But that would mean that the utility of 50% chance of 1 day and 50% chance of 3 days is 0.5*1+0.5*1.75=1.375, which is different from the utility of two days that you would expect.
You can’t calculate utilites anyway; there’s no reason to assume that u(n days) should be 0.5 * (u(n+m days) + u(n-m days)) for any n or m. If you want to include immortality, you can’t assign utilities linearly, although you can get arbitrarily close by picking a higher factor than 0.5 as long as it’s < 1.
But that would mean that the utility of 50% chance of 1 day and 50% chance of 3 days is
0.5*1+0.5*1.75=1.375, which is different from the utility of two days that you would expect.You can’t calculate utilites anyway; there’s no reason to assume that u(n days) should be 0.5 * (u(n+m days) + u(n-m days)) for any n or m. If you want to include immortality, you can’t assign utilities linearly, although you can get arbitrarily close by picking a higher factor than 0.5 as long as it’s < 1.