A while ago I had a vivid dream where there were alternates Alan's sitting in an extremely long row. The nearer Alan's different minutely from me, but as you get further and further from ma (I was in the center) They began to differ more and more from me until finally they became so different they could no longer be considered alternate Alan's I call this dream the million billions of alternate Me's
To solve this difficulty,
Albert and Loewer 1988 proposed the Many Minds interpretation (in which the different worlds are only in the minds of sentient beings). In addition to the quantum wave of the Universe, Albert and Loewer postulate that every sentient being has a continuum of minds.
Whenever the quantum wave of the Universe develops into a superposition containing states of a sentient being corresponding to different perceptions, the minds of this sentient being evolve randomly and independently to mental states corresponding to these different states of perception (with probabilities equal to the quantum probabilities for these states).
In particular, whenever a measurement is performed by an observer, the observer's minds develop mental states that correspond to perceptions of the different outcomes, i.e. corresponding to the worlds A or B in our example. Since there is a continuum of minds, there will always be an infinity of minds in any sentient being and the procedure can continue indefinitely.
This resolves the difficulty: each "I" corresponds to one mind and it ends up in a state corresponding to a world with a particular outcome. However, this solution comes at the price of introducing additional structure into the theory, including a genuinely random process.