I would rather have a small administration team handling them slower, but more effectively, than random users handling them faster, but less effectively. Our administration team handle all reports seriously and fairly because it's their duty, random users will do as many as they can just for bragging rights. You also face the situation of;
What happens if user-x has to deal with a report against user-v, who happens to be their friend? Or against user-f who they hate?
Will they handle it fairly, or will they let their personal feelings get in the way and obscure the result?