Different authors name different theories. Some refer to the goals of punishment as the theories: Retribution, Deterrence, Rehabilitation, and Social Protection, while others refer to the philosophies behind these goals of punishment: utilitarian, retributive, and denunciation theories.
Presently, the U.S. conception of punishment is a combination of the utilitarian, retributive, and denunciation theories. However, the most widely accepted rationale for punishment in the United States is retribution. This is seen in the rationale for a conviction, as the sentence a defendant receives is always, at least in part, a form of retribution. However, a sentence may combine utilitarian principles with retribution. For instance, an offender sentenced to prison for several years satisfy the public 's desire for vengeance, while simultaneously, have educational programs inside the prison that reflects the utilitarian goal of rehabilitation (Punishment - Theories Of Punishment, http://law.jrank.org/pages/9576/Punishment-THEORIES-PUNISHMENT.html).
These theories use a combination of goals for punishment: Retribution, Deterrence, Rehabilitation, and Social Protection and Social Humiliation.
How
References: Macionis, J.J., (2006). Deviance. Society the Basics (8th ed.) New York: Prentice-Hall. As Glenn C. Loury(2007) says in her article Race and the transformation of criminal justice , Why are so many Americans in Prison, Boston Review