Reiman's Problem: While evil gives us the right to punish the wrongdoer with retribution, does it follow that we should act on this right? 

The Kantian idea of respect for persons: Always treat persons as ends, never as mere means. 

To treat a person as ends, we respect the ends they choose for themselves (but we never respect their decision to treat another person as mere means). The whole point of punishing a person is to make a statement to that person.

The Resulting Conflict: By their choices, each person authorizes similar action directed at themselves by others. 

However, to authorize is not the same as to compel.

Sometimes an evil choice authorizes others to do to them what we neither choose to do nor should permit them to do to others - in practical terms, respecting another person with retribution will authorize an action that dehumanizes the person doing the punishing. Example: If we're civilized, we don't want to torture people, so we should not be compelled by a person who tortures a victim into our becoming torturers. We should have the right to substitute a more humane (yet serious) punishment.

Reiman's solution: Pursue the most humane punishment while retaining proportional substitution of severity, provided there is no reduction of deterrence. Civilized people look for a more humane way to make a statement to the guilty person.

             (He is proposing that we use proportional retribution instead of lex talionis.)

Additional problem: do executions deter murder?

If a more humane or "civilized" punishment makes life more dangerous for ourselves and others, then it is morally wrong to be more humane. (TOO LITTLE punishment communicates that we do not think that the wrongdoing is serious, and we will encourage more of it. But it is wrong to encourage more of it.)

So, does being humane with murderers take away a deterrence that we have a right to employ?

We have no good statistics to say that executions deter more than life sentences, and here are four additional reasons not to think it does: 

1. Anyone who is worried about being punished is just as likely to be deterred by life in prison as by execution.
2. Each year, more criminals are killed by policemen while being arrested than are executed. If this does not deter criminals, why would the lower risk of delayed death?
3. If criminals are not coldly calculating their odds, then proponents of executions must think that some general message has deterrence power. But if that is true, then there will also be a counter-balancing general message by not executing, a message of respect for life. This should save lives.
4. If common sense says that #1 is wrong, and executions deter more than life (because most criminals who face death try to get a life sentence, instead), then brutal torture before execution is even harsher. So anyone who wants executions should also want torture. But this would be wrong!