For those that think Carrie will determine whether or not she gets a 5th single...you are wrong. She has no control over that. If the 4th single doesn't do well there will not be a 5th single and even if it does do well there might not be. Arista has complete control over that aspect. Brad didn't get a single after Camoflage underperformed last summer and he definitely made his feelings known that he wanted one. Kenny Chesney(Sony) did not get another single off his new Album after El Cerrito place underperformed and he had made it clear that he wanted 2 songs off there to be singles and they have now moved on to another lead off single. Same thing with Lady A, they were going to release Friday Night but after "Wanted You More" underperformed Capitol said No. Labels aren't going to keep sending singles out off the same Album once they have an underperforming single.
Completely agree, but there is also a factor you are leaving out.
The amount of product left to sell.
Labels, when dealing with the bottomline, have to determine how much good a "next" single will do based on public interest but also how much product is left on the shelves and in werehouses when they decide to pull the plug on an albums life.
Some examples I think we have seen: I think PO was ended earlier than expected because it was determined that a next single would not move much more product since the label was not interested in reprinting or redistributing more product. (now I do think they aer always willing to reprint and redistribute when demand is high, but if it is tapering, they cut things off where they think it is most beneficial to them, not an artist or fans who would like to see another single hit the airwaves.)
In contrast: I think Mirandas Revolution (and possibly Four the Record) were both aggressively marketed cause they decided early on to do a big run and a big push. And I think the life of those records outlasted the sales potencial cause they still had product to move and had no other way to move it except to keep promoting it.
I do think BA was planned to (and expected to) move 2 mil. and therefore will definately have a 4th single. But how hard they have to "push" depends on how well the album keeps selling. If they get close to 2 mil. before a 5th single, I suggest they will pull the plug. If the 4th single underperfoms, they might put out a fifth.
(Again, my theory is based on the fact that I think they printed big numbers of BA in the beginning and will want to move more of it than PO before they are done.)