Michael,
I understand this has worked for you. But why on earth would anyone who has two (or god forbid, three or more) dogs who are fighting loose in the house with no supervision? That is asking for a disaster. Infighting in the ranks means there is pack instability, which means someone does not know their place. There is transgression somewhere. Wild dogs do not waste much time in real fighting; they rely on ritualized displays of power to maintain stability. The more infighting you see, the less centralized the power is (see this with humans too!).
This is not the only reason dogs fight, of course. Two rank animals of the same sex, redirected aggression, mating priviliges, etc are other possible reasons.
Just because you are the top dog, doesn't mean that there is no dog #1, #2, #3, and so on. All the priviliges of the hierarchy are given to each dog, in that order, but no one usurps my authority. My dominant dog is allowed first pets, first training, and the privilege of being the dog I count on for alert duty; she exels at it, and she feels the confidence I have in her for her watchdog capablities. The other two get their due acording to rank and ability. Keeps everyone happy.
I seperate my third dog out, the omega, when I am not home. She is safe, I know the other two dogs are not going to fight (they don't have competing interests), and I come home to an uninjured dog. I do this even tho I know my dogs sleep when I am gone, and even tho my pack is quite stable. It is just not worth the stress.
It is a lot easier to stop aggression in the posturing stage, than it is in the bloodbath, or even fighting, stage. If they were two human siblings, would you allow them to beat each other up, or scream at each other all day long for every little thing? Or would you say 'settle your differences in a manner acceptable to me, or I will settle them for you'?
I allow only one obvious display of power from my dog; if I am petting her, no other dog approaches (on their own), and she has my attention 100%. And if another dog willingly moves out of the way when she approaches, I allow that, (then I put her in a down stay and pet the other dogs). Anything else, and she thinks that she has the power to disipline, which is my exclusive authority. Of course, there are all the subtle displays; head carriage, choice resting place, last to pee in the yard, and what not. Those are not biggies in my pack, because I have given her that right, not because she has assumed the right was hers.
But this is what has worked for me. 'Letting them settle it themselves' would have been an absolute disaster, and she would have eventually bitten me for some small transgression on my part. Nope, not worth it.
Relation is reciprocity. How we are educated by children, by animals!-Martin Buber