Rarely do I think the DP can be a deterrent for criminals, but people like Arias can't be rehabilitated. In this case the punishment should fit the crime.
If given LWOP, she would be the f'kn "Queen Bee" in prison with her groupies behind her.
The death penalty is a deterrent on many levels.
If the guilty murderess is executed, she will never kill again. This is a deterrent, potentially saving other lives.
If the guilty murderess is not killed, she may kill in prison.
Or she may escape prison and kill again.
It is also a deterrent insofar as other murderers, much like this murderess, will claim that they welcome the death penalty. Or, if guilty, that they would deserve or "beg for" it.
In reality, nearly all of them are lying. They plead not guilty, are then convicted, and spend the rest of their lives appealing and begging for pardons and stays of execution.
Each execution sends a message to society that even though there is little morality remaining, some behaviors, such as premeditated murder, will not be tolerated.
We can never know how many murderers, especially those tempted to or actually engaging in premeditation of the crime, do not follow through or 'act out' due to their own fears and their instinct for self-preservation.