The Executive Council (執行部, Shikōbu) is the main force among the students of Todo Academy, becoming 3rd year enforcement group. They keep the order on the school and punish the students that do not follow their rules or in a response to string of violent behavior student could exhibit.
Originally Maya remembers the "Punishment" started as a means for the student council to control public morals. She thought it had became just a formality at school, and at worst the brats will just be beaten to a point where they will be able to recover. His present president (Mitsuomi Takayanagi) is tolerant but that doesn't apply to all of the members of Executive Council. As aspecial exception, an "unlimited" punishment will be inflicted on Bob Makihara and Souichiro Nagi. They have to show those first years just how they will be treated for joining forces with Juken Club (The Executive Council thought they were members of Juken Club). In fact Tsutomu Ryuuzaki raped Bob's girlfriend, Chiaki in Chapter #5.
One hundred years ago, the Executive Council started when the Feudal Clan based administration system was collapsing, and in order to revive the dying "Martial Arts" the predecessor to this school, the "Toubu Training Center" was founded. All of the old Clan's private guards, instructors, and masters were half-forced to assemble. In order to protect the order of the center, it was important to establish absolute rules and power.
The Executive Council is chosen annually by the Election Tournament, where the winning group becomes the new Executive Council for the next school term. Two years ago, Mitsuomi became the leader of the group and his group won the next, keeping their post.