the effect of catastrophe potential on the interpretation of numerical probabilities of the...

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

the Occurrence of Hazards'

BAS VERPLANKEN~ Department of Social Psyehology

University of Nijmegen Nijmegen. The Netherlands

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

Expressions of probability are often important elements of human communication, whether these are used in professional contexts or in everyday con- versation. For instance, a doctor informs her patient about the probabilities of success of a treatment, hurricane watchers give landfall probabilities for an area, researchers discuss the chances of acceptance of a paper, or someone judges whether or not it will rain tonight. Although there are cultural differences in probabilistic thinking (Wright et al., 1978), most languages include a variety of probability expressions, such asprobable, unlikely,possible, or good chance. We may also use numbers to express probabilities, for instance a one-

'The author wishes to thank Astrid Duits, Karin de Jager, Irene Kurpershoek, Marco Leons, Maria Witte, and Loes van Zijl for their contributions in conducting Study 1; and Dancker Daamen, Ad van Knippenberg, and Cees Wegman for their comments on earlier drafts of this paper.

*Correspondence concerning this article should be addressed to Bas Verplanken, Department of Social Psychology, University of Nijmegen, P.O. Box 9104, NL-6500 HE Nijmegen, The Netherlands. e-mail: [email protected].

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Journal of Applied Social Psychology, 1997, 27, 16, pp. 1453-1467. Copyright 0 1997 by V. H. Winston 8, Son, Inc. All rights reserved.

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out-of-five chance to get that job, or a probability of a nuclear power plant meltdown. Whether we use words or numbers to express probabilities, it is necessary to have sufficient consensus about the interpretation of such probabilistic statements in order to communicate effectively. Knowledge of how numerical probabilities are interpreted is important, because misunderstand- ings may not only hinder communication, but may lead to errors or wrong decisions. The present study focuses on the interpretation of numerical probabilities of hazards, and in particular on the role of catastrophe potential of hazards. The study thus addresses the interpretation of small numerical probabilities of occurrence of hazards, such as hazards that are associated with technological or natural disasters, accidents, or health-related behaviors.

Most studies that focus on the interpretation of probability expressions have participants associate numerical values to verbal probability expressions. For instance, Lichtenstein and Newman (1967) presented participants with 41 words and phrases that indicate probabilities, and asked them to give numerical equivalents between 0 and 1. Although the mean numerical values rep- resented the verbal rank order fairly well, there was large variability between participants and great overlap between terms. For instance, the mean numerical value that was attributed to the phrase rather unlikely was .24, but values ranged from .01 to .75 among participants. Lichtenstein and Newman’s study became one of many that demonstrated that the numerical interpretation of probability phrases may be highly ambiguous (e.g., Beyth-Marom, 1982; Brun & Teigen, 1988; Budescu & Wallsten, 1985; Clark, Ruffin, Hill, & Beamen, 1992; Hakel, 1968; Lichtenstein & Newman, 1967; Reagan, Mosteller, & Youtz, 1989; Simpson, 1963; Sutherland et al., 1991; Teigen, 1988b; Wallsten, Budescu, Rapoport, Zwick, & Forsyth, 1986; Zimmer, 1983). These studies suggest that individuals use some unidimensional scale of qualification when asked to interpret probability phrases (cf. Reyna, 1981), which seems to be relatively stable over time (e.g., Beyth-Marom, 1982; Budescu & Wallsten, 1985). On the other hand, individual differences exist, which may stem from the inherent vagueness of verbal probability expressions (Wallsten, Budescu, et al., 1986).

Whereas the elicitation of numbers in response to probability phrases has become a well-established research field, verbal qualifications of numerical probabilities (e.g., large, small) have received less attention. Yet, we are often confronted with numerical probabilities, for instance outcomes of risk analyses of technological projects, accident statistics, or communication about health risks. The present study thus focuses on the interpretation of numerically expressed probabilities in terms of their perceived magnitude.

Interpretations of probability expressions are not independent of context (cf. Parducci, 1968). One might even argue that, unless one focuses on rank

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orders, without a context, interpretations of probability expressions do not make much sense. Context may be provided, for instance, by the perceiver’s knowledge and experience (e.g., Beyth-Marom, 1982; Wallsten, Fillenbaum, & Cox, 1986), the goal of communication (e.g., Budescu & Wallsten, 1990), gain/loss frames (Budescu, Weinberg, & Wallsten, 1988), the presence of multiple alternatives (Teigen, 1988b), or the way that probabilities are presented (Stone, Yates, & Parker, 1994). An important category of context factors may be characteristics of the stimulus domain (e.g., Brun & Teigen, 1988; Wallsten, Fillenbaum, & Cox, 1986). In line with findings that properties of outcomes of events, for instance desirability, may influence probability judgments of those events (e.g., Delaney & Wallsten, 1977; Irwin, 1952; Irwin & Snodgrass, 1966; Svenson, 1975), it can be expected that interpretations of probability expressions can be affected by the nature of events as well. For instance, individuals tended to give higher numerical probabilities in response to verbal expressions when base rates of the respective events were perceived as high (Wallsten, Fillenbaum, & Cox, 1986; Weber & Hilton, 1990), or when risks were perceived as severe (Weber & Hilton, 1990).

It can be expected that characteristics of stimulus events, or stimulus hazards in the present context, may not only affect numerical interpretations of probability phrases, but also the perceived magnitude of numerical probabilities. The focus of the present study is on a cluster of qualitative characteristics of hazards, which may be summarized as the catastrophe potential of hazards. Some hazards, such as traffic accidents, imply the occasional occurrence of single or few fatalities, whereas other hazards involve one instance of sudden death of larger numbers of people, for instance an exploding chemical plant. Studies that addressed the perceptions of risks agree fairly well in distinguishing catastrophe potential as an important underlying dimension (e.g., Englander, Farago, Slovic, & Fischhoff, 1986; Fischhoff, Slovic, Lichtenstein, Read, & Combs, 1978; Johnson & Tversky, 1984; Slovic, Fischhoff, & Lichtenstein, 1985; Teigen, Brun, & Slovic, 1988; Vlek & Stallen, 1981). For instance, on the basis of principal components analysis, Fischhoff et al. found two dimensions that described individuals’ perceptions of risk characteristics concerning 30 activities and technologies. Characteris- tics that loaded on the first dimension were, for instance, voluntariness of the activity, immediacy of effects, personal control of avoiding death, newness, and catastrophe potential (i.e., whether a hazard might kill people one at a time, or large numbers of people at once). For example, pesticides and nuclear power typically were activities that were located at the high end of this dimension, while mountain climbing and alcoholic beverages were at the low end. The second dimension comprised perceived severity of consequences. Vlek and Stallen (1981) elicited judgments of riskiness of 26 activities.

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Multidimensional scaling revealed two underlying dimensions, which were interpreted as the size of a potential accident and the degree of organized safety regulations, respectively. Potentially catastrophic hazards, for instance chlo- rine trains or constructing a residential district near a petrochemical plant, loaded high on the first dimension; while activities involving individual or more chronic hazards, for instance car driving and eating fat, loaded low on that dimension.

It can be assumed that the risk dimensions that determine an individual’s perceptual space, which thus incorporates hazards of various activities and technologies, may provide a context that affects the interpretation of probability expressions. In the present Study 1, participants were presented with 30 hazards which were comparable to those of the risk perception studies cited above. Half ofthese comprise hazards that have catastrophe potential, while half of the stimuli comprise noncatastrophic hazards. Each hazard was accompanied by a numerical probability of occurrence, and participants were asked to give their interpretation of each probability on verbally labeled scales, ranging from vely small to vely large. It was expected that participants would judge a particular numerical probability as higher when it concerned hazards that have catastrophe potential, compared to noncatastrophic hazards.

Obviously, because the stimuli comprised real events, the catastrophic hazard set differed from the noncatastrophic set in more than catastrophe potential only. For instance, catastrophic events occur less frequently than do noncatastrophic events. Also, many events or technologies that involve potentially catastrophic hazards comprise large-scale activities, which benefit society as a whole, but not necessarily an individual; whereas small-scale risky activities are often undertaken by individuals because of the joy, con- venience, or other benefits that make one take the risks for granted (cf. Vlek & Stallen, 1980, 1981). To some extent, there is no way of disentangling these characteristics in the real world, which means that confounds are inevitable when natural stimulus events are used in research like the present one. Thus, in the two sets of events that were used in Study 1, catastrophe potential might well be confounded with perceived base rate, perceived benefits, and the scale of the activities (i.e., at individual or societal level). In order to deal with the possible confound of catastrophe potential and perceived benefits for the individual, participants in Study 1 gave judgments of perceived benefits, which were thus used as covariates. In order to deal with confounds of catastrophe potential on the one hand, and perceived base rate and scale of the event on the other hand, a second study was conducted. In that study a scenario was used which, all other things being equal, described a particular hazard either as a catastrophe or as a chronic hazard in a between-subjects design.


Study 1

Method

Materials, dependent variables, andprocedure. In a pilot study, 59 undergraduate students rated the extent to which they perceived 50 hazards as ones that have catastrophe potential. Catastrophic hazards were defined as hazards that may kill or injure a number of people at once, and noncatastrophic hazards as hazards that may kill or injure people one at a time. The 15 hazards that were judged as most catastrophic and the 15 hazards that were judged as least catastrophic were selected for the main study. Examples of catastrophic hazards were: radioactive contamination of sea water by dumping nuclear waste, poisoning of drinking water by pesticides, a fire in a petrochemical plant near a residential area, a grandstand falling down during a football match, and an eruption of a volcano destroying a nearby built town. Examples of noncatastrophic hazards were: lethal accidents during a motor race, dying during narcosis, contracting heart disease by eating too much fat, being hit by a car while bicycling through town, and police officers getting killed during surveil- lance.

In a second pilot test, the 30 hazards were presented to 40 undergraduate students. They were asked to indicate the extent to which the hazards were potentially catastrophic. Judgments were given on 7-point scales, which were anchored by very catastrophic and not at all catastrophic. As expected, the 15 catastrophic hazards were judged as more catastrophic (m = 1.76) than the 15 noncatastrophic hazards (m = 3.05), F(15,25) = 4 . 8 7 , ~ < .001.

In the main study, the 30 stimuli were presented in a questionnaire, which was filled out during classroom sessions. Participants received an introduction, explaining that they had to judge how large or how small they perceived probabilities of hazards to be that were associated with a number of activities. Each hazard was accompanied by a numerical probability, which was either 1 out of 10, 1 out of 1,000, or 1 out of 100,000. The stimuli were presented by the stem “Suppose that the probability that is [ 1 out of 10 , l out of 1,000, or 1 out of 100,0001. How large or small would you judge this probability?” The response scale contained seven spaces, which were anchored by the labels very small and very large.

Three versions of the questionnaire were prepared. In the first version, the probability 1 out of 10 was attributed to five randomly chosen catastrophic hazards and five randomly chosen noncatastrophic hazards. A 1 out of 1,000 probability was attributed to five other randomly chosen catastrophic and five randomly chosen noncatastrophic hazards, while 1 out of 100,000 was attributed to the remaining five catastrophic and five noncatastrophic hazards. In the

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second and third versions the three probabilities were rotated across the items: In the second version, 1 out of 10 was replaced by 1 out of 1,000, 1 out of 1,000 was replaced by 1 out of 100,000, and 1 out of 100,000 was replaced by 1 out of 10. This procedure was repeated in the third version. Participants randomly received one of the three versions.

For each participant, a mean probability score was calculated for each of the three probability levels (i.e., 1 out of 10,l out of 1,000, or 1 out of 100,000), for catastrophic and noncatastrophic hazards, respectively. Thus, for each participant six mean risk judgments were calculated. Because the hazards associated with the three levels were different for each version of the questionnaire, the implication of this procedure was that the analyses were performed for probability levels across hazards. For instance, the mean ratings ofa 1 out of 1,000 probability of catastrophic hazards comprised different hazards for each of the three versions of the questionnaire.

After all 30 probabilities were rated, participants were asked to indicate the extent to which single individuals benefit from the events to which the hazards are related. The 30 events were rated on response scales that contained seven spaces, from no benefits at all to many benefits. Like was done for the probability judgments; for each participant, a mean perceived benefit score was calculated concerning the respective events for each of the three stimulus probability levels.

Participants and design. Participants were 153 undergraduate students. The design of the experiment was 3 x 2 x 3 (Probability Level: 1 out of 10, 1 out of 1,000, 1 out of 100,000 x Catastrophe Potential: Catastrophic vs. Non- catastrophic Hazards x Questionnaire Version) factorial with repeated measures on probability level and catastrophe potential. Because there were no significant effects of Questionnaire version, this factor will not be considered further.

Results and Discussion

In Figure 1, the mean risk judgments in response to the three probability levels for catastrophic and noncatastrophic hazards are presented. The six risk judgments were subjected to a MANOVA with Probability Level and Catas- trophe Potential as within-subjects factors. Not surprisingly, the effect of probability level was significant, F(2, 151) = 193.97, p < .001. Of interest was a significant effect of Catastrophe Potential, F( 1, 152) = 118 .87 ,~ < .001. As expected, the same numerical probabilities were rated as higher when hazards belonged to the catastrophic than to the noncatastrophic hazard set. Unexpect- edly, the Probability Level x Catastrophe Potential interaction was also significant, F(2, 151) = 12.82, p < .001. The difference between catastrophic and


large very 7t 6

5

4

3

2

very small 1 out of 10 1 out of 1,000 1 out of 10,000

Stimulus probabilities

Noncatastrophic hazards .Catastrophic hazards

Figure I. Mean ratings on a scale in response to the numerical probabilities for catastrophic and noncatastrophic hazards, Study 1.

noncatastrophic hazards was somewhat stronger in response to 1 out of 100,000, t(152) = 1 0 . 0 0 , ~ < .001, than to 1 out of 10, t(152) = 6 . 0 9 , ~ < .001.

In order to test whether perceived benefits could account for the effects of catastrophe potential, the six mean judgments of benefits concerning the risk- involving events (i.e., for catastrophic hazards and for noncatastrophic hazards, for each probability level) were included as covariates. Although perceived benefits explained a significant portion of variance, F( 1, 151) = 6.03, p < .02, the effect of Catastrophe Potential remained highly significant, F(1, 151) = 3 0 . 9 7 , ~ < .001, as did the effect ofprobability Level, F(2, 149) =

191 .35 ,~ < .001, and the Probability Level x Catastrophe Potential interaction, F(2, 149) = 12 .41 ,~ < .001.

In sum, as was expected, participants judged numerical probabilities of hazards that have catastrophe potential as higher than equal numerical probabilities of noncatastrophic hazards. This effect was stronger for 1 out of 100,000 than for 1 out of 10. Because the probabilities covered the area of small numbers, it could be that probabilities like 1 out of 100,000 are more abstract to people than a 1 out of 10 chance. This might make them more susceptible for influences of context. Finally, although the two sets of hazards might have been confounded with respect to perceived benefits for the individual, the present results could only partially be explained by this latter factor. However, other confounds (e.g., perceived base rate or scale of the activities) could still provide

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alternative explanations for the results. Study 2 was therefore conducted to rule out such explanations, and thus to assess the effect of catastrophic potential more precisely.

Study 2

Method

Participants were presented with a scenario, in which they were asked to imagine themselves in the year 2005, which was 10 years ahead at the time the study was performed. It was said that by then the ozone layer had disintegrated to such an extent that heavy measures were needed to protect human beings from negative consequences of higher radiation levels. Among such measures in The Netherlands (where the study was conducted) was a newly developed medicine that would prevent the occurrence of skin cancer. The medicine was distributed through the drinking-water supply systems. The medicine had some risk, however.

There were two versions of the scenario at this point. In the catastrophe version, it was said that due to combinations of high levels of SO2 in the air, together with high radiation levels, the medicine might become fatal for some people. These circumstances could be expected to happen once in 10 years, and would yield 1,000 casualties on that particular day. In the chronic version, it was said that due to combinations of high levels of SO2 in the air, together with high radiation levels, the medicine might become fatal for some people. This could be expected to yield 1,000 casualties spread across a 10-year period. In both versions, it was said that the exact probability that the consequences were as described was still under debate. Participants were then presented with three probabilities (1 out of 10; 1 out of 1,000; 1 out of 100,000). The order of presentation of the three probabilities was counterbalanced. Participants were asked to indicate for each numerical probability how small or how large they judged it to be. The response scale contained nine spaces, from very small to very large.

By describing the risk as a possible 1,000 casualties in a 10-year period (whether these were expected on 1 day, or spread over time), the base rate and scale of the event were kept constant. Positioning the scenario in the future was meant to strengthen this aspect.

Participants were 27 undergraduate students. The design of this study was 3 x 2 x 6 (Probability Level: 1 out of 10, 1 out of 1,000, 1 out of 100,000 x Type of Hazard: Chronic vs. Catastrophic x Order of Presentation) factorial with repeated measures on Probability Level. Because there were no significant effects of Order of Presentation, this factor will not be considered further.


large 8

7

6

5

4

3

2 very small 1

1 out of 10 1 out of 1,000 1 out of 10,000

Stimulus probabilities

Chronic hazards .Catastrophic hazards

Figure 2. Mean ratings on a scale in response to the numerical probabilities for catastrophic and chronic hazards, Study 2.

Results

In Figure 2, the mean ratings for each probability level are presented for the chronic and catastrophic hazard conditions. The results are very similar to those of Study 1. A MANOVA with Probability Level as within-subjects factor and Type of Hazard as between-subjects factor yielded a significant effect of Probability Level, F(2,24) = 3 4 . 5 4 , ~ < .001. Importantly for the present argument, the effect of Type ofHazard was significant, F( 1,25) = 5 . 6 8 , ~ < .03. Par- ticipants in the catastrophic hazard condition judged the numerical probabilities higher than did participants in the chronic hazard condition. The Probability Level x Type of Hazard interaction was not significant, F(2,24) =

0.50, ns.

General Discussion

The two studies provided evidence to suggest that people perceive numerical probabilities as higher when they concern hazards that have catastrophic potential, compared to numerically equal probabilities of noncatastrophic hazards. In Study 1, this was demonstrated by differences in judgments that were made of numerical probabilities of two sets of real-world hazards. Whereas the use of natural stimuli enhances realism and generalizability, a difficulty in

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interpreting these results is that catastrophic potential might be confounded with other characteristics, such as perceived base rate, perceived benefits, and the scale of the respective activities. Perceived benefits could not explain the results of Study 1.

However, although an explanation of the results by base rate differences is not easy (i.e., catastrophic events occur less frequently, but probabilities of these hazards were seen as higher), such alternative explanations could not be completely ruled out. In Study 2, the scenario was formulated such that the chronic hazard version and the catastrophic hazard version were formally equal in base rate and scale. Because the results were practically identical to those of Study 1, both studies together demonstrate that catastrophic potential affects the interpretation of numerical probabilities in the sense that numerical probabilities are seen as higher when hazards involve catastrophic potential compared to noncatastrophic hazards.

It is important to note that the present perspective was not a linguistic one, that is, to document which words would typically be used in response to numerical probabilities. Rather, it was meant to reveal perceptions of probabilities as being large or small, in particular as a function of the perceived catastrophic potential of hazards. Thus, participants were asked to transform their perceptions of numerical probabilities into positions on ordinal scales which were labeled in verbal terms (i.e., from very small to very large). In presenting these scales, no reference to numbers was made whatsoever. People have a strong sense of rank order in terms of verbal probability expressions (cf. Hamm, 1991; Lichtenstein & Newman, 1967). Therefore, although participants were not asked for verbal expressions as such, the ratings can be interpreted as positions on a semantically meaningful (ordinal) dimension; that is, as positions some- where between the verbal expressions very small and very large.

Why would people judge numerical probabilities as higher when these concern hazards that have catastrophic potential, compared to noncatastrophic hazards? One reason might be that verbal qualifications of probability may be used to convey things other than mere probabilities. Although in formal risk analysis, probability and outcome valence are strictly distinguished, this is not always the case in lay perceptions of risk (Teigen, 1988a; Weber, Anderson, & Birnbaum, 1992). Catastrophic hazards may be found more serious and thus less acceptable than noncatastrophic hazards. On the one hand, this might be an intuitive, some may call it irrational, type of judgment. On the other hand, one could reason that a catastrophe may cause more damage than an equal number of single casualties taken together, if one would ever be able to measure this prop- erly. In addition to the damage, pains, and sorrows of the direct victims, a catastrophe may cause severe disruption of the life of a community, psychological trauma that involves disproportionately larger numbers of people, and emotional


disturbances among people who feel at risk in comparable situations. In any case, it is conceivable that people make such evaluations part of their probability ratings. Therefore, higher verbal ratings of catastrophic hazard probabilities cannot be dealt with as biased or irrational judgments, but may rather, partly express participants’ attitudes toward the events that involve the associated risks.

The perceptions of the probability of a hazard may, together with perceived benefits, make up part of one’s overall attitude toward the activity that is associated with the hazard. People tend to achieve consistency in their attitudinal systems (e.g., Rosenberg, 1960). Activities that are associated with catastrophic risks might be more negatively evaluated and might thus be associated with higher risks as well as with fewer benefits. Alhakami and Slovic (1994), for example, found consistently negative correlations between perceived levels of risks and benefits across 40 activities and technologies. They also found that objects ofjudgment toward which respondents had a favorable general attitude were viewed as having high benefits and low risks, whereas unfavorable general attitudes were associated with low benefits and high risks.

Learning more about how people interpret expressions of probability is important, because the use of verbal qualifications or numbers may not only have different consequences for judgment and decision-making processes (e.g., Budescu & Wallsten, 1990; Budescu et al., 1988; Erev & Cohen, 1990; Rapoport, Wallsten, Erev, & Cohen, 1990; Stone & Schkade, 1991; Zimmer, 1983), probabilities are frequently used in public discussions and communications. Nu- merical probabilities, which are often provided by experts, are important in many public debates, for instance about large-scale projects concerning the in- frastructure, when pollution threatens people’s health, or in educational programs about new technologies. In many of these discussions, numerical probabilities are used as arguments. Those who use probabilities as arguments do so under the assumption that each party has the same understanding of the figures or, in other words, that “numbers speak for themselves.” The present results demonstrate that such assumptions may not always hold. Qualitative characteristics of hazards may affect how numerical probabilities are interpreted. As was demonstrated in the present studies, numerical probabilities of potentially catastrophic hazards are perceived as higher, compared to probabilities of noncatastrophic hazards. Such an effect may thus interfere in the communication process. For instance, when an expert uses a 10” probability of a potentially catastrophic accident as a safety argument, he or she must be prepared to find out that the public perceives this as a rather high probability, and thus considers the expert’s probability as a weak argument. This may lead to miscommunication, as can frequently be seen: The public mistrusts experts, while experts consider the public’s reactions as ignorant and improper. An example of such miscommunication might be the debate about nuclear power

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plants, in which experts agree fairly well about numerical probabilities of accidents. However, these relatively small numbers are seen as high probabilities by large groups of citizens, leading to perceptions of risks of nuclear plants as dangerous, and thus to very unfavorable attitudes toward nuclear power, espe- cially after the 1986 Chernobyl catastrophe (e.g., Drottz-Sjoberg & Sjoberg, 1990; Hohenemser & Renn, 1988; McDaniels, 1988; Peters, Albrecht, Hennen, & Stegelmann, 1990; Verplanken, 1989).

While some conservatism in perceiving hazards that involve potential catastrophes may not be so wrong, the present results may also warn against the potential underestimation of chronic hazards. We are frequently confronted with such hazards; for instance pollution, traffic, or health-related behaviors. We may underestimate numerical probabilities that are associated with such hazards, and behave accordingly, thus exposing ourselves unnecessarily to high risk levels. For instance, this might be one of the reasons that a substantial minority keeps on smoking, in spite of statistical figures that clearly indicate the dangers of such behavior.

Knowing more about when numerical probabilities are perceived as small or large may not only contribute to improving our communications and our abilities to predict people’s choices and behaviors. It may also tell more about how people think and make risk judgments, and thus contribute to more funda- mental knowledge of why and when people may feel safe or unsafe.

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