# Is there a way to mathematically describe “surprise”?

Let's say that there are ten people entered into a random drawing, the winner gets some large prize.

If I were one of those ten people, and I were to win, then I would be pleasantly surprised. If some other person were to win, then that person (from their own perspective) would be equally surprised.

Here's where my thoughts get a little fuzzy:

From the perspective of an outside observer (not involved in the random drawing), both of the above outcomes appear equivalent. The fact that somebody won the drawing is not very surprising at all.

Is there any way to measure the true amount of "surprise" in a given situation, in a way that can be agreed upon by everyone?

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Possibly related: Surprisal. Possibly also related: Unexpected hanging paradox – Rahul Sep 26 '13 at 0:29

## 1 Answer

The name for the concept you're describing is "informational entropy". Wikipedia has a good article: http://en.wikipedia.org/wiki/Entropy_%28information_theory%29

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