isn't there a concept of citizen's arrest
I don't see anyone else answering this... yes, there's essentially "citizen's arrest" [almost?] everywhere in the US and I think it all
tends to work similarly, but you're definitely gonna want to be absolutely certain as to how it's treated in your state. It's generally a bad idea to attempt it unless you know you absolutely need to. (Like, let's say you stopped a mass shooter or something. Well, you may as well assume you can arrest him yourself, in that sense.)
The general requirement is that you need to either directly see them committing a felony, or have "direct knowledge" of the felony (a distinction to cover for cases like security guards who see the felony occur on a camera). In this case, I sure af would not arrest the guy because I wouldn't be certain what he did is a felony: in attempting a "citizen's arrest" I would then likely be committing felony unlawful detainment myself (then maybe someone could properly citizen's arrest me in response as they just watched me commit a felony! lul. But again, I know there are some differences between states. I think there might be some where there essentially is no "citizen's arrest".)
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The Case of Ahmaud Arbery:
There's a good case of this that some people might remember, that gave us the "jogger" euphemism for blacks. Ahmaud Arbery was a guy who was robbing random construction sites. Cops went around the neighborhood showing pictures of the guy, asking people if they knew anything about him. A couple weeks later some local citizens spotted said robber "jogging" in the neighborhood (running away after they yelled at him, lul), and then proceeded to follow him to conduct a citizen's arrest... at gunpoint. Arbery then proceeded to go for the shotgun one of them was pointing, and they shot and killed him.
The thing is, Arbery had committed felonies. In Georgia they would have been justified in conducting a citizen's arrest
if they witnessed the felonies OR if they had "direct knowledge" of the felonies. The problem was, they didn't have either. A cop showing you a picture of a guy saying "do you know anything about him?" isn't "direct knowledge" of a felony.
Therefore, their citizen's arrest was unlawful. By pointing a gun at Arbery and telling him to stop, they are committing a variety of felonies themselves now -- including unlawful detainment, for not being legally allowed to stop him.
Under normal circumstances when someone goes for your gun, it's considered a clear-cut use of deadly force (ie., Kyle Rittenhouse, allowing you to use deadly force in response); but since they were now the ones breaking the law, committing the felony of stopping Arbery, they lose one of the necessary factors required for it to be justifiable self-defense, that they weren't in the process of committing a criminal act, and since they shot and killed Arbery...
The title of the crime changes depending on what jurisdiction you're in, but "felony murder" is the most common term for that. It doesn't refer to "a murder that's felonious" (as all murders are), what it's saying is that the killing
is considered to be murder because the killing happened as a result of your felonious behavior. (Like you could rob a store with a fake gun, the security guard shoots at you and misses, accidentally hitting the clerk and killing him... you're the one guilty of felony murder).
So I'd say that's a great example of what would be a "citizen's arrest", in which they totally have the right guy, and the guy is definitely guilty (and definitely not just a random citizen going for a jog), and yet it was a
really bad idea to try to arrest the guy, as those 3 men are now spending the rest of their lives in prison for catching the right guy.
So if you think about conducting a citizen's arrest, you better be damn right about what you're doing. I'd recommend it only in cases of "we really had no choice but to stop him". If you can let him go and let the police handle it, do that instead.
And ofc that's why security guards are almost never in the business of arresting people. A very few serious companies will have them trained to actually carry handcuffs for that purpose. You'll see them armed with a gun FAR more often than you'll see handcuffs on security guards... because the time when it's appropriate to use deadly force are simply a lot more clear-cut than when it would be appropriate to conduct a citizen's arrest.