Improving the Chilean College Admissions System

In “Improving the Chilean College Admissions System,” Rios, Larroucau, Parra, and Cominetti describe the design and implementation of a new system to solve the Chilean college admissions problem. The authors develop an algorithm that (i) obtains all applicant/program pairs that can be part of a stable allocation when preferences are not strict and when all students tied in the last seat of a program (if any) must be allocated and (ii) efficiently incorporates affirmative action, which is part of the system to correct the inefficiencies that arise from having double-assigned students. By unifying the regular admission with affirmative action, the solution proposed and implemented by the authors has improved the allocation of approximately 2.5% of students assigned every year since 2016, helping to improve the overall efficiency of the system.

Graphical One-Sided Markets

We study the problem of allocating indivisible objects to a set of rational agents where each agent's final utility depends on the intrinsic valuation of the allocated item as well as the allocation within the agent's local neighbourhood. We specify agents' local neighbourhood in terms of a weighted graph. This extends the model of one-sided markets to incorporate neighbourhood externalities. We consider the solution concept of stability and show that, unlike in the case of one-sided markets, stable allocations may not always exist. When the underlying local neighbourhood graph is symmetric, a 2-stable allocation is guaranteed to exist and any decentralised mechanism where pairs of rational players agree to exchange objects terminates in such an allocation. We show that computing a 2-stable allocation is PLS-complete and further identify subclasses which are tractable. In the case of asymmetric neighbourhood structures, we show that it is NP-complete to check if a 2-stable allocation exists. We then identify structural restrictions where stable allocations always exist and can be computed efficiently. Finally, we study the notion of envy-freeness in this framework.

Trading Votes for Votes. A Dynamic Theory

We develop a framework to study the dynamics of vote trading over multiple binary issues. We prove that there always exists a stable allocation of votes that is reachable in a finite number of trades, for any number of voters and issues, any separable preference profile, and any restrictions on the coalitions that may form. If at every step all blocking trades are chosen with positive probability, convergence to a stable allocation occurs in finite time with probability 1. If coalitions are unrestricted, the outcome of vote trading must be Pareto optimal, but unless there are three voters or two issues, it need not correspond to the Condorcet winner.

Implementation of Stable Marriage Algorithm in Student Project Allocation

Project allocation is an annual challenge for lecturers and students. The process of allocating project involves matching preferences of students over project and with of staff over the student, and is thus an instance of stable marriage problem from theoretical computer science aspect. The aim is to find a stable allocation of project to students, such that it is impossible to find a project swap that would make all involved parties (both students, both staff) happier. This paper investigated efficacy of stable marriage algorithm and deployed basic Gale Sharply Algorithm into the process of allocating student project. A system was developed using ruby and MySQL to handle the task. The result showed that the algorithm was able to improve the process by enhancing the stability involved.