arXiv subjects

Tom Demeulemeester

Publications and source records attributed to Tom Demeulemeester.

8 recordsLinked to original sources

arXiv2026

Smart Lotteries in School Choice: Ex-ante Pareto-Improvement with Ex-post Stability

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 original coarse priorities. Therefore, this smart lottery mechanism can provide a clear Pareto-improvement in expectation for any cardinal utilities compared to the standard DA with lottery solution, without sacrificing the stability of the final outcome. We show that although the underlying computational problem is NP-hard, we can solve the problem by using advanced optimization techniques such as integer programming with column generation. We conduct computational experiments on generated and real instances. Our results show that the welfare gains by our mechanism are substantially larger than the expected gains by standard methods that realize efficiency improvements after ties have already been broken.

cs.GT↗

arXiv2026

E-comment on 'What's the Matter with Tie-Breaking: Improving Efficiency in School Choice'

The code that was used in Erdil & Ergin (2008, AER) to compute stable improvement cycles sometimes generated unstable matchings. I identify the minor bug in their code that caused this issue, and I present a corrected implementation. While the general insights from the computational experiments obtained by Erdil & Ergin (2008) persist, the true fraction of improving students is slightly smaller than reported, while their average improvement in rank is larger than reported. All theoretical findings in Erdil & Ergin (2008) are unaffected.

econ.TH↗

arXiv2025

Pairwise efficiency and monotonicity imply Pareto efficiency in (probabilistic) object allocation

We consider object allocation problems with capacities where objects have to be assigned to agents. We show that a probabilistically monotonic lottery rule satisfies ex-post Pareto efficiency if and only if it satisfies ex-post pairwise efficiency and ex-post nonwastefulness. This result allows us to strengthen various existing characterization results, both for lottery rules and for deterministic rules, by replacing (ex-post) Pareto efficiency with (ex-post) pairwise efficiency and (ex-post) non-wastefulness, e.g., for characterizations of the Random Serial Dictatorship rule (Basteck, 2025), Trading Cycles rules (Pycia and Unver, 2017), and Hierarchical Exchange rules (Papai, 2000).

econ.TH↗

arXiv2024

Quantifying Core Stability Relaxations in Hedonic Games

We study relationships between different relaxed notions of core stability in hedonic games, which are a class of coalition formation games. Our unified approach applies to a newly introduced family of hedonic games, called $\alpha$-hedonic games, which contains previously studied variants such as fractional and additively separable hedonic games. In particular, we derive an upper bound on the maximum factor with which a blocking coalition of a certain size can improve upon an outcome in which no deviating coalition of size at most $q$ exists. Counterintuitively, we show that larger blocking coalitions might sometimes have lower improvement factors. We discuss the tightness conditions of our bound, as well as its implications on the price of anarchy of core relaxations. Our general result has direct implications for several well-studied classes of hedonic games, allowing us to prove two open conjectures by Fanelli et al. (2021) for fractional hedonic games.

cs.GT↗

arXiv2023

Fair integer programming under dichotomous and cardinal preferences

One cannot make truly fair decisions using integer linear programs unless one controls the selection probabilities of the (possibly many) optimal solutions. For this purpose, we propose a unified framework when binary decision variables represent agents with dichotomous preferences, who only care about whether they are selected in the final solution. We develop several general-purpose algorithms to fairly select optimal solutions, for example, by maximizing the Nash product or the minimum selection probability, or by using a random ordering of the agents as a selection criterion (Random Serial Dictatorship). We also discuss in detail how to extend the proposed methods when agents have cardinal preferences. As such, we embed the black-box procedure of solving an integer linear program into a framework that is explainable from start to finish. Lastly, we evaluate the proposed methods on two specific applications, namely kidney exchange (dichotomous preferences), and the scheduling problem of minimizing total tardiness on a single machine (cardinal preferences). We find that while the methods maximizing the Nash product or the minimum selection probability outperform the other methods on the evaluated welfare criteria, methods such as Random Serial Dictatorship perform reasonably well in computation times that are similar to those of finding a single optimal solution.

cs.GT↗

arXiv2022

Strategyproofness and Proportionality in Party-Approval Multiwinner Elections

In party-approval multiwinner elections the goal is to allocate the seats of a fixed-size committee to parties based on the approval ballots of the voters over the parties. In particular, each voter can approve multiple parties and each party can be assigned multiple seats. Two central requirements in this setting are proportional representation and strategyproofness. Intuitively, proportional representation requires that every sufficiently large group of voters with similar preferences is represented in the committee. Strategyproofness demands that no voter can benefit by misreporting her true preferences. We show that these two axioms are incompatible for anonymous party-approval multiwinner voting rules, thus proving a far-reaching impossibility theorem. The proof of this result is obtained by formulating the problem in propositional logic and then letting a SAT solver show that the formula is unsatisfiable. Additionally, we demonstrate how to circumvent this impossibility by considering a weakening of strategy\-proofness which requires that only voters who do not approve any elected party cannot manipulate. While most common voting rules fail even this weak notion of strategyproofness, we characterize Chamberlin--Courant approval voting within the class of Thiele rules based on this strategyproofness notion.

cs.GT↗

arXiv2022

Rawlsian Assignments

We study the assignment of indivisible goods to individuals without monetary transfers. Existing literature has mainly focused on efficiency and individually fair assignments; consequently, egalitarian concerns have been overlooked. Drawing inspiration from the allocation of apartments in housing cooperatives, where families prioritize egalitarianism in assignments, we introduce the concept of Rawlsian assignment. We show that the Rawlsian assignment is unique and that the rule it induces is efficient and anonymous. The Rawlsian rule is not sd strategyproof, reflecting a fundamental incompatibility between worst-rank minimization and even weak incentive requirements. Nevertheless, it satisfies several robustness properties that limit other forms of manipulation. We illustrate our findings using cooperative housing preference data, showing significant improvements in egalitarian outcomes over both the probabilistic serial rule and the currently employed rule.

econ.TH↗

arXiv2021

A pessimist's approach to one-sided matching

Inspired by real-world applications such as the assignment of pupils to schools or the allocation of social housing, the one-sided matching problem studies how a set of agents can be assigned to a set of objects when the agents have preferences over the objects, but not vice versa. For fairness reasons, most mechanisms use randomness, and therefore result in a probabilistic assignment. We study the problem of decomposing these probabilistic assignments into a weighted sum of ex-post (Pareto-)efficient matchings, while maximizing the worst-case number of assigned agents. This decomposition preserves all the assignments' desirable properties, most notably strategy-proofness. For a specific class of probabilistic assignments, including the assignment by the Probabilistic Serial mechanism, we propose a polynomial-time algorithm for this problem that obtains a decomposition in which all matchings assign at least the expected number of assigned agents by the probabilistic assignment, rounded down, thus achieving the theoretically best possible guarantee. For general probabilistic assignments, the problem becomes NP-hard. For the Random Serial Dictatorship mechanism, we show that the worst-case number of assigned agents is at least half of the optimal, and that this bound is asymptotically tight. Lastly, we propose a column generation framework for the introduced problem, which we evaluate both on randomly generated data, and on real-world school choice data from the Belgian cities Antwerp and Ghent.

cs.DS↗