So just a little reminder that may or may not be redundant among here: don't do this. Don't give more of a chance to the person who screams and acts crazy than to the person who tries to work things out with you the calm, mature way. It's exactly the wrong way to respond if you want to incentivize rational behavior on the part of the other party. The message is basically "I won't listen to any attempt at reasonable discussion, but try going hysterical on me, that one has good odds of success", thereby earning yourself more hissy fits in the future. And especially don't do this as parents, to your kids.

It is worth explicitly noting that this heuristic applies when, and to the extent that, influence over future behavior of the other person or witnesses is the dominant consideration. In a once-off encounter with a street thug or a bank robber different considerations apply. It is not always your responsibility to 'train' people.