In yesterday's post, I offered a criterion for when multiplicity of objects or kinds posited by a theory counts against the simplicity of a theory: namely, when it is a multiplicity of objects or kinds not explained by the theory.
Let's apply this to multiple universe theories, which people do tend to see as offending against simplicity.
Lewis's Modal Realism: Lewis's universes have no explanation of their existence. Their existence is simply a brute fact. Thus, the infinitude of Lewis's universes counts against the simplicity of a theory. Moreover, along with unexplained universes there will be unexplained kinds. Lewis's theory, for instance, implies that there exists a universe where an uncaused griffin exists from the beginning. Likewise, unicorns, Pegasuses, and so on. So Lewis's theory implies the existence of a great diversity of unexplained kinds of things. And that should count against the theory.
Theistic Multiverses: Theistic multiverse theories have an infinity of universes, but these universes are explained by God's goodness in creating all universes that it is worth creating. Thus there is only one unexplained entity in the theory--God--and there is no offense against simplicity.
Physicists' Multiverses: I don't know enough about string-theoretic multiverses to say anything about those here. But inflationary universes that bubble up out of other universes will be exempt from the worry if there is one root universe from which the others come, since then the cost in terms of unexplained entities is the same as that of single universe theories, and there is no offense against simplicity.