If you precommit to act this way, then it’s not the case that [the predictor predicts that you wouldn’t take the small box regardless of what you see in the big one] (since you do take it if the big box is full, so in that case you can’t be predicted not take the small box). By the stated algorithm of box-filling, this results in the big box being empty. The predictor is not predicting what happens in actuality, it’s predicting what happens in the hypothetical situation where the big box is full (regardless of whether this situation actually takes place), and what happens in the hypothetical situation where the big box is empty (also regardless of what happens in reality). The predictor is not deciding what to do in these hypothetical situations, it’s deciding what to do in reality.
Even if the big box is empty and you one-box anyway, the predictor can just say “Yes, but if the big box had been full, you would have two-boxed.” and it’s unclear whether the predictor is accurate or not since you weren’t in that situation.
and it’s unclear whether the predictor is accurate or not since you weren’t in that situation
The predictor acts based on your behavior in both hypotheticals, and from either of the hypotheticals you don’t get to observe your own decision in the other, to verify that it was taken into account correctly.
If the big box is full and you one-box, the predictor can say “Yes, and if the big box had been empty, you would have also one-boxed.” And it’s unclear whether the predictor is accurate or not since you weren’t in that situation. Being wrong in your favor is also a possibility.
You don’t get to verify that your decision was taken into account correctly anyway. If the big box is full and you two-box, the predictor can say “Yes, so you are currently in a hypothetical, in reality the big box is empty.”
If you precommit to act this way, then it’s not the case that [the predictor predicts that you wouldn’t take the small box regardless of what you see in the big one] (since you do take it if the big box is full, so in that case you can’t be predicted not take the small box). By the stated algorithm of box-filling, this results in the big box being empty. The predictor is not predicting what happens in actuality, it’s predicting what happens in the hypothetical situation where the big box is full (regardless of whether this situation actually takes place), and what happens in the hypothetical situation where the big box is empty (also regardless of what happens in reality). The predictor is not deciding what to do in these hypothetical situations, it’s deciding what to do in reality.
Even if the big box is empty and you one-box anyway, the predictor can just say “Yes, but if the big box had been full, you would have two-boxed.” and it’s unclear whether the predictor is accurate or not since you weren’t in that situation.
The predictor acts based on your behavior in both hypotheticals, and from either of the hypotheticals you don’t get to observe your own decision in the other, to verify that it was taken into account correctly.
If the big box is full and you one-box, the predictor can say “Yes, and if the big box had been empty, you would have also one-boxed.” And it’s unclear whether the predictor is accurate or not since you weren’t in that situation. Being wrong in your favor is also a possibility.
You don’t get to verify that your decision was taken into account correctly anyway. If the big box is full and you two-box, the predictor can say “Yes, so you are currently in a hypothetical, in reality the big box is empty.”