This is a very important issue and it must be carefully considered to stay out of trouble. The bottom line is that there is no authority. Let's examine some scenarios...

1) I am accompanying my boss in a nightclub, somebody approaches our table, I stand up and tell them to move along. They usually will, but they have no obligation to, they could just as easily just tell me to go pound sand. my only recourse is to approach the club owner and try to get them to take my side. So if I push it I'm just being a dick. In this case it would be better for me to start talking to the person, offer to buy them and their friends a drink and hope to convince them to move on.

2) A drunk get's offended in a bar and tries to start an actual fight. If the person touches me or my employer then it's game on... within reason. You cannot just assault someone, so you want to use the minimal amount of force necessary to accomplish your goal, and the optimal amount of force is none. That being said, if they have actual malicious intent and commit an actual assault, then it's going to go badly for them, but it will happen in a series of escalations. in other words, You can't just shoot a guy for punching someone, but you sure as hell can pepper spray and then restrain them.

3) A person my employer has enraged starts making threats and shows that they have a gun in their waistband. At this point I could argue in court that it was necessary to shoot them, and maybe win, but it would be a horrible thing, could ruin his life and mine, could injure bystanders (it was crowded when this happened to me) So instead I took the gun away and tackled him to the ground. I broke his trigger finger taking his gun and broke a couple of his ribs landing on him. He got pretty banged up in the restraining process too. I did not draw my sidearm and he was arrested. My actions were considered justified be cause his threat was ruled assault with a deadly weapon. Any citizen could have done the same.