The evidence for this is sought in crime rates in regions and nations where executions are carried out.
Second, supporters or opponents of death penalty need to find out whether this penalty can be acknowledged on moral grounds, solving the problem of whether human beings are justified in killing other human beings.
The issues involved in the discussion of death penalty usually focus around two main parts.
First, this punishment is analysed from a purely utilitarian perspective in an effort to find out whether application of capital punishment really helps to deter crime and reduce the risk of recidivism, when criminals commit repeated crimes.
China accounts for the bulk of these executions - 3,400 cases.
Kuwait is the leader in the number of executions per 100,000 residents - 400 compared to 260 in China and 230 in Iran, the runner-up on the total number, 159 (Wikipedia).
As part of anti-death penalty movement, this call to repeal this measure has been upheld by various international organizations.
For instance, “the United Nations Convention on the Rights of the Child, which among other things forbids capital punishment for juveniles, has been signed and ratified by all countries except the USA and Somalia” (Wikipedia).
Still, I do not believe in death as a form of punishment for drug dealers, however heinous their activities might be, since they did not violate human lives.
Political crimes should not be punished with death either, as this would open the way to political repression and physical elimination of political rivals, as it happened in Stalin's times in the Soviet Union.