Full Idea
Lewis's argument for possible worlds parallels Quine's for the existence of sets: our best overall empirical theory, mathematical physics, quantifies over real numbers, so we have reason to posit real numbers, or the sets to which they may be reduced.
Gist of Idea
Lewis posits possible worlds just as Quine says that physics needs numbers and sets
Source
report of David Lewis (On the Plurality of Worlds [1986]) by Theodore Sider - Reductive Theories of Modality 3.6
Book Reference
'The Oxford Handbook of Metaphysics', ed/tr. Loux,M /Zimmerman,D [OUP 2005], p.194
A Reaction
They both strike me as suspect. Indeed, the extreme implausibility of Lewis's conclusion throws doubt on Quine's original strategy. I'm happy to work with sets and possible worlds, and only worry about ontological commitment at a later stage.