People exhibit overweighting to rare events in many settings. For example, tourists behaviour typically exhibit high sensitivity to the possibility of rare terrorist attacks. Yet in other settings, people behave as if they believe that “it won’t happen to me.” A common example is texting while driving. Recent research suggests that this pattern is a reflection of the fact that people exhibit oversensitivity to rare events when they plan their future actions based on a description of the incentive structure, but experience reverses this bias.
The classical study of human decision-making distinguishes between judgment (estimating probability) and decision processes. Implicit in this two-process distinction is the assumption that people first estimate the probabilities of the feasible outcomes, and then choose between the different options by weighting the outcomes by their estimated probabilities (see Fox & Tversky, 1998). Most previous studies focused on one of the two processes. For example, basic studies of human judgment processes have compared intuitive probability estimates to objective probabilities. An exemplar of these studies (Phillips & Edwards, 1966) is presented in the first row of Table 1. The typical results of these judgment studies suggest that people tend to overestimate small probabilities. Further experimental studies of choice behaviour have examined one shot choices in “decisions from description.” The participants were asked to choose (once) between fully described payoff distributions. The typical results suggest that people tend to overweight the rare events. The second row in Table 1 summarizes one example of this observation.
Table 1: Summary of experimental studies that demonstrate overestimation of small probabilities and overweighting of rare events (following Marchiori, Di Guida, & Erev, 2015)
|Typical experimental task||Typical results and interpretation|
|Judgment (Phillips & Edwards, 1966)
Urn A includes 30 Red Balls and 70 White balls.
Urn B includes 70 Red Balls and 30 White balls.
One of the two urns was randomly selected (the prior probability that A will be selected is 0.5). The experimenter sampled with replacement 4 balls from that urn. All 4 balls are Red.
What is the probability that the selected urn is A?
Mean estimate: 0.23
Bayes’ posterior probability: 0.01
The mean estimate of 0.23 reflects overestimation of the objective small probability (0.01).
|One-shot decisions from description (Kahneman & Tversky, 1979)
Choose between the following two options:
Option S: -5 with certainty
Option R: -5000 with probability of 0.001; 0 otherwise
Choice rate of option R: 20%.
This choice rate suggests that most subjects behave as if the probability of the rare event (-5000) is over-weighted.
|Repeated decisions with experience (Erev et al., 2017).
Each subject faced each problem for 25 trials with feedback from the 6th trial:
Option S: -1 with certainty
Option R: -20 with probability of 0.05; 0 otherwise
Choice rate of option R:
First 5 trials: 48%. Last 20 trials: 65%.
This choice rate suggests that experience (feedback) triggers underweighting of the rare event (-20).
The coexistence of overestimation of small probabilities and overweighting of rare events appears to suggest that people are likely to exhibit extreme oversensitivity to rare events in decisions under uncertainty. Surprisingly, however, recent research shows that the exact opposite is often correct. Studies of decisions in situations in which people can use past experience to estimate the relevant probabilities reveal a bias toward underweighting of rare events (Barron & Erev, 2003; Hertwig et al., 2004). The typical decision maker behaves as if experience leads him or her to believe that “it won’t happen to me”. The third row in Table 1 presents one example of this pattern.
These findings suggest a “description–experience gap” (Hertwig and Erev, 2009): People tend to overestimate the probability of rare events when they are asked to estimate them, and overweight rare events when they response to a description of the potential risks. However, people tend to underweight rare events when they do not respond to descriptions of probabilities but rely instead on their own experiences.
Yechiam, Barron & Erev (2005) highlight one implication of the description-experience gap to the impact of terrorist attack. The gap suggests that tourists that plan their trip based on description of the possible sites are likely to be more sensitive to rare terrorist attacks than local residence that can base their decisions on personal experience. This hypothesis was tested by analysing the impact of the wave of terrorist attacks attacks in Israel, known as the Al-Aqsa Intifada (starting on September 2000 after Ariel Sharon’s visit to the Temple Mount, and lasted three years with at least one attack per month).
To evaluate the effect of the Intifada on tourism, the Israeli Central Bureau of Statistics (2002) calculated the number of bed nights in Israeli hotels by population type (inbound or domestic tourists) prior to and following the outbreak of the Intifada. Bed nights denotes the number of beds occupied overnight by accommodation establishments (World Tourism Organization 1993). The examination included hotels that either were certified by the Ministry of Tourism as tourist hotels or have issued a petition for certification. Overnight stays in these hotels comprise more than 80 percent of the total overnight stays in Israeli hotels. The results (see Figure 1) show an initial drop in overnight stays by both inbound tourists and domestic visitors in October 2000 during the initial terrorist activities. The drop was almost 60 percent for inbound tourists and about 10 percent for domestic ones.
The difference between inbound and domestic tourists increased in the following months. Indeed, after the initial decrease, domestic tourists’ overnights in hotels rebounded and even increased, while the overnights of inbound tourists continued to decrease. For example, a comparison of October 2000 with October 2001 shows an 80 percent decrease for inbound tourists and a 20 percent increase for domestic tourists.
Relationship to Terrorist Networks and Organized Crime
The current analysis suggests that the negative effects of rare terrorist attacks (on the economy) can be reduced by ensuring that citizens continue to partake in relatively safe leisure activities. Interestingly this suggestion summarizes one component of NYC Mayor Rudolph Giuliani’s response to the September 11 attack. Giuliani suggested that citizens should invest less in direct contributions (like helping digging and collecting blankets), and spend more time shopping and dining in New York. While this suggestion seemed counter-intuitive at the time, the current analysis suggests that it was effective in reducing the negative long-term economic effect of the attack.
Note: This article is partially based on the paper “Yechiam, E., Barron, G. and Erev, I., 2005. The role of personal experience in contributing to different patterns of response to rare terrorist attacks. Journal of Conflict Resolution, 49(3), pp.430-439.”
Doron Cohen, Ido Erev (TECHNION, Israel)
Barron, G. and Erev, I., 2003. Small feedback‐based decisions and their limited correspondence to description‐based decisions. Journal of Behavioral Decision Making, 16(3), pp.215-233.
Erev, I., Ert, E., Plonsky, O., Cohen, D. and Cohen, O., 2017. From anomalies to forecasts: Toward a descriptive model of decisions under risk, under ambiguity, and from experience. Psychological review, 124(4), p.369.
Fox, C.R. and Tversky, A., 1998. A belief-based account of decision under uncertainty. Management science, 44(7), pp.879-895.
Hertwig, R., Barron, G., Weber, E.U. and Erev, I., 2004. Decisions from experience and the effect of rare events in risky choice. Psychological science, 15(8), pp.534-539.
Hertwig, R. and Erev, I., 2009. The description–experience gap in risky choice. Trends in cognitive sciences, 13(12), pp.517-523.
Kahneman, D. and Tversky, A., 1979. Prospect Theory: An Analysis of Decision under Risk. Econometrica, 47(2), pp.263-292.
Marchiori, D., Di Guida, S. and Erev, I., 2015. Noisy retrieval models of over-and undersensitivity to rare events. Decision, 2(2), p.82.
Phillips, L.D. and Edwards, W., 1966. Conservatism in a simple probability inference task. Journal of experimental psychology, 72(3), p.346.