I still don't see how statements about disposition in your sense are supposed to have an objective truth value (what does someone look like in visually simplified?), and why you think this disposition is supposed to better correlate with peoples predictions about decisions than the non-random component of the decision making process (total disposition) does (or why you think this concept is useful if it doesn't), but I suspect discussing this further won't lead anywhere.
Let's try leaving the disposition discussion aside for a moment: You are postulating a scenario where someone spontaneously changes from a one-boxer into a two-boxer after the predictor has already made the prediction, just long enough to open the right hand box and collect the $1000. Is that right? And the question is whether I should regret not being able to change myself back into a one boxer in time to refuse the $1000?
Obviously if my behavior in this case was completely uncorrelated to the odds of finding the $1,000,000 box empty I should not. But the normal assumption for cases where your behavior is unpredictable (e. g. when you are using a quantum coin) is that P(two box) = P ( left box empty). Otherwise I would try to contrive to one-box with a probability of just over 0.5. So the details depend on P.
If P>0.001 (I'm assuming constant utility per dollar, which is unrealistic) my expected dollars before opening the left box have been reduced, and I bitterly regret my temporary lapse from sanity since it might have costed me $1,000,000. The rationale is the same as in the normal Newcomb problem.
If P<0.001 my expected dollars right at that point have increased, and according to some possible decision theories that one-box I should not regret the spontaneous change, since I already know I was lucky. But nevertheless my overall expected payoff in all branches is lower than it would be if temporary lapses like that were not possible. Since I'm a Counterfactual muggee I regret not being able to prevent the two-boxing, but am happy enough with the outcome for that particular instance of me.
A common background assumption on LW seems to be that it's rational to act in accordance with the dispositions one would wish to have. (Rationalists must WIN, and all that.)
E.g., Eliezer:
And more recently, from AdamBell:
Within academic philosophy, this is the position advocated by David Gauthier. Derek Parfit has constructed some compelling counterarguments against Gauthier, so I thought I'd share them here to see what the rest of you think.
First, let's note that there definitely are possible cases where it would be "beneficial to be irrational". For example, suppose an evil demon ('Omega') will scan your brain, assess your rational capacities, and torture you iff you surpass some minimal baseline of rationality. In that case, it would very much be in your interests to fall below the baseline! Or suppose you're rewarded every time you honestly believe the conclusion of some fallacious reasoning. We can easily multiply cases here. What's important for now is just to acknowledge this phenomenon of 'beneficial irrationality' as a genuine possibility.
This possibility poses a problem for the Eliezer-Gauthier methodology. (Quoting Eliezer again:)
The problem, obviously, is that it's possible for irrational agents to receive externally-generated rewards for their dispositions, without this necessarily making their downstream actions any more 'reasonable'. (At this point, you should notice the conflation of 'disposition' and 'choice' in the first quote from Eliezer. Rachel does not envy Irene her choice at all. What she wishes is to have the one-boxer's dispositions, so that the predictor puts a million in the first box, and then to confound all expectations by unpredictably choosing both boxes and reaping the most riches possible.)
To illustrate, consider (a variation on) Parfit's story of the threat-fulfiller and threat-ignorer. Tom has a transparent disposition to fulfill his threats, no matter the cost to himself. So he straps on a bomb, walks up to his neighbour Joe, and threatens to blow them both up unless Joe shines his shoes. Seeing that Tom means business, Joe sensibly gets to work. Not wanting to repeat the experience, Joe later goes and pops a pill to acquire a transparent disposition to ignore threats, no matter the cost to himself. The next day, Tom sees that Joe is now a threat-ignorer, and so leaves him alone.
So far, so good. It seems this threat-ignoring disposition was a great one for Joe to acquire. Until one day... Tom slips up. Due to an unexpected mental glitch, he threatens Joe again. Joe follows his disposition and ignores the threat. BOOM.
Here Joe's final decision seems as disastrously foolish as Tom's slip up. It was good to have the disposition to ignore threats, but that doesn't necessarily make it good idea to act on it. We need to distinguish the desirability of a disposition to X from the rationality of choosing to do X.