Yeah, I also had similar ideas for solving anthropics a few years ago, and was surprised when I learned that UDASSA had been around for so long. At least you can take pride in having found the right answer independently.
I think that UDASSA gives P(heads) = 1⁄2 on the Sleeping Beauty problem due to the way it weights different observer-moments, proportional to 2^(-description length). This might seem a bit odd, but I think it’s necessary to avoid problems with Boltzmann brains and the like.
You mean P(monday)? In that case it would be different although have some similarity. Why is the description length of the monday observer moment longer than the tuesday one?
No, I mean Beauty’s subjective credence that the coin came up heads. That should be 1⁄2 by the nature of a coin flip. Then, if the coin comes up tails, you need 1 bit to select between the subjectively identical states of waking up on Monday or Tuesdsay. So in total:
P(heads, Monday) = 1⁄2,
P(tails, Monday) = 1⁄4
P(tails, Tuesday) = 1⁄4
(EDIT: actually this depends on how difficult it is to locate memories on Monday vs. Tuesday, which might be harder given that your memory has been erased. I think that for ‘natural’ ways of locating your consciousness it should be close to 12/ 14 / 14 though)
(DOUBLE EDIT, MUCH LATER: actually it now seems to me like the thirder position might apply here, since the density of spacetime locations with the right memories is higher in the tails branch than the heads)
Yeah, I also had similar ideas for solving anthropics a few years ago, and was surprised when I learned that UDASSA had been around for so long. At least you can take pride in having found the right answer independently.
I think that UDASSA gives P(heads) = 1⁄2 on the Sleeping Beauty problem due to the way it weights different observer-moments, proportional to 2^(-description length). This might seem a bit odd, but I think it’s necessary to avoid problems with Boltzmann brains and the like.
You mean P(monday)? In that case it would be different although have some similarity. Why is the description length of the monday observer moment longer than the tuesday one?
No, I mean Beauty’s subjective credence that the coin came up heads. That should be 1⁄2 by the nature of a coin flip. Then, if the coin comes up tails, you need 1 bit to select between the subjectively identical states of waking up on Monday or Tuesdsay. So in total:
P(heads, Monday) = 1⁄2,
P(tails, Monday) = 1⁄4
P(tails, Tuesday) = 1⁄4
(EDIT: actually this depends on how difficult it is to locate memories on Monday vs. Tuesday, which might be harder given that your memory has been erased. I think that for ‘natural’ ways of locating your consciousness it should be close to 12/ 14 / 14 though)
(DOUBLE EDIT, MUCH LATER: actually it now seems to me like the thirder position might apply here, since the density of spacetime locations with the right memories is higher in the tails branch than the heads)