Consider any theory of composition you like. You can think of the various ways of drawing lines all over the frame and peering at the intersections and whatnot. You can think of theories that involve balance and the distribution of tone. Whatever you like. There are really two quite different tasks this theory can be applied to:
First, you can attempt to explain an existing picture, and why it works.
Second, you can attempt to construct new pictures based on your theory.
The first one is generally a bit fraught. If you're honest with yourself, you will probably find picture after picture after picture that fails on one front or on several. You can tweak your theory to fit, perhaps, but you find yourself in the same position as the stock market analyst. No matter what pattern you find in past market performance, it will probably disintegrate shortly. This is, at least in part, because if you've discerned a pattern, other people have as well, and they'll be betting in such a way as to disrupt the pattern.
Similarly, there's a tendency toward the novel. Any strict patterns in a group of pictures will as likely as not be defied in the next group.
The second task tends to go a bit better. It almost doesn't matter what set of "rules" you have lying around, if you make a bunch of pictures that obey those rules then they will in the first place fit together pretty well, and in the second place will mostly be pretty pleasing to look at. The trouble here is that you tend to get a real sameness across artists. There's a reason painters in a given era all tend to kind of look similar, they all went to the same schools and learned the same theories (and had the same materials and other influences etc, of course). In a medium that thrives on the novel, well, you've got a bit of a problem.
Personally, I look for balance without worrying too much about what that would even mean. Balance, a strong diagonal or arabesque if one is gifted me, and try to keep irrelevant stuff from intruding too violently in the frame. Then I sort it out on the "contact sheet".
Surprisingly often the ones I like meet more of the criteria of my pet theories of composition (Ruskin's, basically), of balance, unity, variety. But the best ones have someone interesting being interesting, somewhere in the frame.