In a surprising post, Steve Levitt comes out in favour of a lottery allocation for classes with permissive re-sale. Apparently, this is what happens at NYU’s law school but I must say that I have little confidence that the so-called efficient outcomes are resulting from the post-lottery trading. For one, bilateral trades in a quick and hasty manner cannot be expected to allow those who most want to attend a particular class to get the opportunity to do so. Second, there is plenty of psychological evidence that there is a ‘bird in the hand’ effect to such things and having won a lottery many might not be as willing to part with their allocation. It is fair in the sense that everyone has an equal chance of earning rents but efficiency cannot be guaranteed.
A better solution is an auction mechanism rather than a lottery. Levitt argues that the Coase-like trading situation helps law students learn about the Coase Theorem. But wouldn’t it be better that they learn about efficiency per se through an appropriate mechanism upfront?
Core Economics 
Perhaps students would learn more if they learnt that systems can also adjust to get a better overall solution.
For example as the first appoximation let everyone make their choices on what they would like to have. Now within the resources of the institution set up the structure of times and teachers to best fit these initial choices. Now publish the new set of classes and go through whatever allocation mechanisms are necessary to fine tune the system.
In other words have a better starting point and you are likely to end up with a better solution.
There are many variations on this. For example I have scheduled assessments with a large number of assessors and students by allowing assessors and students to express their preferences and then finding a schedule to meet those preferences. People were able to say things like “I want to do all assessments on the same day but with a break every two hours” or “I only want to assess this type of work” or “I can only be assessed at these times”
Given all the preferences we now create the schedule that best meets these preferences.
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