[I]f we say 'Humphrey might have won the election (if only he had done such-and-such),' we are not talking about something that might have happened to Humphrey, but to someone else, a 'counterpart'. Probably, however, Humphrey could not care less whether someone else, no matter how much resembling him, would have been victorious in another possible world. (Naming and Necessity, p.45.)
David Lewis responds by suggesting that our counterparts represent us, and so there is a world which represents Humphrey as winning, despite not containing Humphrey himself. Further, he points out that all possible worlds theorists are committed to something along these lines. If we think that possible worlds are merely abstract entities or "ersatz" constructions of some kind, we probably don't think that concrete individuals like ourselves are literally parts of those abstract worlds. Hence Lewis writes:
I think counterpart theorists and ersatzers are in perfect agreement that there are other worlds (genuine or ersatz) according to which Humphrey - he himself! (stamp the foot, bang the table) - wins the election. And we are in equal agreement that Humphrey - he himself - is not part of these other worlds. Somehow, perhaps by containing suitable constituents or perhaps by magic, but anyhow not by containing Humphrey himself, the other world represents him as winning. (On the Plurality of Worlds, p.196)
Lewis has convinced me that he's no worse off than the ersatzer here. I can't see why it should matter how a possible world represents me, in particular whether it does so by way of an abstract representation or a concrete counterpart, so long as the token in question really does refer to me. (It isn't clear to me how such reference is supposed to happen. But never mind that for now.)
However, rather than forgiving Lewis, we might rather extend our criticism to the ersatzer in addition. Why should we care about mere representations of ourselves? Surely what Humphrey cares about is that he, the concrete individual, actually has the modal property of being such that he might have won the election. Merely having someone draw a picture or tell a story about him winning seems beside the point here, and calling that story a "possible world" doesn't seem to help things.
What would help is if we took modality as primitive, and defined possible worlds as representing ways the world really might have been. Then from the PW's representation of Humphrey's victory, we can infer that Humphrey really might have won. But it's the latter fact that's fundamentally important. The possible worlds are just an explicatory gloss.
Lewis gets this backwards, writing: "Thanks to the victorious counterpart, Humphrey himself has the requisite modal property: we can truly say that he might have won." This seems to be suggesting that Humphrey has the modal property in virtue of the representation, rather than vice versa. But then it's hard to see what the so-called "modal property" really comes to. Is it merely to say that Humphrey has a counterpart (representing him) who wins the election? If this is taken as the fundamental modal fact, then it really isn't clear why we should care about it at all! What Lewis means by "might" doesn't seem to have any connection to my understanding of the term.
But that's a more fundamental concern, so for now I'm happy enough to recognize Lewis' success in defending counterpart theory against the standard objection. Michael Loux, in the introduction to The Possible and the Actual: Readings in the Metaphysics of Modality (p.64), complains that modal realism cannot allow for "the idea that one and the same individual exists in more than one possible world". But such complaints confuse composition with representation. Worlds can represent things other than their ontological parts. (Otherwise the ersatzer could never attribute modal properties to anything concrete!) Lewis' worlds may not contain trans-world concrete individuals as common parts. But neither do abstract worlds! Nevertheless, multiple possible worlds can represent one and the same individual, for Lewis just as for Loux.