The two-boxer never assumes that the decision isn’t predictable. They just say that the prediction can no longer be influenced and so you may as well gain the $1000 from the transparent box.
In terms of your hypothetical scenario, the question for the two-boxer will be whether the decision causally influences the result of this brain scan. If yes, then, the two-boxer will one-box (weird sentence). If no, the two-boxer will two-box.
Time is irrelevant to the two-boxer except as a proof of causal independence so there’s no interesting answer to this question. The two-boxer is concerned with causal independence. If a decision cannot help but causally influence the brain scan then the two-boxer would one-box.
Two-boxers use a causal model where your current brain state has causal influence on your future decisions. They are interested in the causal effects of the decision not the brain state and hence the causal independence criterion does distinguish the cases in their view and they need not appeal to time.
They have the right causal model. They just disagree about which downstream causal effects we should be considering.
No-one denies this. Everyone agrees about what the best program is. They just disagree about what this means about the best decision. The two-boxer says that unfortunately the best program leads us to make a non-optimal decision which is a shame (but worth it because the benefits outweigh the cost). But, they say, this doesn’t change the fact that two-boxing is the optimal decision (while acknowledging that the optimal program one-boxes).
I suspect that different two-boxers would respond differently as anthropic style puzzles tend to elicit disagreement.
Well, they’re saying that the optimal algorithm is a one-boxing algorithm while the optimal decision is two-boxing. They can explain why as well (algorithms have different causal effects to decisions). There is no immediate contradiction here (it would take serious argument to show a contradiction like, for example, an argument showing that decisions and algorithms are the same thing). For example, imagine a game where I choose a colour and then later choose a number between 1 and 4. With regards to the number, if you pick n, you get $n. With regards to the colour, if you pick red, you get $0, if you pick blue you get $5 but then don’t get a choice about the number (you are presumed to have picked 1). It is not contradictory to say that the optimal number to pick is 1 but the optimal colour to pick is blue. The two-boxer is saying something pretty similar here.
What “ought” you do, according to the two-boxer. Well that depends what decision you’re facing. If you’re facing a decision about what algorithm to adopt, then adopt the optimal algorithm (which one-boxers on all future versions of NP though not ones where the prediction has occurred). If you are not able to choose between algorithms but are just choosing a decision for this occasion then choose two-boxing. They do not give contradictory advice.