One problem with the draft procedure is that it is not strategyproof: students may potentially get better courses by manipulating their reported preferences.
This procedure reduces the welfare loss due to mistakes in manipulation and lack of knowledge of the position in the choosing sequence.
[5] Another problem with draft is that it only considers the ordinal ranking of the students, and ignores their cardinal valuations.
Economic theorists have proved that random serial dictatorship (RSD) is the only strategyproof mechanism that is ex-post Pareto-efficient and satisfies some other natural properties.
The bids of all students on all courses are ordered from high to low and processed one at a time.
Each bid in turn is honored if and only if the student has not filled his/her schedule and the course has available seats.
[12] Kominers, Rubbery and Ullman[1] introduce a proxy bidding mechanism, which aims to computes high-quality manipulations in behalf of each student.
Eric Budish developed the theory;[12] Othman and Sandholm[13] provided efficient computer implementations.
[15] Recently, Budish, Gao, Othman, Rubinstein and Zhang presented a new algorithm for finding an approximate CEEI, which is substantially faster, attains zero clearing error on all practical instances, and has better incentive properties than the previous algorithm.
[17][18] Overcoming this challenge requires to design a simple language that allows students to describe their preferences in a reasonable time.
Atef-Yekta and Day[20] aim to improve the efficiency of draft mechanisms by incorporating elements of bidding, while still keeping its round-by-round structure that enhances the fairness.
In the cardinal aspect, OC and BPM were the most efficient, but SP-O and TTC-O were the most fair.
They report a field experiment showing the benefits of stable matching mechanisms.
Diebold and Bichler[23] compare various mechanisms for two-sided matching on course-allocation information.
Like in DA algorithm, each student "proposes" to the course ranked the highest in his ordinal ranking; the over-demanded courses then order the students according to their cardinal values, and reject the lowest ones.
They report that, based on theory and field experiments, this scheme improves the efficiency of the allocation.