I think that the many world hypothesis is aesthetic because it doesn't break symmetry. Suppose that in some set-up a particle can move down one path to the right or another path to the left and there are exactly equal probabilities of either path being taken. Choosing one of the paths -- by any mechanism -- seems arbitrary. It is more logical that both paths are taken. But the two possibilities can't interact: two different worlds.
In the world we experience, objects do occasionally move to the right. If there is not an alternate reality in which the object moved to the left, eventually, with either that object's movement, or the object that pushed it, or the object that pushed that, and so on, you have to explain how symmetry was ever broken in the first place.
Physicists don't like spontaneous breaking of symmetry. So much so, that the idea of many worlds suddenly seems totally reasonable.
Later edit: This is similar to the argument Eliezer made, in more detail and with more physics here.
In my understanding, what you have presented is an argument for why MWI is interesting (is has strong aesthetic appeal) and why it's worth looking into seriously (it doesn't seem to have spontaneous breaking of symmetry).
What I'm looking for is a compilation of reasons that I should believe that it is true, basically a list of problems with other interpretations and how MWI fixes it along with refutations of common objections to MWI. I should also note that I'm explicitly asking for rigorous arguments (I actually am a physicist and I'd like to see the math) and not just casual arguments that make things seem plausible.
Eliezer Yudkowsky and Scott Aaronson - Percontations: Artificial Intelligence and Quantum Mechanics
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