLEDGMENTS
The authors thank two anonymous reviewers for their helpful comments on the earlier version of this article. This article is based on work supported by EC Contact LSHB-CT-2004-505243, “Special Non-Invasive Advances in Foetal and Neonatal Evaluation Network” (SAFE).
