If you specify everything about the experiment, then you have added complexity on both sides. But note that things like “a fair coin will be flipped” is not actually possible to specify under SI, which works with deterministic Turing machines. It’s not clear how to specify something that works like that.
And we mostly care about these problems because of the relevance to more realistic versions like doomsday, where we do not have the specification and so you do have asymmetrical complexity. In any real world scenario, you have uncertainty over exactly what is going on, and some of the possibilities are simpler than others and get more weight. But you never really exclude possibilities like “Omega is lying to me about how this works” or “it’s all a simulation”, they just become improbable if you have significant evidence against.
If you specify everything about the experiment, then you have added complexity on both sides. But note that things like “a fair coin will be flipped” is not actually possible to specify under SI, which works with deterministic Turing machines. It’s not clear how to specify something that works like that.
And we mostly care about these problems because of the relevance to more realistic versions like doomsday, where we do not have the specification and so you do have asymmetrical complexity. In any real world scenario, you have uncertainty over exactly what is going on, and some of the possibilities are simpler than others and get more weight. But you never really exclude possibilities like “Omega is lying to me about how this works” or “it’s all a simulation”, they just become improbable if you have significant evidence against.