If the Predictor continues to work in this circumstance, it would be evidence against MWI, since on MWI there are two futures—one in which you push the button and one in which you don’t—that both presumably send signals back to the Predictor. Since only one of these signals can determine the Predictor’s behavior, it will get the prediction wrong for some branches. Consistently finding that you are not in one of these branches becomes more and more improbable as the number of trials increases.
Ted Chiang wrote a one-page short story, What’s Expected of Us, about basically this, and it’s scary. (pdf)
This story struck me as more silly than scary.
My reaction time is less than a second; what happens if I decide to press the button as soon as I hear a Geiger counter click?
You find out whether Geiger counters have free will.
If the Predictor continues to work in this circumstance, it would be evidence against MWI, since on MWI there are two futures—one in which you push the button and one in which you don’t—that both presumably send signals back to the Predictor. Since only one of these signals can determine the Predictor’s behavior, it will get the prediction wrong for some branches. Consistently finding that you are not in one of these branches becomes more and more improbable as the number of trials increases.
It seems like the sort of thing that once upon a time someone could have written about souls instead of free will.