Right back!
[rhinoceros]
It seems to me that the *transparent* boxes make lots of a fifference.
You (the Chooser) stand in front of them and look:
If you see the million dollars in the second box, then you know that
the Predictor predicted that you would choose only this box, and this
is why he put the million there, according to the rules. You decide to
take both boxes. You end up with $1,001,000 and you have proven the
Predictor wrong!
[hell-kite]
My guess is your premise is wrong: Of course it is sensible and
well-nigh "determined" that the Chooser, seeing both boxes filled, will
take both. But, given his clairvoyant abilities, the Predictor WILL
KNOW how the Chooser will behave. If under the circumstance of both
boxes filled, the Chooser will always choose both, THEN THE PREDICTOR
WILL NEVER FILL BOTH BOXES.
He foresees that IF he DOES, THEN the Chooser will take both, so he
DOES NOT. He cannot, as a matter of fact, or else we had a logical
inconsistency: You CANNOT prove the Predictor wrong, because the
Predictor is, by definition of 100%-TRUE-PREDICTION, ALWAYS RIGHT!
[This was my initial answer, but things got more complicated as I
considered your second possibility]
[rhinoceros]
If you see the second box empty, then you know that the Predictor
predicted that you would choose *both* boxes, and this is why he left
the second one empty, according to the rules. You decide to take only
the second box (the empty one), forfeiting $1,000 (it is possible if
you are rich enough) but proving the Predictor wrong again!
[hell-kite]
It occured to me that the transparent box-game is flawed regarding an
imbalance of the Predictors and the Choosers options. In the closed
box-game, both have only two choices: The Predictor can put the million
in the box or not. The Chooser can take only one box or two. In the
transparent version, the Predictor still has only two options, but the
Chooser has his two basic options, plus the option to defect or
cooperate, thus, he has 4 options. Thus, the Predictor cannot
adequately react according to his prediction. Thus, the rules of the
game do not fit anymore.
BUT, note that the Predictor still can predict correctly: He knows how
the Chooser will behave, even though he only has two suboptimal
choices. Thus, this is, imho, not at all an argument for free will. In
the closed box-case, the Predictor never was the cause of the Chooser's
behaviour (except in the sense that his existence constitutes one
aspect of the game). In the transparent box-game, he becomes a causal
force because the decision of the Chooser becomes dependent on his
actions.
Again, I believe the transparent box-game is not valid for
deterministic or anti-deterministic argumentation.
Hopefully coherent,
Björn