In fact, a committee of the National Research Council has concluded that existing studies are far too methodologically flawed to draw conclusions one way or another. Neither side can maintain that they have empirical support. In most years, most states execute no one, and that pattern seems to be on the rise. One cannot study the impact of executions when they are hardly ever imposed, and it is difficult to separate any impact of the death penalty from the large number of other factors that affect the amount and kinds of crime.
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Is the death penalty OK?
Whatever people fear most is likely to deter most. Hence, the threat of the death penalty may deter some murderers who otherwise might not have been deterred.
And surely the death penalty is the only penalty that could deter prisoners already serving a life sentence and tempted to kill a guard, or offenders about to be arrested and facing a life sentence. Perhaps they will not be deterred.
But they would certainly not be deterred by anything else. We owe all the protection we can give to law enforcers exposed to special risks.
BBC - Ethics - Capital punishment: Arguments in favour of capital punishment
Finally, the death penalty certainly "deters" the murderer who is executed. Strictly speaking, this is a form of incapacitation, similar to the way a robber put in prison is prevented from robbing on the streets. Vicious murderers must be killed to prevent them from murdering again, either in prison, or in society if they should get out.
Both as a deterrent and as a form of permanent incapacitation, the death penalty helps to prevent future crime.