Pure reason, combined with adventitious input will indicate that Capital Punishment is not an effective deterrent in many cases.

First, look at the different types of killers:

1) The professional "hit" man(woman). He(she) kills for money or is part of a mob or gang which dispatches ite members to kill for profit, revenge, and/or to establish dominance. This type of murder is detached, unemotional, pre-meditated and planned. Capital Punishment will not deter this type of killer.

2) The psychotic "serial" killer. Although deemed to me mentally ill, this type of killer usually has a grudge against certain types of individuals: coule be prostitutes, male or female children, homosexuals, mother or father figures, etc. This type of killer usually becomes daring as time passes, taunts legal authorities with notes, phone calls, etc., and perhaps has a deep-seated desire to be caught. The very fact that this type of killer keeps killing is prima facie evidence that Capital Punishment is not a deterrent.

3) The "fit of rage" killer. This type of killer is normally a pretty much law-abiding citizen, but gets pushed too far in an argument and (unintentionally) lashes out in a fit of rage, not necessarily meaning to kill. They do not stop and take the time to think out their actions, so Capital Punishment is not a deterrent. They are usually very remorseful about their crime, and very often get a reduced charge of second- or third- degree murder or aggravated homicide. They are not likely to be repeat offenderd.

4) The person who contemplates and pre-meditates murder for a considerable duration of time to gain life insurance and other assets, or to seek revenge for an unfaithful partner, or to get rid of someone who is preventing them from some kind of accomplishment. Capital Punishment might be a considerable deterrent in this case.

There may be crimes other than murder which would make one eligible for Capital Punishment, such as treason, which would appear to fall under category 1 above, or serial rape, which would appear to fall under category 2 above.

Also, there may be other profiles of killers, and you are free to add them to the list.

Capital punishment is almost a bit of a joke because many are never carried out, many are appealed, postponed, commuted to life sentences, etc., all of which actions serve to lessen the deterrent effect thereof. The very fact that many jurisdictions have "automatic appeals" is an indication that they don't really want to enforce Capital Punishment.