From MangaHelpers:
As Japan's population grows older and smaller, and as murder rates skyrocket, the Japanese government began to implement stricter laws against the worst criminals. With even the death penalty lacking the deterring force to stop the most violent criminals, Japan brought back to life a law from the 19th century: the Revenge law. This law allows victims and their related parties to employ a governmental special forces agency to capture and attack the murderer—by reenacting the exact same methods that the murderer used on the victim.
Yamagishi Yuji is the 7th member of the Special Forces "Sukedachi-nin." Each of the members of this special forces has been chosen to enforce the Revenge law because they too have been a victim of past crimes.

Official English Translation