Capital Punishment Whenever the word "capital punishment" comes up, extremists from both sides start yelling out their arguments. One side says deterrence, and the other side says capital punishment is not fair. Three of the most controversial points of capital punishment are: The deterrent effect of capital punishment, fairness with capital punishment, and Cost of the Death Penalty. The people who are against capital punishment say the death penalty is not an effective deterrent to crime. They believe using the death penalty as a deterrent to crime is like trying to knock down a brick wall with a rubber