I didn't closely follow the fuss kicked up by Eugene Volokh's praise for Iran publicly hanging a serial killer, which seems to have ended in a good deal of intelligent analysis all round.
One of the most interesting arguments is that judicial punishment, in addition to its more obvious purposes, performs the useful function of restoring the self-esteem and public status of the victims, which would be damaged by their wrongs going unavenged.
What I didn't see discussed was that this also applies to the judicial system and the state itself. A state which lets crimes go unpunished or nearly so loses respect in the eyes of its people — and not only those who are considering crimes themselves.
What constitutes sufficient punishment depends on the character of the culture itself. In a culture where violent death (legal or illegal) is commonplace, a state that won't even kill people is likely to be seen as ineffectual — even if it is actually quite effective at detecting and deterring crimes. On the other hand, in a society that is free of violence, an execution penalty would make the state seem backward, rather than strong.
In some circumstances then, it might be necessary for a state to use penalties such as Iran does, just to assert its authority.
If one accepts this argument it means that he should be cautious about applying the standards of humane punishment appropriate to his society, to other countries. I am happy living in a country without the death penalty, but I'm not sure it's reasonable to attempt to insist that other countries do the same. The USA is seen, both here and there, as a more violent place. (This may well be an inaccurate view, but for these purposes the perception is probably more important than the reality). Is their retention of the death penalty a rejection of civilised standards, or a rational response to conditions?
There are caveats: the influence would presumably work both ways — while a society conditioned to violence might demand violent punishments, an abandonment of those punishments might delegitimise violence within the society. Furthermore, I think our governments have more status and authority than is good for us, and reducing that might be preferable. But neither of those really apply to states where violence is deeply ingrained, and where the state is in danger of disintegrating altogether.