MHR comments on The Risks and Rewards of Prioritizing Animals of Uncertain Sentience

[MHR]

I’m sure I’m just being dumb here, but I’m confused by this formula:

What’s the sum over p(E_j)? Why doesn’t it end up just summing to 1?

[EdoArad]

Nice spot! I think it should be

$$\sum _{j=i}^n\left(p\right(E_j\left)\right)$$

(found reference here).

Then, we get

$$EV\left(A\right)=\sum _{i=1}^n[(\sum _{j=i}^{n}p\left(E_j\right)-\sum _{j=i+1}^{n}p\left(E_j\right))u\left(x_i\right)]=\sum _{i}p\left(E_i\right)u\left(x_i\right)$$