Algorithmics, Social choice, Market Design, and Other Topics

Working Paper: https://cgi.cse.unsw.edu.au/~haziz/PIRMES.pdf  Abstract: In a typical school choice application, the students have strict preferences over the schools while the schools have coarse priorities over the students based on their distance and their enrolled siblings. The outcome of a centralized admission mechanism is then usually obtained by the Deferred Acceptance (DA) algorithm with random tie-breaking. Therefore, every possible outcome of this mechanism is a stable solution for the coarse priorities that will arise with certain probability. This implies a probabilistic assignment, where the admission probability for each student-school pair is specified. In this paper, we propose a new efficiency-improving stable `smart lottery' mechanism. We aim to improve the probabilistic assignment ex-ante in a stochastic dominance sense, while ensuring that the improved random matching is still ex-post stable, meaning that it can be decomposed into stable matchings regarding the ...