His opinion is that you only really have two choices for a system with inherent uncertainty. Classical probability theory, or quantum amplitudes with the Born rule. I’m not sure to what extent the argument holds up, but he makes some compelling cases that the obvious alterations to probability theory or quantum amplitudes wouldn’t add up to normality.
I also think Scott Aaronson’s view of this issue is interesting: https://www.scottaaronson.com/democritus/lec9.html
His opinion is that you only really have two choices for a system with inherent uncertainty. Classical probability theory, or quantum amplitudes with the Born rule. I’m not sure to what extent the argument holds up, but he makes some compelling cases that the obvious alterations to probability theory or quantum amplitudes wouldn’t add up to normality.