When I sectioned for my Foreign Cultures course a little over a month ago, the Registrar sectioning website did not simply have me jot down my name, and then respond two days later offering me a section time that was good for them and just so happened to coincide with my 10 a.m. Spanish class. No, it allowed me to pick my top five time choices and then did the best it could to respect my preferences while fairly respecting those of my classmates as well.
I recommend a system formatted after online sectioning, where students rank the Houses and the committee does its best to meet the preferences.
Just as online sectioning isn't flawless and some people don't get their first or second choice, not everyone would get their top housing preferences.
But at the bare minimum, more people will be satisfied with their assignment.
Meanwhile, the Housing Office can still flex its muscles and promote diversity by being discreet in its assignments. It already asks for the concentrations of students. It should also ask for the ethnic background and athletic or program involvement of each applicant, too.
If the Housing Office has to sacrifice a first-year's top three housing choices to insure a mixed batch, so be it. At least that person will get his or her fourth choice rather than the tenth.
A place where students eat, sleep, work and socialize is too important and too prominent in students' lives to be random.