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Yasunori Okumura

Publications and source records attributed to Yasunori Okumura.

12 recordsLinked to original sources
arXiv2026

Stable Improvement Cycle Mechanism Versus Efficiency-adjusted Deferred Acceptance Mechanism beyond Weak Priority Orders

This paper compares the stable improvement cycles (SIC) mechanism of Erdil and Ergin (2008) with the efficiency-adjusted deferred acceptance (EADA) mechanism of Kesten (2010) in school choice problems with incomplete priorities. When school priorities are strict partial orders, we show that the EADA mechanism produces a constrained efficient matching. Combined with earlier results for the SIC mechanism, this establishes the outcome equivalence of the two mechanisms: the sets of matchings attainable under them coincide. We then move beyond transitivity and consider acyclic priority relations. On this broader domain, neither mechanism is guaranteed to produce a constrained efficient matching, but their failures take opposite forms. The SIC mechanism may under-improve: its outcome is always stable but may be Pareto dominated by another stable matching. By contrast, the EADA mechanism may over-improve: its outcome is never Pareto dominated by any stable matching but may itself be unstable.

econ.TH↗
arXiv2026

School Choice Problems with Priority Adjustments

This paper studies school choice when each school has an original priority order and an adjusted priority order reflecting policies such as affirmative action. We introduce a weak notion of stability that permits justified envy under one priority order only when the opposite priority relation is supported by the other. We characterize weakly stable matchings as stable matchings under the intersection of the two priority profiles. Using the efficiency-adjusted deferred acceptance algorithm, we obtain a weakly stable matching that cannot be Pareto improved upon, within the set of weakly stable matchings, for any group containing all improved students by the adjustment. We also show that any Pareto improvement over this outcome necessarily creates justified envy under both priority profiles. Finally, our mechanism is responsive to stronger priority adjustments: the outcome under a stronger affirmative action policy is not Pareto dominated by that under a weaker policy for any group containing all students improved by the stronger adjustment.

econ.TH↗
arXiv2026

Equal Treatment of Equals and Efficiency in Probabilistic Assignments

This paper studies general multi-unit probabilistic assignment problems involving indivisible objects, with a particular focus on achieving the fairness notion of equal treatment of equals (ETE) and satisfying various efficiency criteria. We extend the definition of ETE so that it accommodates a wide range of constraints and applications. We introduce the ETE reassignment procedure, which transforms any assignment into one that satisfies ETE, and examine whether the efficiency properties satisfied by the original assignment -- namely, ex-post efficiency, ordinal efficiency, and rank-minimizing efficiency -- are preserved under the ETE reassignment. We show that, while the ETE reassignment of an ex-post efficient assignment remains ex-post efficient, it may fail to preserve ordinal efficiency in general settings. However, since the ETE reassignment of a rank-minimizing assignment preserves rank-minimizing efficiency, there must exist an assignment satisfying both ETE and ordinal efficiency. Furthermore, we propose a computationally efficient method for constructing assignments that satisfy both ETE and ordinal efficiency under general upper bound constraints by combining the serial dictatorship rule with appropriately specified priority lists and the ETE reassignment procedure.

econ.TH↗
arXiv2026

A Simple Method for School Choice Lotteries

This note proposes a simple polynomial-time method for constructing an ex ante stable school-choice lottery satisfying equal treatment of equals (ETE). We show that the ETE reassignment of any constrained efficient stable matching is ex ante stable, satisfies ETE, and is not ordinally dominated by any other ex ante stable lottery. We further show that there exists a constrained efficient stable matching whose ETE reassignment is not ordinally dominated by any ex post stable lottery.

cs.GT↗
arXiv2025

Strategic Analysis of Fair Rank-Minimizing Mechanisms with Agent Refusal Option

This paper investigates the strategic implications of the uniform rank-minimizing mechanism (URM), an assignment rule that selects uniformly from the set of deterministic assignments minimizing the sum of agents' reported ranks. We focus on settings in which agents may refuse their assignment and instead receive an outside option. Without the refusal option, we show that truth-telling is not strictly dominated under any fair rank-minimizing mechanism; that is, one satisfying equal treatment of equals. However, introducing the refusal option significantly changes strategic incentives: specific manipulations, called outside option demotion strategies, dominate truth-telling under the URM. Moreover, such manipulations can lead to inefficient outcomes, as desirable objects may be refused by misreporting agents and consequently remain unassigned. To address this issue, we propose a modification of the URM that restores undominated truth-telling, although it introduces incentives to underreport acceptable objects. Our results highlight a fundamental trade-off in the design of fair rank-minimizing mechanisms when agents can refuse their assignments.

econ.TH↗
arXiv2025

Respecting Linear Orders for Supermajority Rules

We consider linear orders of finite alternatives constructed by aggregating individual preferences. Specifically, we focus on linear orders that respect modified collective preference relations derived from supermajority rules, where modifications are introduced through two procedures if cycles occur. One procedure utilizes the transitive closure, while the other employs the Suzumura-consistent closure, ensuring the elimination of cycles through consistency adjustments. We derive two sets of linear orders that respect these modified collective preference relations derived from all supermajority rules, and show that these sets are generally nonempty. We show that these sets of linear orders closely relate to those obtained by the ranked pairs method and the Schulze method, thereby providing new insights into these influential methods. Finally, we show that any linear order belonging to either set satisfies two important properties: the extended Condorcet criterion and the Pareto principle.

econ.TH↗
arXiv2025

A Stable and Strategy-Proof Controlled School Choice Mechanism with Integrated and Flexible Rules

We examine a controlled school choice model where students are categorized into different types, and the distribution of these types within a school influences its priority structure. This study provides a general framework that integrates existing controlled school choice models, including those utilizing reserve rules, quota rules, and bonus-point rules. Specifically, we introduce an adjusted scoring rule that unifies these rules. By achieving a matching that satisfies the stability defined in this framework, matching authorities can effectively manage the trade-offs inherent in controlled school choice markets. Moreover, the priority order for a school is represented as a weak order with each given assignment, meaning that ties are allowed. Our mechanism ensures a stable matching and satisfies strategy-proofness. In particular, when priority orders are restricted to linear orders with each given assignment, our mechanism guarantees student-optimal stability.

econ.TH↗
arXiv2024

School Choice with Multiple Priorities

This study considers a model where schools may have multiple priority orders on students, which may be inconsistent with each other. For example, in school choice systems, since the sibling priority and the walk zone priority coexist, the priority orders based on them would be conflicting. We introduce a weaker fairness notion called M-fairness to examine such markets. Further, we focus on a more specific situation where all schools have only two priority orders, and for a certain group of students, a priority order of each school is an improvement of the other priority order of the school. An illustrative example is the school choice matching market with a priority-based affirmative action policy. We introduce a mechanism that utilizes the efficiency adjusted deferred acceptance algorithm and show that the mechanism satisfies properties called responsiveness to improvements and improved-group optimally M-stability, which is stronger than student optimally M-stability.

econ.TH↗
arXiv2024

Aggregating Incomplete Rankings

This study considers the method to derive a ranking of alternatives by aggregating the rankings submitted by several individuals who may not evaluate all of them. The collection of subsets of alternatives that individuals (can) evaluate is referred to as an evaluability profile. For a given evaluability profile, we define an aggregating ranking function whose inputs are the rankings of individuals on the alternatives they evaluate. We investigate the properties of aggregating ranking functions, which are modifications of those introduced in previous studies. Whether an aggregating ranking function satisfying a combination of properties exists depends on the evaluability profile. Thus, we identify the necessary and sufficient conditions on evaluability profiles to ensure the existence of the functions satisfying four different combinations of properties. Furthermore, to examine how frequently possible or impossible evaluability profiles occur, we derive the proportion of each type in specific cases.

econ.TH↗
arXiv2024

Social Welfare Functions with Voters Qualifications: Impossibility Results

We consider the social welfare function a la Arrow, where some voters are not qualified to evaluate some alternatives. Thus, the inputs of the social welfare function are the preferences of voters on the alternatives that they are qualified to evaluate only. Our model is a generalization of the peer rating model, where each voter evaluates the other voters (except for himself/herself). We demonstrate the following three impossibility results. First, if a transitive valued social welfare function satisfies independence of irrelevant alternatives and the Pareto principle, then a dictator who is qualified to evaluate all alternatives exists. Second, a transitive valued function satisfying the Pareto principle exists if and only if at least one voter is qualified to evaluate all alternatives. Finally, if no voter is qualified to evaluate all alternatives, then under a transitive valued social welfare function satisfying the weak Pareto principle and independence of irrelevant alternatives, all alternatives are indifferent for any preference profile of voters.

econ.TH↗
arXiv2023

On extensions of partial priorities in school choice

We consider a school choice matching model where the priorities for schools are represented by binary relations that may not be weak order. We focus on the (total order) extensions of the binary relations. We introduce a class of algorithms to derive one of the extensions of a binary relation and characterize them by using the class. We show that if the binary relations are the partial orders, then for each stable matching for the profile of the binary relations, there is an extension for which it is also stable. Moreover, if there are multiple stable matchings for the profile of the binary relations that are ranked by Pareto dominance, there is an extension for which all of those matchings are stable. We provide several applications of these results.

econ.TH↗