First off, I'd like to clear up something Jack Jack has said:
A guy commits murder.
He gets in as a form of detterence
He is not in jail because he commited murder, he is in jail because others will, so that they will not.
Half truth: Though he is in jail so that others won't, he is still imprisoned for his crime (murder)
He is in jail, not for his own crimes, but for the non-crimes of others.
He is in jail for his own crimes, though yes the purpose is future crime deterrence
So he is technically innocent.
No, he is guilty of murder.
Which means we should have no trouble jailing random parserby if it would be detterent in some way.
That would be the only positive aspect of it were it true. Aside from that, the government would be put in a horrible light, people would live in fear, etc...
Punishment is a crime deterrent, but that's not the only effects.
In my opinion, the guy (assuming it's a guy) should be punished. The act of punishment obviously wouldn't be as a detterent but, as said before, retribution. I agree that retribution is wrong, it's a horrible thing, but that doesn't stop me, or anyone else, from wanting it. It's a sick method of relief, but the one people preffer when applicable. It's the same reason why if you're punched in the face, your first thought is to punch back, regardless as to whether it's 'right' and 'just'. It may be argued that this reaction is a survival instinct, but that doesn't account for the anger you feel after the impact, the anger that drives you to punch him back.
Imagine if you arrive home one evening and find the person you love most dead in the kitchen, blood everywhere, obviously a murder. Though you won't necessarily go out and kill the one who did it, you'd want them to be punished, regardless of how it happened. Even if you find out it was an accident, does that really make it ok? Of course not! You'd still want that person to suffer for it! You see that when hear those stories of a family's 'persuit of justice'. Do you really think they're doing it as a 'deterrent for others' as much as it is a retribution?
Retribution is one of the most effective ways to heal the scars of the victims of such a crime. By fighting back against the perpertrator, we feel better, plain and simple. By not 'fighting back' and punishing such a person, we're maximising the hurt suffered by the victims of his offense, the victims who've done nothing wrong.
When a crime is committed, someone always pays. We just choose the guilty or the innocent.
That's my bloodstained 2 cents.