I'm not sure that matrix-within-a-matrix is the right answer, but those aren't reasons it has to be wrong. Choice can be artifical. If the human minds in the matrix (the primary one) reject the idea of the matrix, then they are allowed to be given a false 'choice' to leave that matrix and enter what they believe to be reality, but is really just another matrix. Having been given their choice, they no longer reject the second matrix because they believe they are where they are of their own free will. So maybe it's not so much a matrix within a matrix as it is parallel matrices.
It's kind of like a magician's force. They present you with a question that appears to make their trick random, as if you were telling them exactly what they should do. But in reality they are just interpreting your answer in such a way that they get to do what they were planning all along. The difference is that the audience's minds are satisfied that there was a choice because a question was asked and answered, regardless of whether or not it had any effect on the final outcome.
It's kind of like a magician's force. They present you with a question that appears to make their trick random, as if you were telling them exactly what they should do. But in reality they are just interpreting your answer in such a way that they get to do what they were planning all along. The difference is that the audience's minds are satisfied that there was a choice because a question was asked and answered, regardless of whether or not it had any effect on the final outcome.
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