If we were to apply the death penalty to all felonies, I guarantee you that the amount of larceny, drug trafficking and any other crimes will go down. However I plan to argue that murder, or crimes that result directly in death should be the only capital crimes.
The theory behind the death penalty is that the most important thing for a person is their life. If you take away all a person's possessions including freedom and dignity, the only thing that remains is their life. In order to create a proper incentive system one has to instill inside the populace both a value of their own life and a belief that if they commit the crime they will be caught and put to death.
For the purposes of simplicity we will call our would-be criminal Mr. Poman Rolanski [snicker]
We will also assume that Poman is not mentally insane and more or less a rational human being.
If Poman does not value his own life then the death penalty serves no purpose whatsoever. Think of him as a suicide bomber; no amount of laws will stop him from doing what he wants or feels is proper. This is also the case if someone is getting revenge for a crime committed. If Poman's family was brutally killed by a person or organization, you can rest assured that Poman will be out to kill those responsible regardless of the consequences. This point is also moot if Poman feels the benefit from committing the crime is greater then the cost, which is his life. It is important to note that this can only apply if this person believes in the after life or a benefit that can be enjoyed after death. All capital crimes that fall under this umbrella are revenge motivated crimes and religiously motivated crimes. An important characteristic of these crimes is that neither society nor the law can do anything to stop them.
Even if Poman values his life, there is still a chance that that he will commit a capital crime anyways. If like the majority of criminals, Poman thinks he can get away with the crime by say, escaping to a country that doesn't extradite criminals, then he is more likely to commit the crime. One of the countries most associated with crimes is Mexico and for good reason. There is almost no incentive to "stay clean". In fact only 2 out of every one hundred crimes committed in Mexico are punished. http://tinyurl.com/yhpo3x2.
To put it mathematically
C= perceived cost of crime, L= perceived likelihood of being caught and punished
V= perceived value of life, B= perceived benefit if alive
If B is greater than C then a capital crime is committed, If B is less than C then a capital crime is not committed
It is the responsibility of the society to increase the
Perception is key. For instance if we had the death penalty in place for a crime and in reality sent all criminals to a remote island that no one knew about to do slave labor for the rest of their lives that would be fine, as long as there was a perceived belief that the criminal would be killed. Similarly if the percentage of capital crimes that are punished went up and yet no one felt it, then there would be no increase in L. To quote Daniel Webster
Assuming we succeeded in doing the preceding it is also important that we do not cause perverse motivations. That means that only crimes that lead directly to death are punishable by death. If a crime like rape is capital, then there will be perverse incentives. If rape was a capital crime, and Poman had committed rape then that would have been the first in a series of crime that would have resulted in several deaths. Poman would be forced to kill his victim because the marginal cost of another murder is almost nonexistent while the benefit of eliminating a witness decreases L. Furthermore, Poman would have a great incentive to kill anyone who might have witnessed the crime for the same reason. While the amount of rapes will go down, the amount of murders will surely go up.
It is also important to note that the way the system is currently set up, there is no marginal cost for committing a capital crime as the death penalty can only be applied once. Jail sentencing also has the same problem. There is no difference between 100 years in jail and 1000 years in jail. Several countries fixed this problem of marginal incentive by implementing what is considered to be a barbaric punishment. Singapore has taken to paddling its criminals. While there is no difference between 100 years and 1000 years in jail, there is a huge difference between 10 paddlings and 100 paddlings. By creating a system where the marginal cost of committing another felony is as high as committing the first, Singapore successfully limits its crime.
To conclude incentives is what drives crime.