# Help me understand this expected value calculation

post by AndreaSR · 2021-10-14T06:23:33.750Z · EA · GW · 8 commentsThis is a question post.

Hi there!

I'm looking at one of Bostrom's papers (Existential Risk Prevention as Global Priority, p. 19). He includes this expected value calculation which I just can't make sense of:

"Even if we give this allegedly lower bound on the cumulative output potential of a technologically mature civilisation [he's referring to his estimate of 10^52 future lives here] a mere 1 per cent chance of being correct, we find that the expected value of reducing existential risk by a mere one billionth of one billionth of one percentage point is worth a hundred billion times as much as a billion human lives."

When trying to repeat his calculation, I reason as follows: reducing the risk of losing 10^50 expected lives by 10^-20 - that's the same as increasing the probability of getting 10^50 by 10^-20. So, it should go 10^50*10^-20 = 10^30. However, he writes that the expected value of this change is equal to 10^20 lives. It's a fairly trivial calculation, so I assume there's something obvious I've overlooked. Can you help me see what I'm missing?

## Answers

Your calculation looks correct to me. (WolframAlpha confirms "10^52 * 1% * 1 billionth * 1 billionth * 1%" is 10^30.) It seems that Nick Bostrom is underestimating the expected value by 10^10.

## ↑ comment by JP Addison (jpaddison) · 2021-10-14T11:54:52.384Z · EA(p) · GW(p)

A minor factor of ten billion 😉

Replies from: Linch## 8 comments

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## comment by Linch · 2021-10-14T17:23:42.828Z · EA(p) · GW(p)

Not an excuse, but maybe Bostrom was using the old British definition of "billion," rather than the American and modern British definition of billion?

Replies from: Larks, AndreaSR## ↑ comment by Larks · 2021-10-14T21:44:13.190Z · EA(p) · GW(p)

Even then it seems off?

"Even if we give this allegedly lower bound on the cumulative output potential of a technologically mature civilisation [he's referring to his estimate of 10^52 future lives here]

a mere 1 per cent chance(+52)of being correct, we find that the expected value of reducing existential risk by a mere one billionth(-2)of one billionth(-12)of one percentage point(-12)is worth(-2)a hundred(=)billion(+2)times as much as a billion(+12)human lives."(+12)

52-2-12-12-2 = 24 != 26 = 2+12+12

Replies from: Linch