I understand it to be:

- retribution (revenge)

- deterrence

- rehabilitation

- incapacitation (they can't re-offend if they're in prison or dead)

In these sort of discussions about justice online, the first is often cast as illegitimate, the second as impossible, the third as the gold standard, and the fourth is frequently ignored completely.

Few people ever defend retribution, so I will here. Many people who are victims of crimes have a desire to see retribution done. If the government does not play at least some lip service to the desire for retribution, then more people will take it into their own hands. They'll seek vigilante justice. Vigilante justice is dangerous to society because it's often capricious and disproportionate. It is better for governments to sate the desire for retribution using official processes which can be checked with safeguards, such as trials.

> If the government does not play at least some lip service to the desire for retribution, then more people will take it into their own hands. They'll seek vigilante justice.

If that were the case, we'd see significantly higher amounts of "vigilante justice" in countries that have abolished the death penalty, right?

I think "vigilante justice" is more often than not "vigilante policing", when people believe criminals aren't being sufficiently investigated and arrested, not when people believe criminals aren't being sufficiently executed

The intensity of desire for retribution depends on the cultural context. In any case, you're conflating retribution with the death penalty, but these are not synonymous. Imprisonment is a form of retribution too, as are fines, caning, etc. Any punishment that is unpleasant has an element of retribution.

> we'd see significantly higher amounts of "vigilante justice" in countries that have abolished the death penalty, right?

No. The death penalty is not the only way to satisfy this nature.

+1 for retribution and social benefits mentioned. Should be obvious. People don't watch enough gangster movies. Or, hell, visit one of the regions of the globe with blood feuds. Not great.

The opening scene of The Godfather is about this. An otherwise law abiding man, let down by the criminal justice system, asking the mob boss to deliver vigilante justice.

You forgot one: rehabilitation, or correction

Recidivism