When engaged in rational threat assessment, there are two main factors that need to be considered. The first is the probability of the threat. The second is, very broadly speaking, the severity of the threat. These two can be combined into one sweeping question: “how likely is it that this will happen and, if it does, how bad will it be?”
Making rational decisions about dangers involves considering both of these factors. For example, consider the risks of going to a crowded area such as a movie theater or school. There is a high probability of being exposed to the cold virus, but it is a very low severity threat. There is an exceedingly low probability that there will be a mass shooting, but it is a high severity threat since it can result in injury or death.
While humans have done a fairly good job at surviving, this seems to have been despite our amazingly bad skills at rational threat assessment. To be specific, the worry people feel in regards to a threat generally does not match up with the actual probability of the threat occurring. People do seem somewhat better at assessing the severity, though they are also often in error about this.
One excellent example of poor threat assessment is in regards to the fear Americans have in regards to domestic terrorism. As of December 15, 2015 there have been 45 people killed in the United States in attacks classified as “violent jihadist attacks” and 48 people killed in attacks classified as “far right wing attacks” since 9/11/2001. In contrast, there were 301,797 gun deaths from 2005-2015 in the United States and over 30,000 people are killed each year in motor vehicle crashes in the United States.
Despite the incredibly low likelihood of a person being killed by an act of terrorism in the United States, many people are terrified by terrorism (which is, of course, the goal of terrorism) and have become rather focused on the matter since the murders in San Bernardino. Although there have been no acts of terrorism on the part of refugees in the United States, many people are terrified of refugees and this had led to calls for refusing to accept Syrian refugees and Donald Trump has famously called for a ban on all Muslims entering the United States.
Given that an American is vastly more likely to be killed while driving than killed by a terrorist, it might be wondered why people are so incredibly bad at this sort of threat assessment. The answer, in regards to having fear vastly out of proportion to the probability is easy enough—it involves a cognitive bias and some classic fallacies.
People follow general rules when they estimate probabilities and the ones we use unconsciously are called heuristics. While the right way to estimate probability is to use proper statistical methods, people generally fall victim to the bias known as the availability heuristic. The idea is that a person unconsciously assigns a probability to something based on how often they think of that sort of event. While an event that occurs often will tend to be thought of often, the fact that something is often thought of does not make it more likely to occur.
After an incident of domestic terrorism, people think about terrorism far more often and thus tend to unconsciously believe that the chance of terrorism occurring is far higher than it really is. To use a non-terrorist example, when people hear about a shark attack, they tend to think that the chances of it occurring are high—even though the probability is incredibly low (driving to the beach is vastly more likely to kill you than a shark is). The defense against this bias is to find reliable statistical data and use that as the basis for inferences about threats—that is, think it through rather than trying to feel through it. This is, of course, very difficult: people tend to regard their feelings, however unwarranted, as the best evidence—despite it is usually the worst evidence.
People are also misled about probability by various fallacies. One is the spotlight fallacy. The spotlight fallacy is committed when a person uncritically assumes that all (or many) members or cases of a certain class or type are like those that receive the most attention or coverage in the media. After an incident involving terrorists who are Muslim, media attention is focused on that fact, leading people who are poor at reasoning to infer that most Muslims are terrorists. This is the exact sort of mistake that would occur if it were inferred that most Christians are terrorists because the media covered a terrorist who was Christian (who shot up a Planned Parenthood). If people believe that, for example, most Muslims are terrorists, then they will make incorrect inferences about the probability of a domestic terrorist attack by Muslims.
Anecdotal evidence is another fallacy that contributes to poor inferences about the probability of a threat. This fallacy is committed when a person draws a conclusion about a population based on an anecdote (a story) about one or a very small number of cases. The fallacy is also committed when someone rejects reasonable statistical data supporting a claim in favor of a single example or small number of examples that go against the claim. This fallacy is similar to hasty generalization and a similar sort of error is committed, namely drawing an inference based on a sample that is inadequate in size relative to the conclusion. The main difference between hasty generalization and anecdotal evidence is that the fallacy anecdotal evidence involves using a story (anecdote) as the sample.
People often fall victim to this fallacy because stories and anecdotes tend to have more psychological influence than statistical data. This leads people to infer that what is true in an anecdote must be true of the whole population or that an anecdote justifies rejecting statistical evidence in favor of said anecdote. Not surprisingly, people most commonly accept this fallacy because they want to believe that what is true in the anecdote is true for the whole population.
In the case of terrorism, people use both anecdotal evidence and hasty generalization: they point to a few examples of domestic terrorism or tell the story about a specific incident, and then draw an unwarranted conclusion about the probability of a terrorist attack occurring. For example, people point to the claim that one of the terrorists in Paris masqueraded as a refugee and infer that refugees pose a great threat to the United States. Or they tell the story about the one attacker in San Bernardino who arrived in the states on a K-1 (“fiancé”) visa and make unwarranted conclusions about the danger of the visa system (which is used by about 25,000 people a year).
One last fallacy is misleading vividness. This occurs when a very small number of particularly dramatic events are taken to outweigh a significant amount of statistical evidence. This sort of “reasoning” is fallacious because the mere fact that an event is particularly vivid or dramatic does not make the event more likely to occur, especially in the face of significant statistical evidence to the contrary.
People often accept this sort of “reasoning” because particularly vivid or dramatic cases tend to make a very strong impression on the human mind. For example, mass shootings by domestic terrorists are vivid and awful, so it is hardly surprising that people feel they are very much in danger from such attacks. Another way to look at this fallacy in the context of threats is that a person conflates the severity of a threat with its probability. That is, the worse the harm, the more a person feels that it will occur.
It should be kept in mind that taking into account the possibility of something dramatic or vivid occurring is not always fallacious. For example, a person might decide to never go sky diving because the effects of an accident can be very, very dramatic. If he knows that, statistically, the chances of the accident are happening are very low but he considers even a small risk to be unacceptable, then he would not be making this error in reasoning. This then becomes a matter of value judgment—how much risk is a person willing to tolerate relative to the severity of the potential harm.
The defense against these fallacies is to use a proper statistical analysis as the basis for inferences about probability. As noted above, there is still the psychological problem: people tend to act on the basis on how they feel rather than what the facts show.
Such rational assessment of threats is rather important for both practical and moral reasons. The matter of terrorism is no exception to this. Since society has limited resources, rationally using them requires considering the probability of threats rationally—otherwise resources are being misspent. For example, spending billions to counter a miniscule threat while spending little on leading causes of harm would be irrational (if the goal is to protect people from harm). There is also the concern about the harm of creating fear that is unfounded. In addition to the psychological harm to individuals, there is also the damage to the social fabric. There has already been an increase in attacks on Muslims in America and people are seriously considering abandoning core American values, such as the freedom of religion and being good Samaritans.
In light of the above, I urge people to think rather than feel their way through their concerns about terrorism. Also, I urge people to stop listening to Donald Trump. He has the right of free expression, but people also have the right of free listening.