Identify which type of punishment deters crime most effectively, and discuss whether or not the consequences of punishment provide any benefits for criminals and society.
I believe this question could be more easily answered if it was individualized. Some people can be easily deterred while others can not, just as some can be rehabilitated when others are not open to change or help. As for retribution, I do not believe many criminals see their punishment as "just." A vast majority of released inmates will become repeat offenders within a short amount of time, leading to yet another incarceration. There are those, of course, who will not.
Accountability is the first prerequisite for any type of punishment working. If the guilty see themselves as innocent, they will most likely repeat their offence if given the opportunity in the same or similar situation. Everyone knows the importance of societal protection. Incarceration keeps convicts out of society, in turn, protecting society for a time. But what happens upon their release? There are most certainly consequences for both inmate and society when one is released after many years of incarceration. They may no longer have the acceptable social skills to gain a place within society.
I do not believe there is one answer to this question, because as individuals, each will respond differently to different punishments. I would also like to say that I do not view rehabilitation as a punishment, but rather as a gift. Anytime we get the tools to help ourselves become better, more productive members of society, there will be benefits reaped from all sides.