"Positive reinforcement involves the addition [+] of a reinforcing stimulus [something the horse enjoys, wants, finds desirable, or needs] following a behavior that makes it more likely that the behavior will occur again in the future." ... What this means in simple horse training terms is that.. if you like something the horse does, you offer them something they want or like to increase the likelihood of it happening again. Obviously this is a very simplified version of what's called "+R training", in which all training with the horse is with +R and there's no use of corrections/punishments/or aversive (unpleasant) pressure (theoretically), but this gives you the idea of what it's all about.
With more traditional horse training approaches, you would apply a pressure (such as a leg squeeze, swinging rope, pull on the lead, pulling the leg up, tapping with the whip, walking into your horse, clucking repeatedly, etc.) until the horse responded like you wanted and then you would remove that pressure. The horse would learn that the faster they respond to the pressure, the sooner the pressure goes away and they can get "relief". This is called Negative Reinforcement, (-R or Pressure & Release).
With +R training though, we wait for the horse to voluntarily offers a behavior, or we use guiding tools (like a target) to trigger an action, and then we give the horse something they enjoy as a reward for them doing what we wanted; the horse will want to try again to earn another reward. But.. here's the trick... +R ONLY works if the horse finds the "reward" you offer to be rewarding! We can think we are rewarding our horses all we want with neck pats, but does the horse *actually* find it rewarding? Or maybe it's just a neutral like for Cash; he's neither bothered by it or rewarded by it. It's very probable that he would wander off to go do something more rewarding (like grazing) if I were to continue using this as his reward for touching the target. We can rub our horses' faces all we want... but does the horse enjoy having their face rubbed? Cash certainly doesn't. In fact, for him, as you can see in the video, having his face rubbed is punishing! If every time he touched the target I rubbed his face, he would stop touching the target.
Regardless of when or how much +R we are using, we need to be listening to our horses. As much as we may want to use scratches or rub our horse's face, or tell ourselves our horses like pats on the neck, that's not something we get to decide. The learner dictates what's positively reinforcing and what's not... Just like they get to decide what's punishing or aversive and what's not. So when we are choosing to work with +R, we have to choose what the horse likes, not what we'd like to use because it's convenient or nice for us. Which is exactly why this is a... #tweAreYouListening post on the down low. ;)
As a side note.. You can see some variations of +R in the video. I often combine reinforcers (like the first part) for various reasons.
One; for horses that like scratches but may not find them of very high value, it drags out the reinforcement period without having to give as much food. I'll still give some food, but use the scratches as a bonus to increase the value of the reward without having to increase how much food I'm using.
Two; by combining something neutral or of lower value with a higher value reinforcer I can somewhat condition the lower/neutral value reinforcer to become a higher value one by creating an association with it. This later allows me to begin fading out using the higher value reinforcer as often and use more of the lower one... so in most cases, I can wean off using *as much* food and use more scratches. (but this needs to be done gradually).
Three; it helps pace the training session for "rapid fire" horses. Horses that seem to be ready for the next repetition before they've even gotten the food in their mouth from the last repetition, will only continue to increase in speed and make the training session stressful if something isn't done to slow everything down. But they will also become very frustrated if you just "pause" and don't do anything. So dragging out the reinforcement with rubs and such in between repetitions really helps slow everything down I've found.
Hopefully this was a helpful article and if you have any questions please don't hesitate to comment or email me.