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 I agree with you, but here, we are talking about the legal process by which the person is given the death penalty. That can be unjust even if the death penalty itself is justified when used in a just manner.

Let's take it to first principles. If a guy walks up to you and tells you "I am going to kill you if you don't kill me first" do you have a right to kill him? I'd say yes, what do you think?

Now, you and a group of people are hanging out. Some guy walks up to you guys and said "I'm going to kill one of you, I promise." Do you as a group have the right to kill him? Again, I'd say yes.

We can take that and do this thought experiment and find where it stops being justified. The man says "I'm going to rape all your kids and I won't stop until I'm dead", he doesn't say it verbally but demonstrates it with his behavior, etc. Then, what qualifies as a group? Does a jury that is part of the group qualify? You'll find plenty of scenarios where it is not done in a just manner, or when what someone is going to do if left to their own behavior doesn't justify killing them, but you'll find plenty of scenarios where it is justified. Therefore, the death penalty is just, even if the way it is done in our society is unjust. 
 To your first question, I would have to say no, because a threat of violence (even if backed with a promise) is still just words. One step further, if that threat was then followed by the person punching you in the face, I do not think it is moral to kill (disproportionate reponse...one can only morally kill another human if the person is in danger of being killed himself). If a gun is being drawn, now the situation has shifted to life-threatening and one has a right to protect life (so admitedly, we get into difficult territory delineated exactly where the threat against life precisely occurs, I think this area is ripe for debate and certainly different people perceive threats in varying degrees).

To your second question, essentially my answer above applies although now, with multiple people acting with varying threat perceptions the entire situation has become more difficult to summarize (if that makes sense?)

In the rape example, if the person is actually doing the act, witnesses to the act can morally take increasingly aggressive action toward the perpetrator to the point at which the violation ends. Again, the verbiage "raping until death" consitutes a threat, and is not the same as the act of killing, therefore it is not moral to automatically kill a human in the process of raping (even though it may feel like the "right" thing (emotionally) to do). The rapist should be stopped and penalized proportionately (certainly another area of discussion).

All of the above is not to be lenient on violence shitbags that want to harm innocent people. These individuals should face penalty proportionate to their crimes, but I do not think pre-meditated murder by uneffected agents acting on behalf of the state is proportionate. Additionally, given our highly flawed/corrupt legal and political systems, we need to be careful not to use the mechanism of state-sanctioned violence to kill innocents that manage to get caught-up in the someone elses' crime drama. I always come back to the thought, "What is the maximum number of innocent lives lost (to be clear - false conviction ending in death penalty) I am willing to accept before deciding that the death penalty is not a moral choice of state-sanctioned penalty?" I always land on 0 for this question. 
 
> ...I do not think pre-meditated murder by uneffected agents acting on behalf of the state is proportionate.

I'm 100% with you. The way it's done in our society is unjust. But what I'm trying to get at is, if putting people to death is fundamentally unjust. Most people I've talked to that are opposed to it tie the two inseparably and it clouds the morality of the fundamental question.

As far as your other points, I disagree entirely. Any credible threat of violence can be met with whatever preventative measures the potential victims warrant appropriate. I don't have to wait til I'm about to be killed to protect myself, if I know an attempt on my life is impending I can justifiably act.