> but in the case of both Bostrom's and Kipping's position on the simulation argument, no such process is performed, no empirical evidence is applied to the question

It is not true that no empirical evidence is applied. To start with, future empirical evidence that arises in later historical periods could be very relevant – if a future observer observes running simulations, even nested simulations, that empirical evidence would greatly increase the probability of they themselves also being in a simulation, which would in turn raise the probability of us being in one now. If in the future we observed that technology being developed, but nobody being interested in using it, or a widespread moral prohibition being developed against it which is effectively enforced by the state – that would decrease its probability. If in the future we found ourselves in a state of seemingly terminal technological and economic decline, and our extinction seemed imminent, that would also decrease the probability. If after millions of years of future human technological development, we had still failed to develop this technology, that would support the idea that it is fundamentally infeasible, which in turn would reduce the probability the hypothesis is true.

It also isn't true that no contemporary physical evidence is relevant. If you read Bostrom's original paper, he cites results from physics (the Bremermann‐Bekenstein bound and the black hole limit) to support the idea that ancestor simulations may be feasible. Those results from physics are deduced from theories which are supported by empirical evidence (such as general relativity and quantum mechanics). If different observations had been made, supporting some other theories instead of establishing GR and QM, and from those theories we deduced something other than the Bremermann‐Bekenstein bound and the black hole limit, that might have led to a different conclusion about the physical limits of computation. If we exited in a universe in which the physical limits of computation were much lower, then the feasibility of ancestor simulations would be worse, and hence the simulation hypothesis would be less likely to be true.

> Exactly - neither me, you nor anyone else has any objective reason to believe this value to be more accurate than any other, and invoking the principle of indifference in these circumstances does not alter that fact.

There are two different ways of looking at "objective Bayesian probability": (1) as a school of thought, (2) as a claim about what epistemic probabilities we rationally ought to assign.

If we mean it as (1), then if you are calculating "objective Bayesian probability" according to the teachings of the adherents of that school of thought, then you have correctly calculated the "objective Bayesian probability". Whether you ultimately agree with the "principle of indifference", if that's what that school of thought teaches, it is part of "objective Bayesian probability".

If we are talking about sense (2), which I believe is the operative sense here – well, just as there is notorious disagreement about what is moral, or what morality requires – I would argue there is also heaps of disagreement about what is rational, or what rationality requires – it is just not as well-known (which is something I'd personally like to change).

So one person says "if we know nothing about the truth of hypothesis H, we should use the principle of indifference to assign it a prior probability of 0.5, and that is the epistemic probability we rationally ought to have with respect to it, until such time as we learn more". And you disagree, and say that's not what we rationally ought to do, at least not in this specific circumstance (although you appear to agree it may be what we rationally ought to do in other significantly different circumstances).

I'm not sure that difference in opinion about what is rational is fundamentally any easier to resolve than the notorious differences of opinion about what is moral (consider debates about the morality of abortion, the morality of the death penalty, sexual morality, etc)