However this does not translate into these naive statistical analogies that "in the U.S., ladders kill far more Americans than Muslim terrorists". In the past that number was true because you can trust empiricism when it comes to thin-tailed variables, because things don't change year-on-year and if they do it's nothing dramatic. The probability that the number of people killed by ladders, the probability of that number doubling in the U.S., without any change in the structure, any change in the ladders, any change in the behaviour of Americans, any change in alcohol consumption; the probability of that number doubling between say 2017 and 2018, is something around the order of 10^-10 or 10^-20, it's so small you don't really care, it's very very small. But why you can't say the same about terrorism is in the very same article of the NYT, the same article explained that the odds of "an American being killed by a Muslim terrorist was 1 in 17 million" in 2015, when in 2016 they're "1 in 6 million", about 2 1/2 times. So you realize, because this estimator is very unstable, a year is going to deliver a number that is very different from the previous year. So we end up with Ebola for example, "we're naive to worry about Ebola when alcohol kills so many people" but alcohol is not that multiplicative, it may be an epidemic, but nothing like Ebola, and it has the same instability, Ebola probably could wipe out a lot of people. So the reasoning should be as follows. Consider a tail-event, say you read a newspaper someday, article reads: "100 million people were killed" by 'something'. What is that 'something' more likely to be? 'Fall from ladders' or 'terrorism'? 'Alcohol' or 'Ebola'? So in the tails, the ratio of probabilities is vastly higher than it is in a body. And that's what we're concerned with. When you do risk management, you worry about the tails.
Nassim Nicholas Taleb
