“However, if this were the only rule followed, then whenever one were presented with any kind of evidence, one would have to either reject some of one’s beliefs or else leave one’s beliefs unchanged.”
Let’s say I have a million beliefs. According to the statisticians, I shouldn’t add to or subtract from that set of one million beliefs (that’s part of what it means when they say “never change that set”) except if I have adequate evidence against a belief, then I should reject that belief. So the only case in which we would add to or subtract from the set of one million beliefs is the case there I have adequate evidence against one of those beliefs. So, whenever I am presented with any kind of evidence, either the evidence counts as adequate evidence against one of my beliefs, or it doesn’t. If it doesn’t count as adequate evidence, then according to the statisticians I shouldn’t make any changes to the set of one million beliefs. If it does count as adequate evidence against one of my beliefs, then according to the statisticians that belief should get rejected, and I am left with 999,999 beliefs.
So, since the only case in which we would add to or subtract from the set of one million beliefs is a case where we subtract a belief, this means that we’re never going to be adding to the set of the one million beliefs- if any changes are made, they will be changes involve subtracting beliefs.
“overall correctness of the total set of one’s beliefs”- well, I don’t think the exact definition matters at all for the argument, but I read that as saying something like the following: The MOST correct that the total set of my beliefs could possibly be would be 100% correct- namely, I wouldn’t have a single false belief in my total set of beliefs. So the overall correctness increases to the extent that a higher percentage of my beliefs are correct.
Re how one’s ability to survive correlates with their overall correctness- well, the conclusion of the argument is that the statisticians’ claim is mistaken. Their claim is that the surest way to increase the overall correctness of the total set of one’s beliefs is to follow that one rule discussed above. The person making the argument thinks that the statisticians’ claim is mistaken, because if we just follow that one rule for revising our beliefs, we will end up with fewer and fewer beliefs (because the rule only results in subtracting beliefs from the overall set, and not adding beliefs to the overall set), and, according to the person making the argument, we need many beliefs in order to survive. The problem though, as I think your question shows, is that there is no necessary connection between survival and the overall correctness of beliefs. So your question is right on: One’s ability to survive DOES NOT need to correlate with the overall correctness of one’s beliefs, and that’s what’s wrong with the argument!