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I think he's saying that the error is in the original assignment algorithm: it produces a solution that is not Parto-optimal. If it was, there would be no mutua

• ucaetano 9y ago
  But you can't consider just the current round of students when designing such a system, you need to consider all subsequent rounds. In that case, allowing trades now leads to dissatisfaction in the future. So, while allowing trades now might seem to lead to a pareto-optimal scenario, it doesn't lead to a time-series-pareto-optimal scenario.
  • om2 9y ago
    The alternate system I described doesn't involve "allowing trades" and therefore can't create perverse incentives or affect subsequent rounds. The idea is to make an algorithm that performs a Pareto-optimal assignment algorithmically, so that no possible mutually advantageous trades exist when it is done. It's totally possible for an algorithm to do that, and the current Dutch one clearly doesn't. One possible way is to run the current algorithm, and then as long as the solution is not Pareto-optimal, perform a swap at random from the set of all pairs of students where swapping would improve both of their preferences. This can be proven to converge with sufficient steps. Doing this kind of swap algorithmically has nothing to do with "allowing trades". I'm calling them "swaps" instead of "trades" here to make clear there is no manual action involved on the part of the students. I hope this clarifies what I meant, and why objecting to "allowing trades" does not make sense as a response.