What incentives do teachers, and more specifically school administrators, face when dealing with rowdy, disruptive or violent students?
Let's say that an administrator expels a student for being overly disruptive to the learning environment in some way such as asking loaded questions, having independent thoughts, being bored with dumbed down material, etc. Seriously, lets say that a student is expelled for violence. The costs of this action will be borne by the expelled students and his or her parents. The benefits will be received by the student body and teaching staff as a whole who do not have to deal with the unruly student.
The costs in this case are highly concentrated (all on the expelled student and parent(s)). The benefits are widely dispersed across many students, teachers and administrators. The parents of the expelled student will come to school to plead their case. This could result in the parent agreeing with the administrator or disagreeing with the administrator. If the parent disagrees, this could result in the parent simply pleading their case more passionately or, in the most extreme case, suing the school. This is where the incentives start to show up.
Because costs are concentrated while benefits are widely dispersed, an administrator will be less likely than otherwise to expel unruly students. Just the threat of a lawsuit will cause administrators to think twice about expelling an unruly student, regardless of whether the benefits of this student being gone exceed the costs to the student. Because the costs are so heavily concentrated, those facing the costs will expend significant resources to avoid facing the costs (the parent raising hell or suing to avoid expulsion). Because the benefits are so dispersed across a wider population, those receiving the benefits will each expend few resources to capture those benefits (few parents will attend school board meeting encouraging them to expel our unruly student).
These incentives will result in unruly students not being expelled as often as they should because costs are so concentrated and benefits are so widely dispersed. This scenario certainly applies to administrators at the macro or school level, but also to teachers at the micro or classroom level. Why expel a student and have a parent come chew you out when there are not compensating benefits? Perhaps some people in schools have the nerve to expel such students and some parents fight to keep unruly students out, but my experience, and the incentives faced, tells me that too few are actually expelled.