Probability thought experiment — split brain study

2017-12-13 17:41:40

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