There is some kind of fallacy inherent in the arguments that immigrants are committing crimes but I don’t know if it is a recognized one or has a name.
It is a valid argument to say that immigrants commit crimes at lower rates than the population at large. The response is always that so and so would be alive today if we didn’t have immigrants and while true that seems fallacious considering the crime rate disparity. (I am not using Laken Riley as an example as her perpetrator had previous legal problems which makes that story a bit different.)
IMO that argument boils down to an argument that if we have more people we will have more crime - not necessarily at a higher rate but more in absolute numbers. And of course that is true.
Their argument makes no more sense than saying that we should get rid of people from Burlington because someone in Burlington went to Chapel Hill and committed a crime, a crime that would not have happened had we removed all the people from Burlington 100 miles a way.
Someone needs to develop that thought, maybe wrap it in a mathematical framework, and give it a name.
What do you mean by mathematical? Like arithmetic? I've done the arithmetic many times on the board. Suppose you live in an rea with a 5% homicide rate. That means every resident has a 5% chance of being murdered in a given year. Now suppose the population doubles, with the new entrants having a 1% homicide rate. Now the area has a 3% murder rate. Every resident has a 3% of being murdered. Literally everyone in town is safer, even though some of the new entrants have committed murders. The general formula is extremely simple. I'm not going to try to write it because formatting is a pain but it's Algebra I level if that.
I don't know if the fallacy has a name. I suspect it does. I don't always learn the names of fallacies as I think it's just easier to point out illogic. But I can think of two ways of characterizing it:
1. "But for" fallacy. When a migrant kills an American, the migration is a "but for" cause -- i.e. if the migrant wasn't here, he couldn't have committed the crime. But so many other things have the same causal status. If the victim had been at home instead of out partying (or vice versa, depending on where the killing occurs), s/he would be alive. If the perp wasn't able to buy a cheap used car, s/he wouldn't have wheels and it's hard to be a killer riding the bus. Maybe the perp was angry at being dumped by a former romantic interest. Maybe the perp had been playing football and suffers from CTE, etc.
If any of those factors in the causal chain had been different, the victim would still be alive. But nobody calls for surcharges on used cars, or preventing people from dumping their partners, or banning football, right? It's illegal immigration that caused it, even though the immigration is very far back in the causal chain. Lots of things had to happen between then and now for the killing to happen.
Maybe we can call this the "fallacy of excess causation." Any analysis that relies on "but for" causation will quickly find that everything is a cause of social ills. Thus does everything become a cause and the whole concept of cause loses meaning. The law mostly uses a concept of "proximate causation" which is sort of a cop-out but at least tries to find a way to distinguish who should be held responsible for an action from those who don't deserve it. And one principle is "intervening criminal act," which is to say that we hold the criminal responsible, and anyone who helps the criminal after the fact, but we don't go after the people who acted (even wrongly) prior to the criminal act -- unless the action was specifically designed to aid the crime (i.e. obtaining an illegal gun) or was an obvious result of the action (here, think of the movie Seven and the way John Doe carried out his crime of lust).
2. Another way to think of it is a fallacy of visibility, if that's a thing. Go back to the arithmetic above. Everyone is safer in the town because of the new entrants -- but nobody sees it because you can't see a thing that doesn't happen. Some % of the crimes that would have been committed against an old resident are now being directed at the new entrants, meaning that the original residents should be thankful that someone else was the target of the killer . . . but of course they can't see that. They don't know that they would have been targeted if the new entrant wasn't here. It's arithmetically required, but we don't know who was "saved" by not being targeted.
It's the way people don't see harm prevented, because you have to look closely to see it. This is what RBG famously described, in her Shelby County dissent, as "throwing away the umbrella in a rainstorm because you're not getting wet."
Maybe we should coin a phrase and call it the umbrella fallacy. It's a bad idea to close your umbrella in a rainstorm even if you're not getting wet.