"I did shift from being against the death penalty to thinking that if it has a significant deterrent effect it’s probably justified."

Says Cass Sunstein, quoted in this article by Adam Liptak. For years, death penalty opponents used the argument that all the studies showed that the death penalty did not deter murder. But now — contrary to what we all thought we knew — the studies show deterrence:

According to roughly a dozen recent studies, executions save lives. For each inmate put to death, the studies say, 3 to 18 murders are prevented....

The studies try to explain changes in the murder rate over time, asking whether the use of the death penalty made a difference. They look at the experiences of states or counties, gauging whether executions at a given time seemed to affect the murder rate that year, the year after or at some other later time. And they try to remove the influence of broader social trends like the crime rate generally, the effectiveness of the criminal justice system, economic conditions and demographic changes.

Much more at the link. Of course, the studies are subject to criticism. Obviously, there's no way to know to what extent a decision to commit murder includes a calculation about the death penalty. But if you oppose the death penalty, you can no longer rely on the old article of faith that there is no deterrence, and you have to concede that there may be some deterrence and take that into account.