On Foo.SE, I have voted up a question and down one of its answers. After this, moderators decide it's best to migrate this question to Bar.SE. However, I don't have enough rep for voting privileges on Bar.SE. Are my votes carried over to Bar.SE even if I don't have enough rep to vote there? What if I have enough Bar.SE rep to vote up but not down?
On migration, votes are preserved if the question has a positive score. However, the ownership of those votes is not preserved; the votes are transferred to the Community user at the time of migration. If you voted on the original site (and have the reputation to do so), you can also vote on the destination site. So yes, migration allows double-upvoting. (This also means you can't cancel your vote post-migration, because it's not your vote any more.) Clearing migration history doesn't change any of this.
It would be better if all votes were cleared on migration; that users on Community A thought it was a good question doesn't mean that it's a good fit for Community B. The question should get a fresh start on the new site, and then you wouldn't have any concerns about double-voting. But that's not how it works now.