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Article Excerpt
The ways people assess probabilities in daily life differ in important respects from the ways probabilities are mathematically computed. This has been documented by a number of studies on the psychology of judgment and decision making, particularly within the heuristics and biases approach (Gilovich, Griffin, & Kahneman, 2002; Griffin, Gonzalez, & Varey, 2001; Kahneman, Slovic, & Tversky, 1982). For instance, one does not usually wait for statistical information to tell whether terrorism is a probable threat for airplane passengers, as long as one has incidents of airplane terrorism readily available in memory (the availability heuristic). People consider it more probable that an introvert intellectual is a librarian rather than a salesperson, without taking into account the base rates of librarians and salespersons, by the expedient use of similarity judgments (the representativeness heuristic). The research reported in the present paper is intended to demonstrate that people also use judgments of closeness, or distance, as a convenient cue for estimating risks and probabilities. They keep children (and themselves) at a distance from bonfires, fireworks, dogs, cars, cliffs, and waterfronts because proximity to risk sources is held to be dangerous, whereas distance is believed to offer protection and safety.
In daily life, probabilities and distances are closely correlated. To increase their chances of hitting the bull's eye, the inexperienced darts player walks up to the target as close as his fellow players will permit. To decrease their chances of being accidentally hit, the onlookers step back, increasing their distance from the target. Both parties use a well-tried strategy of manipulating probabilities through approach and avoidance. In most cases, and for several reasons, it works.
It appears that people's thinking in such cases follow a proximity (or closeness) heuristic; that is, a tendency to judge probabilities by monitoring the spatial, temporal, or conceptual distance to a target. The idea of a connection between closeness, propensities, and probability judgments was originally introduced by Kahneman and Varey (1990); closeness as a general cue to probability was further demonstrated in a series of studies by Teigen (1998a). It can be argued that this heuristic is both intuitively compelling and generally valid; in fact, its degree of ecological validity is so high that people tend to think about it as an environmental principle rather than a subjective strategy. Distance is easily perceived and requires no accident statistics. However, the external validity and general obviousness of this principle does not make it less interesting from a psychological point of view. It appears to belong to the class of 'natural assessments' (Tversky & Kahneman, 1983) or 'simple heuristics that make us smart' (Gigerenzer, Todd, & ABC Research Group, 1999), which should be studied from a descriptive as well as from a normative point of view.
As with other heuristics, there may be situations where dictates of proximity are less warranted from a normative perspective. Closeness to an aversive target is not invariably risky, and closeness to an attractive goal does not always increase its probability of attainment. A boxer, who cannot keep out of reach of his opponent, may be safer falling into a clinch. In problem solving, 'hill climbing' (where problem solvers consistently choose the option that brings them closer to the goal) is not always the most successful strategy. Sometimes a detour or a counter-intuitive move away from the goal is required (Reisberg, 2001). In route choices, people will typically choose roads pointing towards the destination, even when shorter routes are available. Accordingly, the path from A to B may differ from the path from B to A (Bailenson, Shum, & Uttal, 1998). In gambling, near misses are often perceived as encouraging, confirming the gambler's strategy and raising hopes for future success (Griffiths, 1999). Slot machines and instant scratch-cards appear to be constructed to give players an illusory feeling of being close to a prize, without actually winning.
Outcome closeness is often assessed after the fact. This can create a hindsight paradox. In typical studies of hindsight bias, respondents estimate the probability of the actual outcome higher after the fact than they did at an earlier stage, even if they are specifically asked to disregard their outcome knowledge (Hawkins & Hastie, 1990). However, when the outcome happens to have a close counterfactual, the opposite may occur (Kahneman & Varey, 1990; Roese, 2004). An athlete or a team losing with a narrow margin 'could' have won, and, in hindsight, will be regarded as probable winners. This was shown in a series of vignette studies where people physically, temporally, or conceptually close to winning were invariably rated as highly probable winners (Teigen, 1998a). They were in fact often perceived as more probable winners than those who actually won, especially those who won with a narrow margin (and thus were close to losing). In this study, closeness also affected the probability of negative events. One scenario (Experiment 2) described a row of cars parked next to a rock wall. A small rockslide takes place, and a stone hits and damages your car. Most participants would rate this as a low-probability event (mean rating = 3.69 on a 1 to 9 probability scale). If the rock hits the car next to you instead, your probability of being hit increased sharply (mean rating = 6.28). In other words, what happened was perceived as less probable than what did not happen, because the counterfactual event could be judged in terms of closeness ('it could have been my car'), whereas the factual event triggered a different set of comparisons ('why should this happen to me?'). To sum up, closeness to success generate 'upward' counterfactuals (thoughts about how a better outcomes could have been achieved), whereas closeness to failure leads to 'downward' comparisons (counterfactual thoughts about a worse outcome; cf. Roese, 1997), suggesting high probabilities of success or failure, respectively.
Outcome closeness can be a matter of degree. In one experiment (Teigen, 1998a, Experiment 5), participants were asked to produced two autobiographical stories, one with a happy ending (entitled 'It went well') and another less fortunate one (entitled 'Too late'). They also rated how close they had been to failure, in the first story, and how close to success, in the second. Finally, one half of the participants rated the probabilities of the factual outcomes, whereas the other half rated the probabilities of the alternative, counterfactual outcomes (failure in the happy story and success in the unhappy one). Closeness scores were significantly correlated with probability ratings in both counterfactual conditions, but not in the factual conditions.
Proximity can also affect probabilistic predictions. Fischhoff, Gonzalez, Small, and Lerner (2003) found that American citizens' judgments of terror risks (e.g. one's probability of being injured in an attack during the next 12 months) were correlated with the respondents' geographical distance from the World Trade Center. The authors speculate that people living in the Mid-Atlantic states had been more exposed to media coverage and personal stories connected to the September 11 assaults, and also that they felt more at risk because they were living in the same geographical region as the terrorists' main targets. The last explanation suggests that distance is used as a probability cue.
In contrast to the study by Fischhoff et al. (2003), the research to be reported in the present article is more concerned with immediately perceived distances than geographical distances measured in miles. People often find themselves in situations where dangers are averted 'in the last moment' or with narrow margins. If they use proximity as a probability cue, they may think of a negative, disastrous outcome as highly probable, despite the fact that it did not happen. Proximity may in such situations override other risk indicators (e.g. accident frequencies), leading to an overestimation of accident probabilities. The present studies were designed to demonstrate and to explore some consequences of this mechanism.
In the first four studies, probabilities are assessed retrospectively, showing how perceived closeness to accidents can lead to inflated accident probability judgments. Experiment 1 illustrates how an accident victim may think of an accident as improbable, whereas someone close to the accident may think of it as more probable. Experiment 2 reports p(death) estimates from people who claim they have been in a life-threatening situation,...
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