People think that if someone kills another person, he or shes deserves to have his or her life taken in return. Second, capital punishment is really effective. We can say that it's more effective than life imprisionment cause people usually fear death. The more severe the punishment is, the less people are apt to do crimes. There is another effectiveness.
Capital punishment costs less than life imprisionment.
Third, capital punishment can deter murder. When a person is about to commit murder, if he or she recalls the capital punishment, he or she would have difficulty in doing murder because of fear. Professor Issac Ehrlich says that each additional execution prevents 8 people from commiting murder. That is, death penalty instills a psychological resistance to the act of murder, so it can prevent a person from commiting murder. Of course, there is opposite opinion, also.