You have power. Kind of.
Picture this—one of Delta Shmoop's chapters, Phi Shmoop, is throwing an ice cream social for all of its new pledges. Delta Shmoop is one of the 26 sororities apart of Panhellenic and therefore cannot haze. They, however, decide to have their new pledges eat ice cream while forcing them to do the Macarena. Brain freeze is a serious condition, and you cannot condone this behavior. You advise that the President at Delta Shmoop headquarters put Phi Shmoop on probation. Sorority probation means no formals and no new t-shirts. This is devastating for them.
Sometimes when a sorority has gone above and beyond depravity they get shut down or worse; they can't participate in recruitment. This is the kiss of death for sororities, and if this happens there is no recovering.
Unfortunately you're not in charge of this decision. You just give constructive advice, and it is then up to that sorority to deal with it's own chapter'.s misfortunes.
So by power we really mean you sometimes get to voice your own opinion.