Saturday, December 5, 2009

Deferred acceptance in Ghanian school choice

Kehinde Ajayi, a Ph.D. Candidate in the Department of Economics at the University of California, Berkeley, is studying school choice in Ghana. She recently sent me a 2005 document from Ghana's (then) Ministry of Education and Sport "that the government produced when the Computerised School Selection and Placement System (CSSPS) was initially introduced."

It describes a version of a deferred acceptance algorithm (a clearinghouse algorithm that has been discovered a number of times and places, but that game theorists associate with Gale and Shapley 1962), and describes an essential feature, which is that if student A would have displaced student B at school S had he ranked school S first, he will also displace student B at school S even if he ranks school S second (or lower). This is what makes it safe to list schools in your true order of preferences.

"4.2 Displacement
a. Selection on Merit
The computer places all qualified candidates into their first choice schools using the ranking order. The aggregate score of six subjects of each candidate is used to do the ranking.
b. Displacement of 1st choice candidates by 2nd choice candidates as a matter of merit or better performance
The ranking may displace 1st choice candidates with 2nd choice candidates; this will be on merit and not choice. The following table is an illustration:
"Kwasi and Kofi make the following choices of schools and programmes.
...[Table showing that Kwasi, with an aggregate 'score' of 400 ranks Anglican as his second choice, while Kofi, with a score of only 350 ranks Anglican as his first choice...]
"Suppose the cut-off for Science Programme for Opoku Ware is 420 and that for Anglican School is 350, Kwasi is sent to Anglican to compete with first choice candidates for science Programme because his aggregate score is just below the cut-off for Science Programme for Opoku Ware School. Kwasi is then sent to Anglican to compete with the first choice science candidates. Since Kwasi’s aggregate score is higher than that of Kofi’s, Kwasi will then displace Kofi."

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