The threat of death does not deter individuals from committing crimes.
C.P. certainly would have some rational backing to it, if it effectively discouraged people from committing heinous crimes. However, it's existence does not prevent crimes, reducing its value from little to none.
According to a survey of the former and present presidents of the country's top academic criminological societies, 88% of these experts rejected the notion that the death penalty acts as a deterrent to murder.
Also:
Consistent with previous years, the 2008 FBI Uniform Crime Report showed that the South had the highest murder rate. The South accounts for over 80% of executions. The Northeast, which has less than 1% of all executions, again had the lowest murder rate.
Despite the South's great effort to deter individuals from committing such awful acts, it still has the highest murder rate in the nation. Doesn't seem to be working.