Edward Stringham, editor of a 720-page book on the subject, makes the case for free-market justice in The Washington Times. I'm so pleased to see such radical ideas in a quasi-mainstream paper that I hate to carp about the piece, but this really isn't the strongest possible argument for his position:
Imagine if Duke University controlled law enforcement in the area around the university, rather than the city, county and local court system. It is hard to imagine any private organization behaving as unjustly as the government did [when falsely accusing Duke lacrosse players of rape]. The university would have been guided in its behavior not only by the pursuit of justice and truth, certainly the top considerations, but by the impact of the allegations on all of its constituencies—students, alumni, faculty, the athletic community, donors and its neighbors in Durham.
Now, there are good reasons for Duke to operate its own security patrols on its own property and in the neighborhoods around the campus—indeed, it already does. There are good reasons for Duke to have its own internal arbitration systems—and again, it already does. But when a person who is neither a student nor an employee of the college accuses a student of a crime, it's not obvious at all that the university should have jurisdiction. Not under our current system, and not under the system Stringham proposes.
Nor would either party necessarily want Duke to have jurisdiction. Sometimes university courts work well. Sometimes they're models of injustice. In Stringham's polycentric system, there might be better alternatives. (Considering some of the ways the Duke community actually handled the scandal, there had better be better alternatives.)
Full disclosure: I grew up in Chapel Hill, where I was raised to view everything Dukean with suspicion.