MWI view: There are many experimenters, in fact there is a continuum of them for each "run" of the experiment. The "setup" of each run that produces the mixed state in the bowl of marbles is splitting the whole universe (at the speed of light) and also splits the experimenters. Some of them are now in the "red" universe, and some of them are now in the "blue" universe and give matching answers. The percentage of them giving each answer is the same as in the situation above, but this percentage applies to even one run of the experiment.
However, the many experimenters and their percentages is not observable in a single experimental run from inside their universe. The experimenters cannot communicate, so after each run they only have 1 bit of information each (red or blue). They need to repeat the experiment to gain more than one bit of information.
However, now, their states are different. Some experimenters have a different history to the others. They aren't all the same any more! There's no "reset" button. This is the core of many of the "mysteries" and "apparent superluminal communication" in QM. There's no mystery. The state -- including the experimenters -- is splitting.
The classic "superluminal" communication isn't: Entangled opposite particles are simply saying that some universes have the (A,B) pair, others have the (B,A) pair. When you find out that you have the "A" particle, you instantly know that in your universe the other guy must have the "B" particle. There's no communication, instead the experiment is all about finding out one bit of information about "where you are" in the multiverse.