I was trying really hard to stay off this thread, and I probably wont be back to it, because I've had enough of internet forum arguments
I just wanted to say my little part.
I will say though, not as a response to any of the other replies, just to the initial question - No, I do not believe in pretty much any methodology of training based on dominance theory. To make a very long story short, the initial research that backed the entire idea of dominance theory has been seen to be faulty, and dominance theory training has been debunked. The study that started this all was done on wolves (which while similar are NOT our domesticted dogs) in captivity. The fact that small captivity caused them to behave in a different manner than they naturally do, combined with the fact that the researcher was incorrectly observing certain behaviors and putting human emotions behind them resulted in data that just isn't true. Anyone interested can google dominance theory debunked and I'm sure you'll find a lot of info.
I am a positive reinforcement trainer by trade. I used to use aversive methods (prior to my education and career) and I have seen what (good, correct) positive reinforcement training can do. Positive doesn't mean permissive, and it doesn't mean shoving cookies in your dogs face. While MOST of teaching the behaviors is food based reward (if that is a high motivator for the dog) that isn't all it is about. It is based in, well really it IS, behavioral science.
Regardless I don't MIND using treats. Why should I? What is so bad about it? I know I don't work without a paycheck! If my boss (well bad example, I am my boss, but shh) told me she was only going to pay me in hugs, or told me that I will just be shocked, or rolled over and pinned down for being late, or calling out, or messing up some paper work I'd quit in a second. And maybe bite her on the way out
I'm not trying to say anything bad about the methods any of the members reading use, everyone is free to make their own decisions about the methods they use. However we should ALL educate ourselves on our choices, so I strongly suggest reading up on dominance theory, on the pitfalls of punishment and what the fall out can be, and also on how to correctly execute punishment (it actually is a very tricky thing to do right). But through my education, my personal readings, and my experience and observations I strongly believe that positive reinforcement is the way to go, and the methodology I choose to use.
As I said before I don't want to get into a debate or argument, and please no one take offense, we all have our own views. If anyone is further interested in learning I can recommend some great books to read (two I already saw listed) and give some online resources. Feel free to PM me :)
EDIT: Oh also, I just wanted to note that the word "dominance" is often incorrectly used. Dominance is not a personality trait. Actually it describes the relationship between individuals. This means that it can be a fluid thing. A may be the "dominant" one over B when it comes to picking a toy, but then defers to B when it comes to the best napping spots. Just wanted to note that since it is a widely misused phrase nowadays in the animal world.