Simplifying greatly, you could say that the early part of that debate was dominated by sociologists who found no deterrent effect, and the latter part has been dominated by economists, who have found that every execution deters a number of murders, with most studies finding that it deters between 5 and 15 murders.In an earlier study on the subject of the death penalty and deterrence (where we learn for instance that one "common mistake is to compare states with death penalty laws to states without them", ignoring "the fact that the states with the laws do not always impose the death penalty"), Jim Miller used the case of BTK serial killer Dennis Rader as an illustration.
If the death penalty does deter, then the two sides in the argument over the death penalty have similar moral problems. Supporters of the death penalty must admit that it is possible that some innocents will be executed. Opponents of the death penalty must admit that it is possible that, without the death penalty, more innocents will murdered than would be murdered otherwise. (And each side tends to believe that what is possible never happens, or almost never happens.)