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Probability thought experiment — split brain study
I recently read this post: The operation of chance in a deterministic world which focused on how we can recover probability even in a world devoid of true randomness.
It got me thinking about how we can reconstruct probability even if we have complete knowledge of the process. A lot of this thinking was inspired by Derek Parfit's idea of psychological continuity. Sorry if this is too much philosophy for a stats forum, but I think it's appropriate.
The idea stems from split brain studies, where we supposedly can live an almost completely (outwardly, at least) normal life with half a brain. Here's the scenario:
Assume the person here is unaware of the overall experiment (ethical issues aside).
We start with a single person in a single room.
We put the person to sleep and clone them (the clones are completely indistinguishable, so there is no concept of the "original person" -- if you need to, imagine the original person disappears and is replaced by two clones, one