How could it be conclusively proven that the death penalty deters potential criminal better than life imprisonment?

Answer 1

It would be impossible to prove conclusively. Scientific laws are proven through a century or more of repeating experiments and observing the same result. Even so, these principles can not be considered conclusive, there is always a probability greater than zero that you will throw a Baseball into the air and it will float away instead of returning to the ground. In social science this is even more true. Any claim will be countered by additional research that contradicts to one extent or another the validity of the original finding. On any given public policy issue you will invariably find a range of conclusions that are mutually exclusive of each other. Does class size matter for student outcomes for example? While the majority of studies have answered "yes" a substantial number have answered found no effect from decreased class size on student outcomes or a conditional effect or even a negative impact from class size reduction. Don't expect conclusive answers on any public policy question. The best you can hope for is that a number of well executed studies will agree on a given effect such as death penalty is a greater deterrent than a life sentence. In particularly emotionally charged issues such as this, however, there will always be studies that find contradicting evidence.