Because the machine can't deduce each student's preferences. I suspect the problem is essentially unsolvable, without requiring each student to fully write out

Because the machine can't deduce each student's preferences. I suspect the problem is essentially unsolvable, without requiring each student to fully write out the order of his/her school preferences. Otherwise there will inevitably (if the solution to the Stable Marriage problem is optimal in this regard) be undecidable cases that would have to be dealt with in a second round.