This is a linkpost for https://philpapers.org/archive/ROBCEI-2.pdf
Seeing that there was some interest in Bostrom's simulation argument before (http://lesswrong.com/lw/hgx/paper_on_the_simulation_argument_and_selective/), I wanted to post a link to a paper I wrote on the subject, together with the following text, but I was only able to post into my (private?) Drafts section. I'm sorry I don't know better about where the appropriate place is for this kind of thing (if it's welcome here at all). The paper: http://www.cs.toronto.edu/~wehr/rd/simulation_args_crit_extended_with_proofs.pdf
This is a very technical paper, which requires some (or a lot) of familiarity with Bostrom/Kulczycki's "patched" Simulation Argument (www.simulation-argument.com/patch.pdf). I'm choosing to publish it here after experiencing Analysis's depressing version of peer review (they rejected a shorter, more-professional version of the paper based on one very positive review, and one negative review that was almost certainly written by Kulczycki or Bostrom themself).
The positive review (of the earlier shorter, more-professional version of the paper) does a better job of summarizing the contribution than I did, so with the permission of the reviewer I'm including an excerpt here:
Bostrom (2003) argued that at least one of the following three claims is true: (1) the fraction of civilizations that reach a 'post-human' stage is approximately zero; (2) the fraction of post-human civilizations interested in running 'significant numbers' of simulations of their own ancestors is approximately zero; (3) the fraction of observers with human-type experiences that are simulated is approximately one.
The informal argument for this three-part disjunction is that, given what we know about the physical limits of computation, a post-human civilization would be so technologically advanced that it could run 'hugely many' simulations of observers very easily, should it choose to do so, so that the falsity of (1) and (2) implies the truth of (3). However, this informal argument falls short of a formal proof.
Bostrom himself saw that his attempt at a formal proof in the (2003) paper was sloppy, and he attempted to put it right in Bostrom and Kulczycki (2011). The take-home message of Sections 1 and 2 of the manuscript under review is that these (2011) reformulations of the argument are still rather sloppy. For example, the author points out (p. 6) that the main text of B&K inaccurately describes the mathematical argument in the appendix: the appendix uses an assumption much more favourable to B&K's desired conclusion than the assumption stated in the main text. Moreover, B&K's use of vague terms such as 'significant number' and 'astronomically large factor' creates a misleading impression. The author shows, amusingly, that the 'significant number' must be almost 1 million times greater than the 'astronomically large factor' for their argument to work (p. 9).
In Section 3, the author provides a new formulation of the simulation argument that is easily the most rigorous I have seen. This formulation deserves to be the reference point for future discussions of the argument's epistemological consequences."
I got from it that for the Simulation Argument to work, it is important what constants we assume in each clause, in relation to each other. So checking each disjunctive claim separately allows one to do a sorta sleight-of-hand, in which one can borrow some unseen "strength" from the other claims - and there actually isn't enough margin to be so lax. Is this correct?
OK, I've re-read the original papers carefully to check this.
Your criticism of Patch 1 is entirely based on the wording of "For example, in an appendix we show how by assuming that the difference is no greater than a factor of one million we can derive the key tripartite disjunction".
The wording is indeed misleading and wrong, but to be fair - only in this one sentence. In all other places the authors are consistent in saying that you need the factor to be no greater N/1000000, or an "astronomically large number", with the understanding that an "astronomically large number" divided by 10^6 is still an "astronomically large number".
So overall the criticism is sorta uninteresting - I think you are attacking a particularly strawmanned version of the "patch" paper.
As for Patch 2, didn't read yet.
I think that was B/K's point of view as well, although in their review they fell back on the Patch 2 argument. The version of my paper they read didn't flesh out the problems with the Patch 2 argument.
I respectfully disagree that the criticism is entirely based on the wording of that one sentence. For one thing, if I remember correctly, I counted at least 6 prose locations in the paper about the Patch 1 argument that need to be corrected. Anywhere "significant number of" appears needs to be changed, for example, since "significant number of" can actually mean, depending on the settings of the parameters, "astronomically large number of". I think presenting the argument without parameters is misleading, and essentially propaganda.
Patch 2 has a similar issue (see Section 2.1), as well as (I think) another, more serious issue (Section 3.1, "Step 3").