To get back on track, concerning this topic, I think everyone here is well aware that there are abusive people out there, who feel they must dominate a horse out of down right physical force, fear, even pain, but that has zero to do with the original topic, which was willing compliance.
So, to sum thing sup, far as I'm concerned, willing compliance is a learned behavior, using communication tools the horse evolved to understand, being a herd prey species, in a fair manner that creates trust and respect in a horse
Whether mainly R+ , R- or a combo is used, depends on past history of the horse, but fear or abuse is never part of that package
The horse thus responds willingly to cues he understands, in a relaxed and trusting manner, instead of having a ;make me attitude
While working for a treat, is a clear form of communication, and has it;s definate uses, esp on an abused horse, that needs to learn trust, it also does not it itself, indicate ' willing compliance, as you can't separate that 'compliance from the antisipated food reward
There is a time, on a horse , that has no past baggage, understands a request, but fails to comply , to use the 'ask, ask louder, then demand' while then always giving the horse in the future, a chance to respond to that very light ask first, to then make that willing compliance an ingrained response. Horses are creatures of habit
You don't shout , when a whisper works.
I do believe , it was tOm Dorrance himself, where I got the quote,'be as gentle with a horse as possible, but also as firm as needed, to make that horse a'good citizen'
Willing compliance is not following you around at leisure, although nothing wrong with that, but it is responding to a request, that he understands, and one that is asked using the lightest aid possible, in a willing manner, with no sign of stress, such as tail swishing, mouth gaping, tense body, ect, but with soft eyes, relaxed body and willing attitude.
That's my story, and nothing more I don't know hoe physical pain, force, intimidation, horse not wanting to be with you, ect, ect, ever became part of this thread
Use what works, for you and the horse you are working with. If the horse is happy, not stressed and does the job you want, even if just hanging out, then those methods are right for you and that horse.