Nate Soares on the Ultimate Newcomb's Problem

Hi! Transparent Newcomb means you consider Newcomb's problem but the box is transparent so the agent knows whether it's empty or full. We then need to specify which counterfactual Omega predicts (agent seeing empty box, agent seeing full box, or some combination of both) but for our present purpose it doesn't matter. EDT is undefined because e.g. if you see a full-box in the relevant counterfactual then you cannot condition on two-boxing. This can be circumvented by adding a little noise, i.e. a small probability of Omega mispredicting.

Yes, in noisy transparent Newcomb EDT and CDT also agree but disagree with FDT.

The consequences of not having enough time to think.

winning more utility

more money.

EDIT: It's not clear what effects the amount of time restriction has. 'Not enough time to factor this number' could still be a lot of time, or it could be very little.

Yes that was my reasoning too. The situation presumably goes:

1. Omicron chooses a random number X, either prime or composite
2. Omega simulates you, makes its prediction, and decides whether X's primality is consistent with its prediction
3. If it is, then:
   1. Omega puts X into the box
   2. Omega teleports you into the room with the boxes and has you make your choice
4. If it's not, then...? I think the correct solution depends on what Omega does in this case.
   1. Maybe it just quietly waits until tomorrow and tries again? In which case no one is ever shown a case where the box does not contain Omicron's number. If this is how Omega is acting, then I think you can act as though your choice affects Omircon's number, even though that number is technically random on this particular day.
   2. Maybe it just picks its own number, and shows you the problem anyway. I believe this was the assumption in the post.

If the agent is EDT and Omicron chooses a prime number, then Omega has to choose a different prime number. Fortunately, for every prime number there exists a distinct prime number.

EDT's policy is not "two-box if both numbers are prime or both numbers are composite", it's "two-box if both numbers are equal". EDT can't (by hypothesis) figure out in the allotted time whether the number in the box (or the number that Omicron chose) is prime. (It can readily verify the equality of the two numbers, though, and this equality is what causes it -- erroneously, in my view -- to believe it has control over whether it gets paid by Omicron.)

This doesn’t seem true, at least in the sense of strict ranking? In the EDT case: if Omega’s policy is to place a prime in Box 1 whenever Omicron chooses a composite number (instead of matching Omicron when possible), then it predicts the EDT agent will choose only Box 1 and so is a stable equilibrium. But since it also always places a different prime whenever Omicron chooses a prime, EDT never sees matching numbers and so always one-boxes, therefore its expected earnings are no less than FDT

The variables with no specified value in the template given aren't the problem. The fact that the template has the form that it does is the problem. That form is unjustified.

The only information we have about Omega's choices is that choosing the same number as Omicron is sometimes possible. Assuming that its probability is the same - or even nonzero - for all decision theories is unjustified, because Omega knows what decision theory the agent is using and can vary their choice of number.

For example, it is compatible with the problem description that Omega never chooses the same number as Omicron if the agent is using CDT. Evaluating how well CDT performs in this scenario is then logically impossible, because CDT agents never enter this scenario.

Like many extensions, variations, and misquotings of well-known decision problems, this one opens up far too many degrees of freedom.