Lets restate this philosophical problem as a problem of ontology
Imagine that you want to write a computer program that perfectly simulates what’s going on at the quantum level
Now the problem comes down to asking how many classes you need to define in your domain model
When you run your program will there be only one class of object instantiated (the wave class) or are there two different types of objects (of wave class and particle class) ?
The many worlds interpretation is equivalent to saying you only need to define one class in your model (wave class) because wave objects are all there are
Other interpretations are equivalent to saying you need to define at least two different classes (waves and particles) since both types of object can be instantiated and you also therefore need to define the interface showing the message passing between the two different types of object as per the rules of object oriented programming
When restating the problem in this way much confusion immediately clears
It should be obvious that the many worlds interpretation has much greater simplicity and clarity and that all other interpretations are in fact a return of dualism in disguise (with all the associated problem thereof). It is for that reason that many worlds wins hands down.
Just simulating the wave dynamics is not enough. You have to generate some further object from the waves, in order to get something in your simulation with the properties of reality. For example, you can repeatedly apply the Born rule as in Copenhagen to get a single stochastic history of particles, in which events occur with the appropriate frequencies. Or you could specify a deterministic rule for branching and joining, in which worlds are duplicated in different quantities at moments of branching in accordance with the Born rule, to create a determinist...
http://www.scottaaronson.com/blog/?p=1103
Eliezer's gung-ho attitude about the realism of the Many Worlds Interpretation always rubbed me the wrong way, especially in the podcast between both him and Scott (around 8:43 in http://bloggingheads.tv/videos/2220). I've seen a similar sentiment expressed before about the MWI sequences. And I say that still believing it to be the most seemingly correct of the available interpretations.
I feel Scott's post does an excellent job grounding it as a possibly correct, and in-principle falsifiable interpretation.