In a deterministic model there is no fundamental probability, we can agree on that. In classical systems, probability arises from the lack of knowledge of all physical of factors influencing the experiment or from the chaotic evolution of the dynamics.
In MWI the probability of quantum events seems to arise from the branching of the worlds. As observers, get split into separate worlds from their own counterparts, there is a fundamental lack of knowledge as different worlds cannot interact. Thus a particular observer can never have the full picture of all the worlds, thus needs to describe their results in terms of probabilities.
As discussed in previous posts, if the amplitudes are symmetrical ##\frac1{\sqrt2}(|+\rangle+|-\rangle)## then for Alice the branching is clear, the world splits into two after measurement, let's say ##\frac1{\sqrt2}(|+\rangle|A_+\rangle+|-\rangle|A_-\rangle)##, where ##A_{\pm}## represents Alice seeing a (+) or a (-).
However if the state is ##\frac12|+\rangle+\frac{\sqrt{3}}2|-\rangle## then the same happens, ##\frac12|+\rangle|A_+\rangle+\frac{\sqrt3}{2}|-\rangle|A_-\rangle## but we still seem to have two worlds? Why Alice would feel that is more probable to get ##|-\rangle## if she repeats the experiment?
Sure there would be a special Alice that measures always (+), and another that always measures (-), but in the long run the average Alice would measure (-) 75% of the time. If we are naive, and we say that the worlds split always in two like in a tree diagram, then this cannot be the case.
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The average Alice at the far ends of the tree, after a large ##N## of measurements should be able to trace back her previous results and come up with the right probabilities for the state (25% +, 75% -) but a binary tree provides 50-50%.
How to make the probabilities right? Maybe the worlds split into a finite number larger than 2 to make the results make sense. But if for example the relative weight is irrational between the two states, then we have infinitely many worlds that must split in order to make the probabilities correct. So you have to introduce some continuous density weight to the worlds. Then it looks more like a fluid going down a series of pipes of different diameters. These models exist but I do not know if there is a consensus about it.
Wikipedia summarizes the attempts in
Born rule: