It’s already been done a few times unofficially. Both pro and con capital punishment advocates as well as probability phobics have objections, but they will be refuted when I write lengthier explanations. Basically, it’s a pot odds problem.
There are at least three categories of folks who would be concerned about my idea. One, ironically, would be some of those who are opposed to capital punishment completely. Because their reason for opposition is not simply because an innocent person may be executed. But since they know that many are opposed to the death penalty mainly for that reason only, they would worry that if my idea was adopted, they would have fewer allies to help them to abolish it completely. A second group are those who have a problem with assigning a probability based on judgement or opinion rather than indisputable things like cards and dice. Finally, I believe that a third group would come into being if my sliver of doubt idea was implemented. I speak of people who will feel uncomfortable with the idea that when a convict escapes the death penalty but not life imprisonment due to slight doubt, while his guilt is still beyond reasonable doubt, it means that the government is admitting that just maybe they are imprisoning an innocent person for life. That is obviously always true, But my scheme would make it official.
In spite of all that, my idea should be a slam dunk as long as we are still executing people. The pot odds are just too high. The risk is keeping someone in jail forever who some think deserve to die. A lot different than freeing him. The reward is just possibly preventing an innocent man from being executed.
I am not opposed to capital punishment, but would support a commutation of a death sentence if there is any doubt as long as that situation is a combined with a more rapid enforcement where there is no doubt.