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risks that they should consider. For example, in the late 1970s, Howard Kunreuther undertook what would become an important study on flood and earthquake insurance purchases in California. He discovered that people in flood- and earthquake-prone areas often neglected the risk, failing to purchase insurance even when it was subsidized. By doing so, these individuals were ignoring not a 1 in 100,000 possibility but perhaps a 1 in 100 or even a 1 in 50 possibility with grave consequences that could have been alleviated affordably. It is somewhat striking to realize that even today, although information about the risk of earthquakes is well known in California, fewer than 1 in 5 households are insured.

One might think that the prior probability of a virgin risk is zero. Once the event in question occurs, however, it can happen again. A rational person confronted with the occurrence of a virgin-risk event would surely reconsider what his prior assessment of the risk should have been had he thought about the possibility. Although Carl Glatfelter Jr. of McSherrystown, Pennsylvania, never imagined that a car would crash through the front wall of his home, pushing him out a back window,1 if he’d been forced to place a probability on it he might have given it a 1 in 100 million chance per year. At least until it happened.

It is notoriously difficult, however, to assess what one’s prior assessment of the risk would have been had one thought of the event before it actually occurred. Most Americans had never contemplated the possibility of a terrorist attack in this country at the level of 9/11. After it occurred, an attack of that magnitude—or much worse—was not beyond belief, and indeed was thought to have a positive probability of happening again. Thus, most Americans’ subjective assessment of terrorism risk should have been far higher after 9/11 than before, despite measures taken to lower such risks after 9/11, since the near-zero prior probability should overwhelm any subsequent response that may have lowered the objective risk. A survey of law school students published in 2003 by economists Kip Viscusi and Richard Zeckhauser in the Journal of Risk and Uncertainty, however, found that around 40 percent of respondents believed their personal risk assessment was higher before the attacks than currently.2 In another study of professional-school students and undergraduate business students in 2005, they showed that over two-thirds of respondents exhibited the same phenomenon.3 These respondents experienced a recollection bias, whereby after the occurrence of a low-probability event, one thinks that one’s prior risk assessment was much higher than it actually was. This could be due to an attempt to reduce cognitive dissonance, for self-justification, or simply to misremembering.

It may also be a variant of hindsight bias, in which knowing the outcome alters an individual’s assessment of how likely it was to have occurred. For example, in a 1975 study by psychologist Baruch Fischhoff, who is also a contributor to this book, subjects were given passages to read about the Gurkha raids on the British in the early 1800s. Some were told how the conflict ended, and others were not. When asked what the probability of occurrence of each outcome was, those who knew the outcome gave it a much higher probability. With such “secondary hindsight bias,” individuals are unaware that the occurrence of an event influences what they believe ex post that they would have estimated ex ante. This bias prevents individuals from accurately reconstructing after an event what their prior assessment of the likelihood of that event really was before it happened, making Bayesian updating especially problematical for virgin risks.

What if individuals could accurately assess the prior probability they would have attached to an event had they thought about it? Fully proper prediction of the future risk requires more—namely a probability distribution over a hypothesized true probability p, which is updated once an event happens. Consider the difficulty. An event