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Cruel and Unusual: Should Capital Punishment Hurt?
The prospect of pain makes the punishment more effective as it gives another reason to cooperate with the authorities.
The prospect of not merely death but a painful death can be a decisive factor in convincing a criminal to cooperate with the authorities prior to their conviction - for example, by providing information in order to mitigate the punishment.
If the prospect of receiving the death penalty itself is not a sufficient motivation for those accused of crimes to cooperate with authorities, the addition of pain is unlikely to make a difference.