FYI, the controversy with the doomsday argument is the distinction between Self-Indication Assumption versus the Self-Sampling Assumption. The question comes down to whether you are a priori more likely to live in a world in which more people exist (over all time) or not. Does the existence of more consciousness make it more likely that you, a 'randomly' chosen consciousness, exists in the first place? If so, then that factor exactly cancels out the doomsday argument. [3]

[1] https://en.wikipedia.org/wiki/Self-indication_assumption [2] https://en.wikipedia.org/wiki/Self-sampling_assumption [3] https://en.wikipedia.org/wiki/Self-Indication_Assumption_Doo...

The doomsday argument is sound. It's controversial with the assumptions about population growth, which plain don't make sense—I don't claim to understand what happens, but I think that an argument would need to be made for the entire population basically vanishing when it hits the cap. There are certainly scenarios that would lead to that (e.g. nuclear war over resources could plausibly destroy statistically significant human populations enough to allow for extinction), but again, it requires argument.

Or another way, you at least need to argue AGAINST rational rationing of existing resources to make calculating potential populations over all time quite difficult and run up against heat death calculations.

That said, I love both these thought experiments because they highlight how hard it is to figure out population growth with (theoretically) rational populations.