I actually think something like this could work with the existing stats we have right now.
Training and Cohesion.
Imagine a unit with low cohesion and low training would be more...ahem...wanton in their walking around a region.
As training and cohesion increases, their chances of randomly doing this go down until a 100% on both would make them generally unwilling to do it without orders.
Then maybe have the chances go up and down based on the allegiance of the region they are in. They would be least likely to do it in a region of your own duchy. A bit more likely to do it in another duchy of your realm. It would be more pronounced in foreign regions. Less pronounced in federated regions. A little more in allied regions. More in peaceful, or neutral regions. And they'd be downright enthusiastic in their attempts to find fun and sun in regions they are at war with.
What might be even MORE interesting would be to modify all the current "looting" reports so they only happen during turn change. Handle them like "hunting" commands, where you can command them anytime during the turn, and then they activate during the turn change. That way every looter in the region gets a chance to get a little bit out of the region rather than having a militia form and stop them from trying part way through the turn. AND it would mask whether or not the looting was done via orders or this random mechanic based on troop discipline.
A player could send his unit out to loot a region and then claim "I didn't order them. They did it on their own. I will surely discipline them." And nobody could tell for certain. It would make for an interesting complication to gameplay.
All interesting possibilities. It certainly does make sense for training and cohesion to be a part of it but I think Morale should as well.
