The invasion

Imagine that you are a general at a military compound near the border. From your vast experience, you know that when enemy troops mass at the border, the probability of an invasion towards your territory is 75%.

But…

You don’t have direct access to information about enemy troops and you have to rely on your intelligence sources. As it turns out, when an intelligence report states that the enemy troops are massing, they are really there!

Now…

Your sources tell you that enemy troops are at the border. What is the probability of an invasion?

The nice thing about this problem is that it can be applied to many fields, including business or finance, where news about an event gives clues about the occurrence of another underlying event, which is what you are actually interested in.

The answer, though, is unsettling.

No… It is not 75%.

In fact, it could be virtually anything between 0% and 100%.

When one thinks of 75%, one is making the wrong assumption that the intelligence draws a random enemy action. However, perhaps the enemy is cunning, in that the intelligence sources see their troops only when there is no invasion planned (then the answer would be 0%).

This question is taken from a 1980 article by the famous social scientist Hillel J. Einhorn and shows us how our judgments can be driven by true yet worthless and irrelevant information.

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