Thanks for pointing that out. My arguments above do not apply.
I’m still skeptical. I buy anthropic reasoning as valid in cases where we share an observation across subjects and time (eg, “we live on a planet orbiting a G2V-type star”, “we inhabit a universe that appears to run on quantum mechanics”), but not in cases where each observation is unique (eg, “it’s the year 2021, and there have been about 107,123,456,789 (plus or minus a lot) people like me ever”). I am far less confident of this than I stated for the arguments above, but I’m still reasonably confident, and my expertise does still apply (I’ve thought about it more than just what you see here).
This could mean you would also have to reject thirding in the famous Sleeping Beauty problem. Which contradicts a straightforward frequentist interpretation of the setup: If the SB experiment was repeated many times, one third of the awakenings would be Monday Heads, so if SB was guessing after awakening “the coin came up heads” she would be right with frequentist probability 1⁄3.
Of course there are possible responses to this. My point is just that: rejecting Katja’s doomsday argument by rejecting SIA style anthropic reasoning may come with implausible consequences in other areas.
Thanks for pointing that out. My arguments above do not apply.
I’m still skeptical. I buy anthropic reasoning as valid in cases where we share an observation across subjects and time (eg, “we live on a planet orbiting a G2V-type star”, “we inhabit a universe that appears to run on quantum mechanics”), but not in cases where each observation is unique (eg, “it’s the year 2021, and there have been about 107,123,456,789 (plus or minus a lot) people like me ever”). I am far less confident of this than I stated for the arguments above, but I’m still reasonably confident, and my expertise does still apply (I’ve thought about it more than just what you see here).
This could mean you would also have to reject thirding in the famous Sleeping Beauty problem. Which contradicts a straightforward frequentist interpretation of the setup: If the SB experiment was repeated many times, one third of the awakenings would be Monday Heads, so if SB was guessing after awakening “the coin came up heads” she would be right with frequentist probability 1⁄3.
Of course there are possible responses to this. My point is just that: rejecting Katja’s doomsday argument by rejecting SIA style anthropic reasoning may come with implausible consequences in other areas.