arXiv subjects

Josue Ortega

Publications and source records attributed to Josue Ortega.

16 recordsLinked to original sources

arXiv2026

Efficiency Adjustments Break the Logarithmic Rank Barrier

We study the expected average rank achieved by the Efficiency-Adjusted Deferred Acceptance (EADA) mechanism in i.i.d.\ matching markets. While student-proposing Deferred Acceptance gives students an expected average rank of logarithmic order, we prove that EADA's expected average rank is at most $4\log\log n+O(1)$. Therefore, EADA improves the asymptotic order of students' assignments. At the cost of a weaker bound, $O((\log\log n)^2)$, we extend this conclusion to a much larger class of mechanisms. Namely, every Pareto-efficient mechanism that weakly Pareto-dominates DA breaks DA's logarithmic barrier. These are the first asymptotic guarantees for the expected average rank of EADA and of the broader class of Pareto-efficient improvements of DA. The conclusions extend to many-to-one markets with bounded quotas and random markets with correlated preferences.

cs.GT↗

arXiv2026

Asymptotic Equivalence of Immediate and Deferred Acceptance

Immediate Acceptance (IA, also known as the Boston mechanism) is commonly used to assign students to schools because it produces a Pareto-efficient matching if parents report their preferences over schools truthfully, unlike student-proposing Deferred Acceptance (DA). In this paper, we ask: does IA produce meaningfully better average ranks than DA, conditional on truth-telling? We show that, in i.i.d. one-to-one random markets, IA's expected average rank is asymptotically $\log n$, just like DA's. Therefore, IA's Pareto efficiency does not translate into a first-order improvement in expected average rank. This conclusion extends to variations of IA as well as to many-to-one markets.

econ.TH↗

arXiv2026

The Large and Likely Inefficiency of Stable Matching Mechanisms

We prove that any stable matching mechanism suffers from systematic inefficiency of striking magnitude: in large random markets, any stable allocation is Pareto-inefficient with high probability, and almost all students can simultaneously improve their placements without harming anyone else. We establish this result by showing that the envy digraph generated by the student-proposing Deferred Acceptance mechanism contains a unique giant strongly connected component, implying that nearly all students are improvable via trading cycles. Finally, we show that every maximal cycle packing covers almost all students, revealing a surprising asymptotic equivalence among all efficient mechanisms that Pareto-dominate DA.

econ.TH↗

arXiv2026

A Note on the Strategic Vulnerability of the Boston Mechanism in Random Markets

We provide the first asymptotic analysis of the Boston Mechanism under equilibrium play in random markets. We provide two results. First, while 63\% of students receive their first preference under truthful reporting-outperforming any other known mechanism in the literature-this rate converges to zero in any Nash equilibrium of the corresponding preference revelation game as the market size grows. Second, we show there exists a Nash equilibrium where the average student receives a dramatically inferior assignment: in markets with 1,000 students, the average placement shifts from the 7th choice (under truthfulness) to the 145th choice, representing a change from logarithmic to nearly linear average rank.

econ.TH↗

arXiv2025

The Trade-off Between Minimal Instability and Larger Improvements over Deferred Acceptance

The celebrated Efficiency-Adjusted Deferred Acceptance mechanism (EADA) improves the efficiency of the DA algorithm via consented priority violations. Notwithstanding its many merits, we show that EADA can improve only two students when an alternative mechanism that Pareto-dominates DA could benefit all but one student. This shortfall in the number of students improved is not exclusive of EADA but extends to all setwise minimally unstable mechanisms, i.e. those that generate a set of blocking pairs that is never a strict superset of that of another mechanism. The incompatibility between number of students improved and minimal instability disappears when blocking pairs are compared cardinally rather than by set inclusion. In some problems, EADA can be doubly dominated: improving fewer students while generating more blocking pairs.

econ.TH↗

arXiv2025

What Pareto-Efficiency Adjustments Cannot Fix

The Deferred Acceptance (DA) algorithm is stable and strategy-proof, but can produce outcomes that are Pareto-inefficient for students, and thus several alternative mechanisms have been proposed to correct this inefficiency. However, we show that these mechanisms cannot correct DA's rank-inefficiency and inequality, because these shortcomings can arise even in cases where DA is Pareto-efficient. We also examine students' segregation in settings with advantaged and marginalized students. We prove that the demographic composition of every school is perfectly preserved under any Pareto-efficient mechanism that dominates DA, and consequently fully segregated schools under DA maintain their extreme homogeneity.

econ.TH↗

arXiv2024

School choice with independent versus consolidated districts

This paper studies the welfare effects of school district consolidation. Using incomplete rank-ordered lists (ROLs) submitted for admission to the Hungarian secondary school system, we estimate complete ROLs assuming that parents do not use dominated strategies and that the matching outcome is stable. These estimates aid in constructing a counterfactual district-based assignment and discerning the factors driving parents' preferences over schools. We find that district consolidation leads to large welfare gains in Budapest, equivalent to students attending a school five kilometres closer to their residences. These gains offset the additional travel distances incurred in the consolidated assignment. 73\% of matched students benefit from district consolidation, while fewer than 3\% are assigned to a less preferred school. Students from smaller and less under-demanded districts benefit relatively more, as well as those with high academic ability. Using reported preferences instead of estimated ones also yields large gains from district consolidation.

econ.GN↗

arXiv2023

The cost of strategy-proofness in school choice

We compare the outcomes of the most prominent strategy-proof and stable algorithm (Deferred Acceptance, DA) and the most prominent strategy-proof and Pareto optimal algorithm (Top Trading Cycles, TTC) to the allocation generated by the rank-minimizing mechanism (RM). While one would expect that RM improves upon both DA and TTC in terms of rank efficiency, the size of the improvement is nonetheless surprising. Moreover, while it is not explicitly designed to do so, RM also significantly improves the placement of the worst-off student. Furthermore, RM generates less justified envy than TTC. We corroborate our findings using data on school admissions in Budapest.

econ.TH↗

arXiv2022

On the integration of Shapley-Scarf housing markets

We study the welfare consequences of merging Shapley--Scarf markets. Market integration can lead to large welfare losses and make the vast majority of agents worse-off, but is on average welfare-enhancing and makes all agents better off ex-ante. The number of agents harmed by integration is a minority when all markets are small or agents' preferences are highly correlated.

econ.TH↗

arXiv2020

Fairness and Efficiency in Cake-Cutting with Single-Peaked Preferences

We study the cake-cutting problem when agents have single-peaked preferences over the cake. We show that a recently proposed mechanism by Wang-Wu (2019) to obtain envy-free allocations can yield large welfare losses. Using a simplifying assumption, we characterize all Pareto optimal allocations, which have a simple structure: are peak-preserving and non-wasteful. Finally, we provide simple alternative mechanisms that Pareto dominate that of Wang-Wu, and which achieve envy-freeness or Pareto optimality.

cs.GT↗

arXiv2019

Obvious Manipulations in Cake-Cutting

In cake-cutting, strategy-proofness is a very costly requirement in terms of fairness: for n=2 it implies a dictatorial allocation, whereas for n > 2 it requires that one agent receives no cake. We show that a weaker version of this property recently suggested by Troyan and Morril, called non-obvious manipulability, is compatible with the strong fairness property of proportionality, which guarantees that each agent receives 1/n of the cake. Both properties are satisfied by the leftmost leaves mechanism, an adaptation of the Dubins - Spanier moving knife procedure. Most other classical proportional mechanisms in literature are obviously manipulable, including the original moving knife mechanism. Non-obvious manipulability explains why leftmost leaves is manipulated less often in practice than other proportional mechanisms.

cs.GT↗

arXiv2019

Integration in Social Networks

We propose the notion of $k$-integration as a measure of equality of opportunity in social networks. A social network is $k$-integrated if there is a path of length at most $k$ between any two individuals, thus guaranteeing that everybody has the same network opportunities to find a job, a romantic partner, or valuable information. We compute the minimum number of bridges (i.e. edges between nodes belonging to different components) or central nodes (those which are endpoints to a bridge) required to ensure $k$-integration. The answer depends only linearly on the size of each component for $k=2$, and does not depend on the size of each component for $k \geq 3$. Our findings provide a simple and intuitive way to compare the equality of opportunity of real-life social networks.

cs.SI↗

arXiv2018

The Strength of Absent Ties: Social Integration via Online Dating

We used to marry people to whom we were somehow connected. Since we were more connected to people similar to us, we were also likely to marry someone from our own race. However, online dating has changed this pattern; people who meet online tend to be complete strangers. We investigate the effects of those previously absent ties on the diversity of modern societies. We find that social integration occurs rapidly when a society benefits from new connections. Our analysis of state-level data on interracial marriage and broadband adoption (proxy for online dating) suggests that this integration process is significant and ongoing.

physics.soc-ph↗

arXiv2018

Social Integration in Two-Sided Matching Markets

When several two-sided matching markets merge into one, it is inevitable that some agents will become worse off if the matching mechanism used is stable. I formalize this observation by defining the property of integration monotonicity, which requires that every agent becomes better off after any number of matching markets merge. Integration monotonicity is also incompatible with the weaker efficiency property of Pareto optimality. Nevertheless, I obtain two possibility results. First, stable matching mechanisms never hurt more than one-half of the society after the integration of several matching markets occurs. Second, in random matching markets there are positive expected gains from integration for both sides of the market, which I quantify.

econ.GN↗

arXiv2018

Multi-unit Assignment under Dichotomous Preferences

I study the problem of allocating objects among agents without using money. Agents can receive several objects and have dichotomous preferences, meaning that they either consider objects to be acceptable or not. In this setup, the egalitarian solution is more appealing than the competitive equilibrium with equal incomes because it is Lorenz dominant, unique in utilities, and group strategy-proof. Moreover, it can be adapted to satisfy a new fairness axiom that arises naturally in this context. Both solutions are disjoint.

econ.GN↗

arXiv2016

Playing Tennis without Envy

A group of friends organize their tennis games by submitting each their availability over the weekdays. They want to obtain an assignment such that: each game must be a double tennis match, i.e. requires four people, and nobody plays in a day he is unavailable. Can we construct assignments that will always produce efficient, fair, and envy-free outcomes? The answer is no, and extends to any sport that requires any group size.

math.HO↗