School placement solution

This year’s Nobel Prize in Economics has been awarded jointly to Alvin Roth and Lloyd Shapley “for the theory of stable allocations and the practice of market design”.

These theories seem very relevant to Malta and the Church school placement problem.

Church school placements in Malta occur in two main streams. In the first instance, those applicants that satisfy the “initial criteria” are immediately allocated a place in a Church school.

In the second instance, students who do not satisfy the initial criteria will enroll in a participation lottery, whereby those successful (and, in this case, the order of the draw is not important) will win the right to participate in a second lottery, the choice lottery. The draw from the choice lottery will, in turn, determine the order in which students are given the right to choose the school they would like to attend.

The fact that students’ education, a key decision that will affect their future, is left to the game of chance does not feel right.

The process is inefficient. The selection of students and the order of choice is determined by two lotteries, which do not necessarily return the best outcome for the school, or the student. Enter microeconomics.

On a number of occasions, microeconomics, through game theory, has allowed mankind to solve some worldly problems. In most capitalistic markets, equilibrium is found when demand and supply interact, when price interacts with demand and supply to obtain equilibrium.

If, for instance, steel is in short supply, the price will increase and only those willing to pay the higher price will get the goods, thereby using the scarce resource where it is most needed.

Price, however, cannot always be relied upon to assist in all rationing decisions. Other more meaningful factors may come in to play. For instance, it is not socially acceptable, at least, in western cultures to let money or camels determine who one should marry.

Gale and Shapley set out to discover the more meaningful factors beyond camels and they explore, with the help of “a marriage problem”, the best method to assign individuals to each other.

The end result is to ensure that each couple is stable in their relationship. Stability would result when every individual is at least as happy in their relationship as under any other stable assignment. Gale and Shapley also show that there exists a marginal advantage for the proposer vis-à-vis the acceptor.

Very clearly, this means that, due to the selection method invoked, there is a win-win situation that is not being exploited and, therefore, society in general is losing out.

If we were to apply the findings of the Gale and Shapley paper to the Church school rationing problem one would ask prospective students to rank the schools in order of preference.

Schools would, in turn, rank students in order of preference. Ranking methods are not the scope of this discussion and, although subjective taste may come into the decision, methods may be applied, with the assistance of psychologists, to remove subjectivity from the ranking exercise (especially with regard to schools ranking students). One method could be the use of special aptitude tests that assess talents, not merely intelligence.

Since the proposer has an advantage over the acceptor, in the schooling problem, students would assume the role of the proposer thereby ensuring students achieve their optimum position whereas schools would fill the role of acceptors.

Notwithstanding this, schools would still be better off when compared to their position under the lottery system as they would achieve a stable solution. The stable solution would, in the real world, translate into stronger, more effective schooling. This concept has been developed further by Roth.

The theories outlined in this text have already been tried and tested and have been used in the US to resolve similar problems. Roth subsequently also used this theory to match kidney donors to patients, work that is said to have saved lives.

At times, the solution to a problem is already available and resides in the strangest of places; one simply needs the patience and the knowledge to know where to look.

In this case, economics, normally confined and quickly dismissed as a tool to solve economic woes, has provided solutions to some of the anguishes experienced in the education and health sectors.

Andrew Neal Farrugia is an economist.


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