Another argument that definitely doesn’t rely on any sort of “doors” for why physical risk might be preferable to logical risk is just if you have diminishing returns on the total number of happy humans. As long as your returns to happy humans are sublinear (logarithmic is a standard approximation, though anything sublinear works), then you should prefer a guaranteed shot at 12 the Everett branches having lots of happy humans to a 12 chance of all the Everett branches having happy humans. To see this, suppose U:N→R measures your returns to the total number of happy humans across all Everett branches. Let N be the total number of happy humans in a good Everett branch and M the total number of Everett branches. Then, in the physical risk situation, you get
Uphysical risk=U⎛⎜
⎜⎝M2∑i=1N⎞⎟
⎟⎠=U(MN2)
whereas, in the logical risk situation, you get
Ulogical risk=12U(0)+12U(M∑i=1N)=12U(MN)
which are only equal if U is linear. Personally, I think my returns are sublinear, since I pretty strongly want there to at least be some humans—more strongly than I want there to be more humans, though I want that as well. Furthermore, if you believe there’s a chance that the universe is infinite, then you should probably be using some sort of measure over happy humans rather than just counting the number, and my best guess for what such a measure might look like seems to be at least somewhat locally sublinear.
Another argument that definitely doesn’t rely on any sort of “doors” for why physical risk might be preferable to logical risk is just if you have diminishing returns on the total number of happy humans. As long as your returns to happy humans are sublinear (logarithmic is a standard approximation, though anything sublinear works), then you should prefer a guaranteed shot at 12 the Everett branches having lots of happy humans to a 12 chance of all the Everett branches having happy humans. To see this, suppose U:N→R measures your returns to the total number of happy humans across all Everett branches. Let N be the total number of happy humans in a good Everett branch and M the total number of Everett branches. Then, in the physical risk situation, you get Uphysical risk=U⎛⎜ ⎜⎝M2∑i=1N⎞⎟ ⎟⎠=U(MN2) whereas, in the logical risk situation, you get Ulogical risk=12U(0)+12U(M∑i=1N)=12U(MN) which are only equal if U is linear. Personally, I think my returns are sublinear, since I pretty strongly want there to at least be some humans—more strongly than I want there to be more humans, though I want that as well. Furthermore, if you believe there’s a chance that the universe is infinite, then you should probably be using some sort of measure over happy humans rather than just counting the number, and my best guess for what such a measure might look like seems to be at least somewhat locally sublinear.