There are some interesting statistical thought experiments related to observers and the Anthropic Principle such as the Doomsday Argument formulated by a physicist Brandon Carter and later improved by others, e.g. Nick Bostrom.
The many-worlds interpretation of quantum mechanics has a radical impact on these considerations because each Everettian branching creates many new worlds some % of which have their own observers, adding to the total count of observers.
Recently I was wondering - in similar way to how the Doomsday Argument asserts that subjectively you are most likely to find yourself somewhere "in the middle" of all observers which will ever have existed - is there some way to deduce likelihoods (relative count) of possible future lives in a MWI universe, for example depending on their length?
Consider all possible future lives branching out from a specific point in one's life, e.g. birth. Now sort all of them based on their length. Some will be very short, some longer, some very long. In a population of different people lengths of these lives would follow some typical survival-rate curve. However, because of the huge world-branching factor in a quantum multiverse - it would seem that the longer lives would actually be far more numerous than the short ones because the longer they last the more "survival branches" they could produce. Intuitively I would say that the longest possible life would be the most likely/numerous one of all, possibly resulting in something similar to "quantum immortality". But how can this be proven formally? What mathematical methods can be used to approach this problem?
And would this assertion hold in the extremes? For example a 30-year-old person has a much higher probability of surviving until 40 than a 110-year-old has surviving until 120, much less a 120-year-old until 130. Lets say 50% vs 0.01% vs 0.00001%, creating respective relative counts of survival branches.
Another aspect to consider is that maybe it would be better to count individual "observer moments" as units in the statistics instead of whole lives. In that case the longer lives might have another advantage over the short ones because they have more moments for an observer to "find themselves in".