Round-Trip Fallacy (Confusion of the Inverse)

I have so much evidence—Can Zoogles be (sometimes) Boogles?—Corroboration shmorroboration—Popper’s idea

As much as it is ingrained in our habits and conventional wisdom, confirmation can be a dangerous error.

Assume I told you that I had evidence that the football player O. J. Simpson (who was accused of killing his wife in the 1990s) was not a criminal. Look, the other day I had breakfast with him and he didn’t kill anybody. I am serious, I did not see him kill a single person. Wouldn’t that confirm his innocence? If I said such a thing you would certainly call a shrink, an ambulance, or perhaps even the police, since you might think that I spent too much time in trading rooms or in cafés thinking about this Black Swan topic, and that my logic may represent such an immediate danger to society that I myself need to be locked up immediately.

You would have the same reaction if I told you that I took a nap the other day on the railroad track in New Rochelle, New York, and was not killed. Hey, look at me, I am alive, I would say, and that is evidence that lying on train tracks is risk-free. Yet consider the following. Look again at Figure 1 in Chapter 4; someone who observed the turkey’s first thousand days (but not the shock of the thousand and first) would tell you, and rightly so, that there is no evidence of the possibility of large events, i.e., Black Swans. You are likely to confuse that statement, however, particularly if you do not pay close attention, with the statement that there is evidence of no possible Black Swans. Even though it is in fact vast, the logical distance between the two assertions will seem very narrow in your mind, so that one can be easily substituted for the other. Ten days from now, if you manage to remember the first statement at all, you will be likely to retain the second, inaccurate version—that there is proof of no Black Swans. I call this confusion the round-trip fallacy, since these statements are not interchangeable.

Such confusion of the two statements partakes of a trivial, very trivial (but crucial), logical error—but we are not immune to trivial, logical errors, nor are professors and thinkers particularly immune to them (complicated equations do not tend to cohabit happily with clarity of mind). Unless we concentrate very hard, we are likely to unwittingly simplify the problem because our minds routinely do so without our knowing it.

It is worth a deeper examination here.

Many people confuse the statement "almost all terrorists are Moslems" with "almost all Moslems are terrorists." Assume that the first statement is true, that 99 percent of terrorists are Moslems. This would mean that only about .001 percent of Moslems are terrorists, since there are more than one billion Moslems and only, say, ten thousand terrorists, one in a hundred thousand. So the logical mistake makes you (unconsciously) overestimate the odds of a randomly drawn individual Moslem person (between the age of, say, fifteen and fifty) being a terrorist by close to fifty thousand times!

The reader might see in this round-trip fallacy the unfairness of stereotypes—minorities in urban areas in the United States have suffered from the same confusion: even if most criminals come from their ethnic subgroup, most of their ethnic subgroup are not criminals, but they still suffer from discrimination by people who should know better.

"I never meant to say that the Conservatives are generally stupid. I meant to say that stupid people are generally Conservative," John Stuart Mill once complained. This problem is chronic: if you tell people that the key to success is not always skills, they think that you are telling them that it is never skills, always luck.

Our inferential machinery, that which we use in daily life, is not made for a complicated environment in which a statement changes markedly when its wording is slightly modified. Consider that in a primitive environment there is no consequential difference between the statements most killers are wild animals and most wild animals are killers. There is an error here, but it is almost inconsequential. Our statistical intuitions have not evolved for a habitat in which these subtleties can make a big difference.