So Jim said in his most recent Q&A at Barbara Bookstores that do we really think that anyone running the White Council is really what they look like.
Now you can take that a couple of ways:
1. The Merlin isn't actually running the White Council. He is just a figure head or someone's puppet.
2. The Merlin isn't what we think he is. Human, not human, black council who knows.
3. The Senior Council report to Something Else. Maybe Vadderung, maybe some other Big Deal.
If 1 is true, I'd say that 3 could also be true. However if 1 is true and 3 is not, then which member of the White Council is actually the boss? Cristos (seems unlikely), LtW (possibly, but probably not), Eb (hell of a sucker punch, but there you have it), Rashid (very possible yet seems a bit busy), Martha Liberty (would be fascinating, I think, but considering she supported Harry in Summer Knight seems unlikely), Ancient Mai (the least known, so probably the most likely after the Merlin).
However, it also could be that Arthur Langtry isn't what he seems. Could he be something else?
And if the SC do report to Something, what is that thing? Vadderung would be the right choice as he taught the OG Merlin yet he seems a bit busy and it would seem to run counter to his whole "I'm gonna teach you, but then it's up to you".