Yes, you’re quite right!

The intuition becomes a little clearer when I take the following alternative derivation:

Let us look at the change in expected value when I increase my capabilities. From the expected value stemming from worlds where I win, we have . For the other actor, their probability of winning decreases at a rate that matches my increase in probability of winning. Also, their probability of deploying a safe AI doesn’t change. So the change in expected value stemming fro m worlds where they win is .

We should be indifferent to increasing capabilities when these sum to 0, so .

Let’s choose our units so . Then, using the expressions for from your comment, we have .

Dividing through by we get . Collecting like terms we have and thus . Substituting for we have and thus

This link (and the one for “

Whydo we fear the twinge of starting?”) is broken (I think it’s an admin view?).(Correct link)