Hi, the chipper Tweet says. Please Like my FB page and I'll Like yours!
Well, part of you may recoil from the prospect of wheeling and dealing with strangers. But it's a jungle out there and we haven't seen even the tip of the iceberg of Online Popularity Games. Plus, Amazon does note the number of Likes. So what you may do in this instance is be upfront and above board, Liking as requested then sending back this Tweet: Glad to Like. Will you in turn Like my Author (or FB) page at (link provided).
You might be surprised to receive a Tweet in response, thanking you for Liking...but ignoring your own request.
What to do? You might send a followup, stating that you were pleased to do it...but that you've noted that s/he hasn't reciprocated. Why not? You made what you regarded as an honest deal and don't want to jump to conclusions.
When hours pass and you've still gotten no response, it's not looking good. Why not check the Tweeter's FB page and see what you see? What if you see a dramatic increase in the number of Likes since the first Tweet?
You could do worse than conclude that many others were approached with the same offer. You have three courses of action:
1) Let it slide and shake your head at such childish shenanigans.
2) Withdraw your Like and say nothing.
3) Withdraw your Like and send a DM stating that you've done so.
I opt for the third door--with the caveat of keeping the note civil. And you?