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wedrifid comments on Problem of Optimal False Information - Less Wrong
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Everett branches don't (necessarily) work like that. If 'you' are a person who systematically refuses to play such games then you just don't, no matter the branch. Sure, the Omega in a different branch may find a human-looking creature also called "Endovior" that plays such games but if it is a creature that has a fundamentally different decision algorithm then for the purpose of analyzing your decision algorithm it isn't "you". (There are also branches in which an actual "you" plays the game but only as a freak anomaly of an event like the way an actual 'me' in a freakishly small Everett branch walked through a brick wall that one time. Still not exactly something to identify with as 'you' doing it.)
Eh, that point probably was a bit weak. I probably could've just gotten away with saying 'you are required to choose a box'. Or, come to think of it, 'failure to open the white box and investigate its contents results in the automatic opening and deployment of the black box after X time'.
Or, for that matter, just left it at "Omega will kill you outright". For flavor and some gratuitous additional disutility you could specify the means of execution as being beaten to death by adorable live puppies.
I observe that there have been many human utility functions where people who would prefer to be killed than to make choices offered to them that would keep them alive. So if the intention in the problem is to get you to choose one of the boxes, offering the 3rd choice of being killed doesn't make sense.