My objection to this argument is that it not only assumes that Predictoria accepts it is plausibly being simulated by Adversaria, which seems like a pure complexity penalty over the baseline physics it would infer otherwise unless that helps to explain observations,
Let’s assume for simplicity that both Predictoria and Adversaria are deterministic and nonbranching universes with the same laws of physics but potentially different starting conditions. Adversaria has colonized its universe and can run a trillion simulations of Predictoria in parallel. Again for simplicity let’s assume that each of these simulations is done as something like a full-scale physical reconstruction of Predictoria but with hidden nanobots capable of influencing crucial events. Then each of these simulations should carry roughly the same weight in M as the real Predictoria and does not carry a significant complexity penalty over it. That’s because the complexity / length of the shortest program for the real Predictoria, which consists of its laws of physics (P) and starting conditions (ICs_P) plus a pointer to Predictoria the planet (Ptr_P), is K(P) + K(ICs_P|P) + K(Ptr_P|...). The shortest program for one of the simulations consists of the same laws of physics (P), Adversaria’s starting conditions (ICs_A), plus a pointer to the simulation within its universe (Ptr_Sim), with length K(P) + K(ICs_A|P) + K(Ptr_Sim|...). Crucially, this near-equal complexity relies on the idea that the intricate setup of Adversaria (including its simulation technology and intervention capabilities) arises naturally from evolving ICs_A forward using P, rather than needing explicit description.
(To address a potential objection, we also need that the combined weights (algorithmic probability) of Adversaria-like civilizations is not much less than the combined weights of Predictoria-like civilizations, which requires assuming that phenomenon of advanced civilizations running such simulations is a convergent outcome. That is, it assumes that once civilization reaches Predictoria-like stage of development, it is fairly likely to subsequently become Adversaria-like in developing such simulation technology and wanting to use it in this way. There can be a complexity penalty from some civilizations choosing or forced not to go down this path, but that would be more than made up for by the sheer number of simulations each Adversaria-like civilization can produce.)
If you agree with the above, then at any given moment, simulations of Predictoria overwhelm the actual Predictoria as far as their relative weights for making predictions based on M. Predictoria should be predicting constant departures from its baseline physics, perhaps in many different directions due to different simulators, but Predictoria would be highly motivated to reason about the distribution of these vectors of change instead of assuming that they cancel each other out. One important (perhaps novel?) consideration here is that Adversaria and other simulators can stop each simulation after the point of departure/intervention has passed for a while, and reuse the computational resources on a new simulation rebased on the actual Predictoria that has observed no intervention (or rather rebased on an untouched simulation of it), so the combined weight of simulations does not decrease relative to actual Predictoria in M even as time goes on and Predictoria makes more and more observations that do not depart from baseline physics.
Let’s assume for simplicity that both Predictoria and Adversaria are deterministic and nonbranching universes with the same laws of physics but potentially different starting conditions. Adversaria has colonized its universe and can run a trillion simulations of Predictoria in parallel. Again for simplicity let’s assume that each of these simulations is done as something like a full-scale physical reconstruction of Predictoria but with hidden nanobots capable of influencing crucial events. Then each of these simulations should carry roughly the same weight in M as the real Predictoria and does not carry a significant complexity penalty over it. That’s because the complexity / length of the shortest program for the real Predictoria, which consists of its laws of physics (
P) and starting conditions (ICs_P) plus a pointer to Predictoria the planet (Ptr_P), isK(P) + K(ICs_P|P) + K(Ptr_P|...). The shortest program for one of the simulations consists of the same laws of physics (P), Adversaria’s starting conditions (ICs_A), plus a pointer to the simulation within its universe (Ptr_Sim), with lengthK(P) + K(ICs_A|P) + K(Ptr_Sim|...). Crucially, this near-equal complexity relies on the idea that the intricate setup of Adversaria (including its simulation technology and intervention capabilities) arises naturally from evolvingICs_Aforward usingP, rather than needing explicit description.(To address a potential objection, we also need that the combined weights (algorithmic probability) of Adversaria-like civilizations is not much less than the combined weights of Predictoria-like civilizations, which requires assuming that phenomenon of advanced civilizations running such simulations is a convergent outcome. That is, it assumes that once civilization reaches Predictoria-like stage of development, it is fairly likely to subsequently become Adversaria-like in developing such simulation technology and wanting to use it in this way. There can be a complexity penalty from some civilizations choosing or forced not to go down this path, but that would be more than made up for by the sheer number of simulations each Adversaria-like civilization can produce.)
If you agree with the above, then at any given moment, simulations of Predictoria overwhelm the actual Predictoria as far as their relative weights for making predictions based on M. Predictoria should be predicting constant departures from its baseline physics, perhaps in many different directions due to different simulators, but Predictoria would be highly motivated to reason about the distribution of these vectors of change instead of assuming that they cancel each other out. One important (perhaps novel?) consideration here is that Adversaria and other simulators can stop each simulation after the point of departure/intervention has passed for a while, and reuse the computational resources on a new simulation rebased on the actual Predictoria that has observed no intervention (or rather rebased on an untouched simulation of it), so the combined weight of simulations does not decrease relative to actual Predictoria in M even as time goes on and Predictoria makes more and more observations that do not depart from baseline physics.
My response is its own post: https://www.lesswrong.com/posts/KAifhdKr96kMre2zy/changing-my-mind-about-christiano-s-malign-prior-argument