Another 10 min schooling session this morning as I had no time for anything more. He was very good but he is a terrible anticipator. If I ask for canter at one bottom corner, he will offer canter at every bottom corner. How on earth do I keep him guessing?
Just my two cents & feel free to ignore Jane but for me, it slightly depends on the context and stage of training as to how I'd correct it.
If the horse had been a bit lazy, behind my aids and I'd been working on improving their sharpness, I'd let it slide for a little while and just go with it when they offer the canter. I think it can be quite disheartening and counter productive for a sticky horse to be asked to go forwards but too quickly told 'Yeah, go forwards but just not like that'. For me, it's more important a backwards thinking horse wants to go forwards than when that happens, initially. You can build on being particular later but only if you don't kill their desire to try first.
Equally, I would ignore it initially in a horse that had been submissive and I don't mean submissive in a positive way (as in submissive to the aids) but more in a shut down and not allowed or had the confidence to bring their character through. I'd see it as quite a positive thing they offering their opinion on something. For me, it's a real step in the right direction of building a partnership built on trust and fun.
Again, later down the line (maybe the next session, maybe a week or a month) depending upon the horse, I'd begin to be more particular and change things up.
But, if I was riding a horse that either tended to believe 'Go Faster' is always the answer or I was riding a horse that had a naturally quite big personality and tested the rider's boundaries, I'd be much quicker to re-direct and mix it up. And I'd really mix it up. Sometimes I'd walk in a corner, sometimes a turn on the forehand, a change of direction, a 10 metre circle, a rein back, literally as much as I could think of. I'd try to be thinking a corner or two ahead of myself too, so I have a plan before we get there. In my mind, if I was riding that corner 10 times, I'd want to do anything but canter at least 7 times.
I feel Sid might sit in the first and last description slightly, based on what you've shared previously but I might be totally wrong! It's just what I'd play with. So I'd maybe allow it once or twice and then kinda keep a playful 'Nice try buddy but can you do this instead?' approach before re-asking for canter.
With P I have to allow him enough room to not feel wronged but also not so much room that he escalates and takes over, as he's not so subtly plotting word domination and I think he'd achieve it if allowed (no one is ready for that kind of revolution).