The jury sentencing a person to death is a specific deterence to that individual because that person is dead and unable to commit murder. People in favor of the dealth penalty usually argue that the death penalty is so harsh that is deters OTHER people from committing murder because those potential murderers don't want to die themselves. If one trys to argue for deterence against people other than the person being murdered by the state, then one would need to provide statistics that can prove humans have avoided committing capital crimes so as to prevent themselves from being murdered by the state.