arXiv subjects

M. Bumin Yenmez

Publications and source records attributed to M. Bumin Yenmez.

17 recordsLinked to original sources

arXiv2026

Pair rationality and top trading cycles on single-peaked and single-dipped domains

In a recent study, Ekici and Yenmez (2026) characterize top trading cycles (TTC) on the unrestricted domain by strategy-proofness, individual rationality, and pair rationality, uncovering a correspondence between the axiomatic foundations of TTC and deferred acceptance, matching theory's two canonical rules. We show that their characterization fails on the single-peaked domain, but it holds on the single-dipped domain even without strategy-proofness. They also show that pair rationality can be replaced in their characterization by two weaker conditions concerning agents' first and second choices. In contrast, this replacement fails on the single-dipped domain, even when strategy-proofness is imposed.

econ.TH↗

arXiv2026

Minimally rational reallocation of objects

Matching theory has largely evolved around two canonical rules: deferred acceptance (DA) in the marriage problem and top trading cycles (TTC) in the object reallocation problem. Although the two rules operate through different procedures, we show that they rest on a common axiomatic foundation. In the marriage problem, stability decomposes into individual rationality and pair rationality, and a classic result characterizes DA by these two axioms together with strategy-proofness for the proposing side. We show that individual rationality, pair rationality, and strategy-proofness likewise characterize TTC. More strongly, three weak rationality axioms concerning individuals and pairs, together with strategy-proofness, uniquely determine TTC. Even weak rationality requirements therefore rule out strategy-proof implementation when there is a cap on the size of exchange cycles.

econ.TH↗

arXiv2026

Priority Blockers: Welfare and Incentives in Matching under General Constraints

Institutions often face constraints richer than a single capacity. Protecting the priority of a student who cannot be accommodated may then block a lower-priority student who fits. We introduce COP-and-Choose, a cumulative offer process followed by a choice step, and show that its greedy version, which skips such blockers, leaves no student worse off than any fair matching or Knapsack Deferred Acceptance (KDA). Greedy is the unique consistent rule preserving this guarantee. With substitutability and size monotonicity at every school, greedy is strategy-proof and Pareto-undominated among strategy-proof mechanisms. If either fails at a school, one additional capacity-one school yields a market where, under every proposal order, greedy is manipulable and no strategy-proof mechanism weakly Pareto dominates it. In a three-resource refugee-resettlement calibration with simulated preferences, 19--33 percent of families gain relative to KDA and none lose, while 21--83 percent strongly envy another family.

econ.TH↗

arXiv2026

Diversity as Majorization

How should institutions compare group diversity, and which group should they select when they value diversity and merit? We take a target-based approach that evaluates the entire group composition without treating any type as intrinsically diversity-enhancing. Because different diversity indices may rank groups differently, we instead adapt majorization to construct an ordinal diversity preorder. We show that its maximally diverse selections are exactly those maximizing every index in a broad class. This characterization yields a reserve-and-quota policy that selects a maximally diverse group and, among such groups, the highest-merit agents. Any alternative is less diverse, less meritorious, or both.

econ.TH↗

arXiv2026

Distributional Preferences for Market Design

Institutions selecting students, employees, or members value both about who is selected and the resulting group's composition. We study ``distributional'' preferences over group composition, and identify an upper-bound property and two exchange properties. With the upper-bound property, the exchange properties are necessary and sufficient for two results: the greedy rule is the unique choice rule that is non-wasteful, distributionally maximal, and free of justified envy; it is also path independent. In matching markets, deferred acceptance is the unique mechanism satisfying the three axioms, individual rationality, and strategy-proofness. Our framework accommodates intersectional identities and subsumes models based on reserves and matroids.

econ.TH↗

arXiv2026

Acceptant Expansions of Path-Independent Choice Rules

A choice rule is $q$-acceptant if it chooses $\min\{q,|X|\}$ alternatives from each set $X$. We show that a path-independent rule of maximum cardinality at most $q$ need not have a $q$-acceptant path-independent expansion, refuting Chambers and Yenmez (2017, Theorem 4). We construct a one-school matching market whose unique stable matching leaves a seat vacant that no path-independent expansion of the school's rule fills. Every path-independent rule satisfying the law of aggregate demand has such an expansion. We characterize the choice rules admitting an acceptant expansion by monotone selections of rejected alternatives.

econ.TH↗

arXiv2026

Rawlsian equity: a new notion of fairness for the assignment problem

We introduce Rawlsian equity, a notion of fairness for allocating indivisible objects among agents without object-specific entitlements. Rawlsian equity requires that an object not be assigned to an agent who ranks it more highly than another agent unless the latter receives a more preferred object. We show that the set of Rawlsian equitable allocations coincides with the set of stable allocations in an auxiliary market where object priorities depend on agents' preference reports. The agent-proposing deferred acceptance algorithm computes the agent-optimal element of this set, but no Rawlsian equitable rule is strategy-proof in general.

econ.TH↗

arXiv2026

Endogenous Inequality Aversion: Decision criteria for triage and other ethical tradeoffs

Medical ``Crisis Standards of Care'' call for a utilitarian allocation of scarce resources in public emergencies, whereas standards of care under normal conditions place relatively greater priority on the worst-off. Inspired by such triage rules, we study social welfare criteria whose distributive trade-offs depend on society's well-being, as captured by aggregate welfare. Because the welfare level determines the applicable aggregation criterion, while that criterion in turn determines welfare, the resulting criteria are self-referential. We provide an axiomatic foundation for a family of welfare criteria that become more utilitarian as aggregate welfare falls and more Rawlsian as it rises, thereby formalizing triage guidelines. We also characterize the converse case, in which priority to the worst-off increases as aggregate welfare falls.

econ.TH↗

arXiv2025

Diversity in Choice as Majorization

We propose a framework that uses majorization to model diversity and representativeness in school admissions. We generalize the standard notion of majorization to accommodate arbitrary distributional targets, such as a student body that reflects the population served by the school. Building on this framework, we introduce and axiomatically characterize the $r$-targeting Schur choice rule, which balances diversity and priority in admissions. We show that this rule is optimal: any alternative rule must either leave seats unfilled, reduce diversity, or admit lower-priority students. The rule satisfies path independence (and substitutability), which guarantees desirable outcomes in matching markets. Our work contributes to the ongoing discourse on market design by providing a new and flexible framework for improving diversity and representation.

econ.TH↗

arXiv2025

Market Design with Distributional Objectives

We provide optimal solutions to an institution that has distributional objectives when choosing from a set of applications based on merit (or priority). For example, in college admissions, administrators may want to admit a diverse class in addition to choosing students with the highest qualifications. We provide a family of choice rules that maximize merit subject to attaining a level of the distributional objective. We study the desirable properties of choice rules in this family and use them to find all subsets of applications on the Pareto frontier of the distributional objective and merit. In addition, we provide two novel characterizations of matroids.

econ.TH↗

arXiv2024

Rationalizing Path-Independent Choice Rules

Path independence is arguably one of the most important choice rule properties in economic theory. We show that a choice rule is path independent if and only if it is rationalizable by a utility function satisfying ordinal concavity, a concept closely related to concavity notions in discrete mathematics. We also provide a rationalization result for choice rules that satisfy path independence and the law of aggregate demand.

econ.TH↗

arXiv2024

Constitutional Implementation of Affirmative Action Policies in India

India is home to a comprehensive affirmative action program that reserves a fraction of positions at governmental institutions for various disadvantaged groups. While there is a Supreme Court-endorsed mechanism to implement these reservation policies when all positions are identical, courts have refrained from endorsing explicit mechanisms when positions are heterogeneous. This lacunae has resulted in widespread adoption of unconstitutional mechanisms, countless lawsuits, and inconsistent court rulings. Formulating mandates in the landmark Supreme Court judgment Saurav Yadav (2020) as technical axioms, we show that the 2SMH-DA mechanism is uniquely suited to overcome these challenges.

econ.TH↗

arXiv2023

Fair Allocation of Vaccines, Ventilators and Antiviral Treatments: Leaving No Ethical Value Behind in Health Care Rationing

A priority system has traditionally been the protocol of choice for the allocation of scarce life-saving resources during public health emergencies. Covid-19 revealed the limitations of this allocation rule. Many argue that priority systems abandon ethical values such as equity by discriminating against disadvantaged communities. We show that a restrictive feature of the traditional priority system largely drives these limitations. Following minimalist market design, an institution design paradigm that integrates research and policy efforts, we formulate pandemic allocation of scarce life-saving resources as a new application of market design. Interfering only with the restrictive feature of the priority system to address its shortcomings, we formulate a reserve system as an alternative allocation rule. Our theoretical analysis develops a general theory of reserve design. We relate our analysis to debates during Covid-19 and describe the impact of our paper on policy and practice.

econ.TH↗

arXiv2023

Efficient Market Design with Distributional Objectives

Given an initial matching and a policy objective on the distribution of agent types to institutions, we study the existence of a mechanism that weakly improves the distributional objective and satisfies constrained efficiency, individual rationality, and strategy-proofness. We show that such a mechanism need not exist in general. We introduce a new notion of discrete concavity, which we call pseudo M$^{\natural}$-concavity, and construct a mechanism with the desirable properties when the distributional objective satisfies this notion. We provide several practically relevant distributional objectives that are pseudo M$^{\natural}$-concave.

econ.TH↗

arXiv2022

Market Design with Deferred Acceptance: A Recipe for Policymaking

We introduce a method to derive from a characterization of institutional choice rules (or priority rules), a characterization of the Gale-Shapley deferred-acceptance (DA) matching rule based on these choice rules. We apply our method to school choice in Chile, where we design choice rules for schools that are uniquely compatible with the School Inclusion Law and derive a set of matching properties, compatible with the law, that characterizes the DA rule based on the designed choice rules. Our method provides a recipe for establishing such results and can help policymakers decide on which allocation rule to use in practice.

econ.TH↗

arXiv2021

Can Economic Theory Be Informative for the Judiciary? Affirmative Action in India via Vertical and Horizontal Reservations

Sanctioned by its constitution, India is home to the world's most comprehensive affirmative action program, where historically discriminated groups are protected with vertical reservations implemented as "set asides," and other disadvantaged groups are protected with horizontal reservations implemented as "minimum guarantees." A mechanism mandated by the Supreme Court in 1995 suffers from important anomalies, triggering countless litigations in India. Foretelling a recent reform correcting the flawed mechanism, we propose the 2SMG mechanism that resolves all anomalies, and characterize it with desiderata reflecting laws of India. Subsequently rediscovered with a high court judgment and enforced in Gujarat, 2SMG is also endorsed by Saurav Yadav v. State of UP (2020), in a Supreme Court ruling that rescinded the flawed mechanism. While not explicitly enforced, 2SMG is indirectly enforced for an important subclass of applications in India, because no other mechanism satisfies the new mandates of the Supreme Court.

econ.TH↗

arXiv2019

Interdistrict School Choice: A Theory of Student Assignment

Interdistrict school choice programs-where a student can be assigned to a school outside of her district-are widespread in the US, yet the market-design literature has not considered such programs. We introduce a model of interdistrict school choice and present two mechanisms that produce stable or efficient assignments. We consider three categories of policy goals on assignments and identify when the mechanisms can achieve them. By introducing a novel framework of interdistrict school choice, we provide a new avenue of research in market design.

econ.TH↗