For reference, before reading this post, read the posts on Meaning of Probability in an MWI and Measure of Consciousness versus Probability.
Here, I'll outline the way in which the Computationalist philosophy of mind suggests that it might be possible to calculate the measures of consciousness for various outcomes.
My goal in this is to either derive from the MWI the Born Rule (which allows us to calculate the probabilities in QM), thus providing strong support for the computationalist view of the MWI, or to show that the experimentally discovered Born Rule is inconsistent with these popular views of mind and physics.
Computationalism is basically the idea that a brain gives rise to conscious observations due to its mathematically describable functioning: the motions of its parts together with the laws of physics that restrict and determine those motions.
With the existence of consciousness thus being in principle describable mathematically, we can hypothesize that it might be possible to analyze the mathematical description of a physical system, and based on it determine not only whether consciousness is present, but also to determine that multiple different types of observations are being made in different parts of the system. We can make a reasonable guess as to the nature of those observations.
We can also attempt to determine what the "quantity of consciousness" is for each significantly different type of observation. If we can, then we have a measure distribution, which we can compare to what the Born Rule predicts.
In doing so, it is necessary to work with computations as proxies for the conscious observations which are assumed to accompany them. The nature of the link between computations and conscious observations, while an important topic in its own right, is for the most part not something we need to analyze for this purpose, which is fortunate as understanding it is famously hard.
In comparing the computationalist + MWI prediction to the Born Rule, it would not be a problem if there are very small deviations which would not yet have been detected experimentally. In theory, such a situation could open the door to a straightforward experimental test of the computationalist approach to the MWI, which would be a great thing to have. However, it seems likely that IF small deviations are predicted then any such deviations would be too small to ever measure.
On the other hand, if the measure distribution we get does NOT agree with the Born Rule even approximately, then the computationalist picture of the MWI would be refuted.
Unfortunately, all of this is easier said than done. While the general idea of Computationalism is fairly popular, it has not yet been developed into something precise enough to carry out this program. Needless to say, experiments can be of no help in this regard.
As will be explained in detail in forthcoming posts, I have made proposals as to how to make computationalism precise enough. While it is technically challenging to state necessary and sufficient conditions to be able to say that a given computation is carried out by a given system, I am satisfied that this can be done and that my proposal is at least quite close to the correct way to do so.
Given such conditions, the next thing that we need is a way to determine the accompanying quantity of consciousness. Hopefully, we can avoid dealing with the link between computation and consciousness even here, by determining as a proxy the "quantity of each computation" that is present, and assuming that it is proportional to the quantity of consciousness.
However, the link may not be so easily bypassed, as it turns out that there are different options for determining the "quantity of computation" and naturally the "right" choice would be the one that best suits the application we have in mind, namely consciousness. It is not clear, however, what that one is.
Given the choices that I would tend to pick based upon subjective criteria of what "seems most natural" to me, the application of those choices to the standard physics of the MWI apparently DOES NOT give the Born Rule. This fact is not sufficient for me to declare that the MWI has been disproven; however, it does help motivate a search for MWI proposals that include modifications of physics, as well as further work on how to determine "quantities of computations".
I would like other people to learn of and study these issues. Perhaps, in the future, people who have studied these issues deeply and explored the implications and alternatives in great detail will find that the criteria which happen to give the Born Rule from the unmodified MWI are the same that they prefer for quite different reasons.
