School choice systems affect the educational paths of millions of students. But even well-intended reforms can have limits – especially when they focus on improving efficiency without addressing deeper distributional concerns.
In their new discussion paper “What Pareto-Efficiency Adjustments Cannot Fix”, Josué Ortega, Gabriel Ziegler, R. Pablo Arribillaga, and Geng Zhao examine a central question in modern school choice design: Can reforms that make the Deferred Acceptance algorithm more efficient also fix persistent problems such as poor student outcomes and segregation?
A widely used algorithm – with known shortcomings
Many school systems use the Deferred Acceptance (DA) algorithm to assign students to schools. DA has two major advantages. It produces stable assignments (meaning no student and school would both prefer to be matched with each other instead), and it encourages families to state their true preferences because strategic manipulation does not help.
However, DA can also produce outcomes that are widely seen as unsatisfactory. Some students end up with schools far down their preference list, even when better outcomes seem possible. DA has also been linked to segregation patterns in some settings, with disadvantaged groups concentrated in certain schools.
These concerns have motivated researchers to develop improved versions of DA.
What “efficiency improvements” aim to do
Many proposed reforms are based on a specific idea: Pareto improvement. A change is a Pareto improvement if it makes at least one student better off without making any other student worse off.
This is an attractive goal in public policy. If nobody loses, the reform can appear both fair and politically feasible. In school choice, several prominent mechanisms try to achieve exactly this – often by allowing limited priority violations, but only with consent from affected students.
The authors study this broad family of approaches, which they call stable-dominating rules: assignment rules that (i) always do at least as well as DA for every student, and (ii) are Pareto-efficient (meaning no further Pareto improvement is possible).
A key message: some problems remain even after efficiency fixes
The paper’s central finding: efficiency adjustments alone cannot solve some of DA’s most important other shortcomings.
The authors focus on two concerns that are often raised by policymakers and the public:
Their results show that even if DA is improved in a Pareto sense, these problems can remain essentially unchanged.
Poor rank outcomes can persist – even when DA is already efficient
A first contribution of the paper is to show that DA’s “rank problem” can arise in a particularly troubling way.
Stacking the cards in favor of DA, the authors focus on a case where the DA outcome is already Pareto-efficient. That means there is no way to make any student better off without harming another student. In such cases, any reform that promises Pareto improvements over DA has no room to operate: it must return the same outcome as DA.
Yet in these cases, the DA outcome can still look socially undesirable. Several students receive schools in the bottom half of their preference lists, and the worst-off student can receive their least-preferred school. At the same time, the authors show that other Pareto-efficient matchings exist that would look much better by other common standards – such as giving more students their top choices and improving the outcome for the worst-off student.
This matters because it highlights a gap between “efficiency” and “good outcomes.” A matching can be efficient and still produce results that many would consider inequitable.
Quantifying the limitation: how bad can it get?
To make this more concrete, the authors provide worst-case bounds. They compare stable-dominating rules to two benchmark rules that are not meant as practical proposals, but as useful standards:
Their main theoretical result shows that stable-dominating rules can perform very poorly compared to these benchmarks. In the worst case, the average student’s rank and the worst-off student’s rank can be about n/2 times worse, where n is the number of schools.
In simple terms: as school systems get larger, the gap between “Pareto-efficient improvements” and “best possible outcomes” can grow substantially.
Segregation may remain unchanged under tiered priorities
The paper’s second main contribution focuses on segregation. The authors study settings with tiered priorities, where students fall into priority groups (tiers), and every school ranks all students in tier 1 above all students in tier 2, and so on.
This kind of structure is not just theoretical. Some systems give universal priority to certain categories, such as children in state care or citizens versus non-citizens.
Under such tiered priorities, the authors prove an invariance result: the number of students from each tier at each school stays exactly the same under any stable-dominating rule.
This means that even if a reform improves assignments within a tier, it cannot change the overall demographic composition of schools across tiers. If a school is fully segregated under DA – accepting students only from one tier – it will remain fully segregated after the reform.
Why this matters for policy
The paper’s message is not that Pareto improvements are useless. Many students can benefit from such reforms, and the literature shows these improvements can matter in practice.
But the authors’ results deliver a cautionary conclusion: if policymakers want to improve equity, protect the worst-off students, or reduce segregation, efficiency adjustments alone may be insufficient.
This is especially important because efficiency-focused reforms can sound like an easy win: improving outcomes without creating losers. The paper shows that this promise comes with limits. Some of the most pressing concerns in education policy are not just about efficiency, but about distribution – who benefits, who loses, and how unequal the outcomes are.
In short, the study helps clarify what Pareto-based reforms can realistically achieve – and what they cannot.
A broader lesson for market design
Beyond school choice, the paper contributes to a wider debate in economics: whether “efficiency” is enough as a guiding policy principle.
The authors provide a rigorous analysis of a broader point often made in welfare economics: an outcome can be efficient but still socially unsatisfactory. In school choice, that dissatisfaction may appear as low-ranked assignments for many students, or persistent segregation across schools.
The paper therefore strengthens the case for combining efficiency reforms with additional policy tools that directly target equity and integration goals.
About the Authors
Josué Ortega
Senior Lecturer in Economics at Queen’s University Belfast. His research focuses on market design, matching mechanisms, and school choice.
Gabriel Ziegler
Postdoctoral Research Associate at Freie Universität Berlin and the Berlin School of Economics. His research interests include information economics and game theory.
R. Pablo Arribillaga
Researcher at the Department of Mathematics, Universidad Nacional de San Luis. His research focuses on game theory and applied mathematics.
Geng Zhao
PhD Student at the University of California, Berkeley. His research includes matching markets, mechanism design, and theoretical microeconomics.
