This year the Nobel Prize in economics was won by Alvin Roth and Lloyd Shapley, I hadn’t know what they’d done, but The Economist has an explanation:
Basically, they used game theory to devise an algorithm to pair people and opportunities, or, in the example first given, to pair men and women:
In romantic comedies, each man and woman marries their own true love. In real life, some people settle for second-best, which can lead to lots of trouble. If John and Mary love each other but are married to other people, they will be tempted to leave their current partner and marry each other. But if John loves Mary, while Mary loves her husband more than John, both will stay put.
Mr Gale and Mr Shapley devised an algorithm for matching an equal number of men and women that would guarantee this second, more stable outcome. Each man and woman ranks their preferred partners. Each man proposes to his highest-ranked woman. Each woman rejects all the proposals she gets except the highest-ranked among them. But she does not accept the proposal, in case a man she prefers even more proposes next time. The algorithm is rerun until all women have a satisfactory proposal.
This algorithm deals with economic exchanges in situations where monetary pricing does not work.
This suggests a superior alternative to the points system. The points system is based on a money analogy; students win a certain amount of money, “points”, based on how well they do in the Leaving Cert, 100 points for an A1 at honors level down to 5 points for a D3 at pass level, with a maximum of six subjects counted. Students bid with these points for places in third level courses.
The points system has some advantages, it is safe from the obvious forms of patronage and corruption, it is less time consuming than systems that are not based on an automatic algorithm and, in the parlance of education, it is aligned, to get a desirable place in third level you need to do well in your school studies and that’s assumed to be a good thing. It is, however, a terrible system.
One problem, one of the main problems, with the points system is that it doesn’t match students to courses. Instead it reduces the students exam record to a single number and uses that to distribute places. This is obviously idiotic and the concomitant pressures and distortions devalue the whole second level educational experience. I think Roth and Shapley’s algorithm can fix this.
In the new system each course would publish an order list of results. My old department in TCD might for its mathematics degree list, for example,
- A1 in Mathematics and A1 in Applied Mathematics, an A or B in Physics and 450 points overall with all language A and B counting for 75 points.
- A1 in Mathematics and A1 in Applied Mathematics, an A or B in Physics and 450 points overall,
- A1 in Mathematics, an A or B in Physics and 450 points overall
and so on, down to the lowest acceptable result. As now, students would make a long list of courses they are interested in.
After the exams, each course would propose to the best students that list it, judged according to its published preference list. Each student would then reject all but the course highest on their list and the highest would be retained as a “proposal”. The process would then iterate, all the rejected course places would be offered to students lower down the preference list, students who get a better place proposed to them than the one they had retained from the last round would reject their old proposal and retain the new one. Roughly speaking this would keep going until either every student had a proposal or every place is a proposal. At that point the proposals would become offers. Of course, all this proposing and rejecting would be automatic, taking place on the CAO computer.
This system retains the desirable properties of the points system while avoiding its most obvious failing. It would select students for courses based on the suitability of their exam performance profile for the course rather than on their overall point level. This would force third level course directors to think hard about their ordering of preference criteria. To attract and accept the best students for the course they would forced to think clearly about how those students could be recognized from their Leaving Cert scores. This is a good thing, not a bad one.
Obviously there are lots of other problems with the points system; some problems are Leaving Cert curriculum problems which are exacerbated by the points system and others relate to its inflexibility in dealing with social disadvantage. The latter could be accommodated within this proposal by allowing preference descriptions which include, for example, the status of the school as serving a disadvantaged area or cohort.