Statistics are famous for their pliability, as anyone who has heard of Mark Twain will attest. Proponents on either side of a policy position often have”hard numbers” to support their view. When costs or benefits are uncertain, there must be some way to measure risk. Attitudes toward risk can have a powerful influence on which policy positions one finds acceptable.
One way that risk calculations become difficult is when there is a very, very small chance of a very, very bad outcome. Conservatives make use of this logic when they suggest that potential murderers facing a small chance of the death penalty will be dissuaded from their crime. Or, conversely, that a small chance of the criminal killing again is bad enough to justify execution. Liberals employ this same type of reasoning when they talk about potentially extreme consequences of global warming: even a small risk of the Eastern seaboard disappearing would be disastrous.
Humans are very bad at estimating probabilities, particularly when they are below 1 percent. Daniel Kahneman discusses this in his book Thinking Fast and Slow, where he gives an example of the difference between a 0.001% risk of death and a 0.00001% chance. To the human eye/brain the difference seems minuscule, but in practical terms it means 3,000 Americans dying or 30. Combine this with the fact that it is easier to recall vivid memories like September 11, and you have foolish policies that require Americans to remove their shoes and stand in a full-body scanner to reduce their risk of dying in a plane hijacked by suicide bombers from practically zero to slightly-less-than-practically zero.
Kahneman offers a quote from Paul Slovic that summarizes the discussion well:
Whoever controls the definition of risk controls the rational solution to the problem at hand. If you define risk one way, then one option will rise to the top as the most cost-effective or the safest or the best. If you define it another way, perhaps incorporating qualitative characteristics and other contextual factors, you will likely get a different ordering of your action solutions. Defining risk is thus an exercise in power. (original article here)
And until we get our philosopher-king, the ones who understand risk will likely not be the ones holding the keys to the kingdom. But we can at least be aware of when the small-chance/very-bad-outcome argument is being used to frighten us into irrationality.
Further reading: “Risk and Safety,” Aaron Wildavsky and Adam Wildavsky.