Stop and frisk

Person A: A form of Cherry Picking, he is only saying that it saves lives, not mentioning the cost or downsides.

Person B: He is doing the same thing with the "Banning cars" part, but I think that was more rhetoric or sarcastic.

Those are the two I can see.

Person A: Stop and frisk saves lives, there fore we should implement stop and frisk.

Faulty generalization: reach a conclusion from a weak premise. Or at least Hasty Generalization: fallacy of a lonely fact.

Stop and frisk saves lives, there fore we should implement stop and frisk.

The claim sure calls for a lot of assumption and implication on our parts. First of all, what exactly are we stopping and frisking for? Is it a rock concert and we're looking for contraband, cameras, alcohol, paraphernalia, etc.? Does confiscation of these actually save lives? I'm not sure that's a valid claim or conclusion. Assuming we are talking about Mayor Bloomberg's Stop and Frisk policy in New York City the controversial racial profiling policy proved to be illegal but nevertheless led to crimes being lowered significantly in certain minority communities. Saving lives was an ancillary benefit, but the effort itself focused on diminishing the amount of illegal hand gun possession and lowering crime. Equating Stop and Frisk with saving lives is a weak premise at best.

Therefore, we should implement Stop and Frisk.

They did, it helped lower crime rates, but was grossly prejudicial to over 90% of those who were stopped and frisked who were never charged with any crime whatsoever.  So we're dealing with a hasty generalization: 

Sample S is taken from population P.

Sample S is a very small part of population P.

Conclusion C is drawn from sample S and applied to population P.

Person B: But the cost is too high

Is it? That's a whole new argument that may or may not be true, but it has no relationship to the original claim of saving lives. It seems to be a bit of a Red Herring.

Think of all the innocent people needlessly harassed.

Indeed, this is a perfectly logical argument that can be statistically supported.

Banning cars would save lives too, so lets ban cars.

Huh? That's definitely a Straw Man argument. Hand guns are illegal in New York City. They are lethal weapons that can be used in self-defense or to commit crimes. Cars are legal methods of transportation and commerce. To compare hand guns with automobiles is a false equivalence. Can car accidents occur? Yes. But they cannot be concealed and their use is vital to the commercial livelihood of a city and its patrons and citizens. The claim that banning automobiles would save lives is dubious. Pedestrians are killed everyday by falling cranes, crumbling scaffoldings, and cell phone distraction. Would you compare banning hand guns to banning walking? Of course not. 

Stop and frisk saves lives, there fore we should implement stop and frisk.

There is a missing premise here, but the premise can be implied... that we want to save lives. This is fine as a starting point for a discussion, but it simply is one of the "pros" for the pros and cons of such a policy (assuming it is factually accurate). No fallacy.

But the cost is too high, think of all the innocent people needlessly harassed. Banning cars would save lives too, so lets ban cars. 

This is a simple response pointing out of the "cons" on the pros and cons list (assuming factually accurate). It is then followed by an analogy with a touch of sarcasm. Personally, I think it is a strong analogy that points out we must consider the total cost of our policies beyond simply "saving lives." No fallacies here either.

The car analogy is a false equivalence.