A few questions:
- From your example, students only express a preference for those sections they are interested in. They do not rate all sections?
Can it be assumed that they have eual distaste for all unrated sections?
- Can a student be in more than one section?
It radically alters the complexity if they can.
- Do all sections have to have students?
In effect, this question really amounts to: "Do the numbers of places per section, total to the number of students?"
Also: "Less than?" and "More than?"
- What are the orders of magnitude you are dealing with?
'20 students split across 5 sections with 4 places each' is a whole different kettle of fish to '2000 students across 50 courses with 0 to 20 places each'.
One is easily solved by brute force with a 'judgement criteria', the other requires a heuristic.
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