There’s this myth common to segments in the right and in the left that states that most violent crimes are committed by people suffering from temporary or persistent insanity, so that such crimes could not be deterred by prospective legal punishment.
Maybe that myth comes close to the truth in places like Denmark. The economic incentive to become a violent criminal in Denmark is very small, and most violent crimes are indeed the result of mental instability.
But this is arguably not the truth for certain places in the U.S., and it’s certainly not true for most places in the developing world (think Brazil or Colombia). In these places, being a member of a drug dealing armed cartel is a career option for many people, and they carry on executions and raids as a part of their daily business.
These places require a more ruthless justice system in order to reduce the prospective gains some people expect from entering in the crime world.
To think that a lenient justice system is the root cause for widespread criminal violence is not only very naive, it’s also a self-inflicted wound. Italy understood the lesson when they decided to give their mafia bosses a taste of rough justice (although not through death penalty).
Stats can be a very effective tool if the people crunching the number hold some understanding of the underlying relations of cause and effect governing the phenomenon they are trying to capture and quantify.
For instance, you have to compare comparables. It makes no sense comparing the incidence of violence in Somalia and Norway and attribute it to the death penalty.
It is a trade-off. You grant the justice system a significant power in order to make it more effective against criminals, but this power has also negative consequences towards non-criminals. And as any trade-off, it is perceived differently in different circumstances.
These things are well understood by the common people. Almost every pool taken in Brazil on the subject shows that the population is massively supportive of a death penalty initiative, since the country is croweded with vicious criminals and has one of the most lenient, emasculated and slow justice systems in the western hemisphere.
A similar pool would not show that germans or swedes are favorable to capital punishment, since for them, such a tradeoff would not be interesting. Gang and random violence are not as much of problem in Stokholm or Berlin as in Rio de Janeiro and Sao Paulo, so germans and swedes can afford not to execute their incidental murderers and rapists.