Let us consider some concepts related to Max Tegmark's "level 4 multiverse" concept, where all possible mathematical or computational structures exist, and those with appropriate complexity and structure can be thought of as universes. Of course this is not widely accepted but as an exercise, let us pursue what it says about the Fermi paradox. It leads to a curious connection between this paradox and the oft-noded property that our universe is seemingly fine-tuned for life.
Let's also take the evidence at face value: we see no aliens because there are no aliens. In the entire visible universe there is only one planet with intelligent life, our own. What does multiverse theory say about this odd fact?
If all possible universes exist then there will exist universes that are dense with intelligent life as well as ones like our own that are extremely sparse. Observers will exist who see both kinds of universes. At first it might be thought that since observers are far more numerous in life-dense universes, most will be of that kind, so our observations of sparseness are even harder to explain. It might even be considered to invalidate multiverse theory.
Of course if you think that, you ignore human ingenuity at rescuing failed theories. Instead, we will invoke a manifestation of Occam's Razor and say that certain universes are inherently of larger "measure" in the universe, namely those of simpler structure, which take less information to describe. We will leave the notion of measure vague except to say that all else equal, universes of higher measure are more likely to be experienced.
Now we have a hope of explaining the Fermi paradox, or at least characterizing it in multiverse terms. It must be that universes which are very sparse in life have significantly higher measure than those which are dense. Sparse universes must have simpler laws of physics and/or initial conditions, so that they can be described with less information than life-dense ones.
If we consider all possible universes and rank them by complexity, it seems plausible that extremely simple universes are not suitable candidates for intelligent life. We need a certain threshold of complexity and variety for life to form and evolve intelligence. As we move up the scale, we would first hit universes which allow life, but just barely. They would not be particularly hospitable to life and while it might form and even thrive to a limited degree, it would be extremely rare. And finally we would reach universes of substantial complexity and richness, some of which might be very good homes to life, where life and intelligence flourishes and is widespread and common.
This gives us the germ of an explanation, then: simpler universes would be of higher measure, and it is likely that the simplest universes which nevertheless allow life to form would just barely allow it to happen, so life would be sparse in such universes. However, it is not a full explanation because it leaves open the question of what increment of life-density is gained by adding a delta of universe-complexity. If going to a universe that is 1% more complex makes life 100% more common, our explanation fails, as we would then expect to see most life in dense universes, even taking measure into consideration. So in this context, the Fermi paradox can be understood as a prediction about the nature of certain mathematical systems, and of how complexity facilitates the formation of subsystems analogous to what we would call intelligent life.
As far as the connection to the fine tuning, it would go as follows. Go back to the ranking of universes by complexity, and focus on the ones that are just barely complex enough for life to form. As we noted, in such universes life would be rare. Its presence might well be a function of initial conditions, such that only certain special values would allow life. And among those conditions we might consider the various magic parameters which have been found to be fine-tuned to be beneficial. Universes with relatively simple laws which just barely support life, but where nevertheless life has attained a toe-hold, would commonly offer such seeming coincidences of various parameters and initial values that conspire to allow life to exist. This would then correspond to our observations.
Summing up, the level 4 multiverse concept, augmented with a notion of measure corresponding to complexity of physical laws, ties together the Fermi paradox and the fine-tuning. Both are seen as manifestations of the higher measure of uinverses which are just barely complex enough to allow intelligent life to form.
