DanielFilan comments on Stupid Questions December 2014 - Less Wrong Discussion
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I'm sorry, but "sort of thing which is liable to lead to crazy behaviour" won't cut it. Could you give an example of crazy behaviour with this preference ordering? I still think this approach (not counting measure as long as some of me exists) feels right and is what I want. I'm not too worried about discontinuity at only x=0 (and if you look at larger multiverses, x probably never equals 0.)
To argue over a specific example: if I set up something that chooses a number randomly with quantum noise, then buys a lottery ticket, then kills me (in my sleep) only if the ticket doesn't win, then I assign positive utility to turning the machine on. (Assuming I don't give a damn about the rest of the world who will have to manage without me.) Can you turn this into either an incoherent preference, or an obviously wrong preference?
(Personally, I've thought about the TDT argument for not doing that; because you don't want everyone else to do it and create worlds in which only 1 person who would do it is left in each, but I'm not convinced that there are a significant number of people who would follow my decision on this. If I ever meet someone like that, I might team up with them to ensure we'd both end up in the same world. I haven't seen any analysis of TDT/anthropics applied to this problem, perhaps because other people care more about the world?)
Another way to look at it is this: imagine you wake up after the bet, and don't yet know whether you are going to quickly be killed or whether you are about to recieve a large cash prize. It turns out that your subjective credence for which branch you are in is given by the Born measure. Therefore, (assuming that not taking the bet maximises expected utility in the single-world case), you're going to wish that you hadn't taken the bet immediately after taking it, without learning anything new or changing your mind about anything. Thus, your preferences as stated either involve weird time inconsistencies, or care about whether there's a tiny sliver of time between the worlds branching off and being killed. At any rate, in any practical situation, that tiny sliver of time is going to exist, so if you don't want to immediately regret your decision, you should maximise expected utility with respect to the Born measure, and not discount worlds where you die.