arXiv subjects

Bertan Turhan

Publications and source records attributed to Bertan Turhan.

10 recordsLinked to original sources

arXiv2026

Affirmative Action in India with Hierarchical Reservations

India implements the world's most complex affirmative action program through vertical and horizontal reservations. Although applicants can belong to at most one vertical category, they can qualify for multiple horizontal reservation categories simultaneously. We examine resource allocation problems in India, where horizontal reservations follow a hierarchical structure within a one-to-all horizontal matching framework. We introduce the hierarchical choice rule and show that it selects the most meritorious set of applicants. We thoroughly analyze the properties of the aggregate choice rule, which comprises hierarchical choice rules across all vertical categories. We show that the generalized deferred acceptance mechanism, when coupled with this aggregate choice rule, is the unique stable and strategy-proof mechanism that eliminates justified envy.

econ.TH↗

arXiv2023

Inconsistency of Score-Elevated Reserve Policy for Indian Affirmative Action

India has enacted an intricate affirmative action program through a reservation system since the 1950s. Notably, in 2008, a historic judgment by the Supreme Court of India (SCI) in the case of Ashoka Kumar Thakur vs. Union of India mandated a 27 percent reservation to the Other Backward Classes (OBC). The SCI's ruling suggested implementing the OBC reservation as a soft reserve without defining a procedural framework. The SCI recommended a maximum of 10 points difference between the cutoff scores of the open-category and OBC positions. We show that this directive conflicts with India's fundamental Supreme Court mandates on reservation policy. Moreover, we show that the score-elevated reserve policy proposed by S\"onmez and Yenmez (2022) is inconsistent with this directive.

econ.TH↗

arXiv2023

Matching with Generalized Sequential Choice Rules

This paper studies a many-to-one matching between individuals and institutions where institutions comprise multiple divisions and face cross-divisional constraints. We introduce a parametrized family of choice rules, which we call generalized sequential (GSq), that encompasses many different choice rules encountered in practice and in market design literature. We show that the cumulative offer mechanism (COM) is the unique stable and strategy-proof mechanism in a matching problem where all institutions have a GSq choice rule. We present two real-world applications in which choice rules in the GSq family emerge naturally: affirmative action in India's public higher educational institutions and government jobs, and high school admissions in China.

econ.TH↗

arXiv2023

The Over-and-Above Implementation of Reserve Policy in India

The over-and-above choice rule is the prominent selection procedure to implement affirmative action. In India, it is legally mandated to allocate public school seats and government job positions. This paper presents an axiomatic characterization of the over-and-above choice rule by rigorously stating policy goals as formal axioms. Moreover, we characterize the deferred acceptance mechanism coupled with the over-and-above choice rules for centralized marketplaces.

econ.TH↗

arXiv2022

How to De-Reserves Reserves: Admissions to Technical Colleges in India

We study joint implementation of reservation and de-reservation policies in India that has been enforcing a comprehensive affirmative action since 1950. The landmark judgement of the Supreme Court of India in 2008 mandated that whenever OBC category (with 27 percent reservation) has unfilled positions they must be reverted to general category applicants in admissions to public schools without specifying how to implement it. We disclose the drawbacks of recently reformed allocation procedure in admissions to technical colleges and offer a solution through de-reservation via choice rules. We propose a novel priority design, Backward Transfers (BT) choice rule, for institutions and the deferred acceptance mechanism under these rules (DA-BT) for centralized clearinghouses. We show that DA-BT corrects the shortcomings of existing mechanisms. By formulating the legal requirements and policy goals in India as formal axioms, we show that the DA-BT mechanism is the unique mechanism for concurrent implementation of reservation and de-reservation policies.

econ.TH↗

arXiv2021

Designing Direct Matching Mechanism for India with Comprehensive Affirmative Action

Since 1950, India has been implementing the most comprehensive affirmative action program in the world. Vertical reservations are provided to members of historically discriminated Scheduled Castes (SC), Scheduled Tribes (ST), and Other Backward Classes (OBC). Horizontal reservations are provided for other disadvantaged groups, such as women and disabled people, within each vertical category. There is no well-defined procedure to implement horizontal reservations jointly with vertical reservation and OBC de-reservations. Sequential processes currently in use for OBC de-reservations and meritorious reserve candidates lead to severe shortcomings. Most importantly, indirect mechanisms currently used in practice do not allow reserve category applicants to fully express their preferences. To overcome these and other related issues, we design several different choice rules for institutions that take meritocracy, vertical and horizontal reservations, and OBC de-reservations into account. We propose a centralized mechanism to satisfactorily clear matching markets in India.

econ.TH↗

arXiv2020

Assignment Maximization

We evaluate the goal of maximizing the number of individuals matched to acceptable outcomes. We show that it implies incentive, fairness, and implementation impossibilities. Despite that, we present two classes of mechanisms that maximize assignments. The first are Pareto efficient, and undominated -- in terms of number of assignments -- in equilibrium. The second are fair for unassigned students and assign weakly more students than stable mechanisms in equilibrium.

econ.TH↗

arXiv2020

Slot-specific Priorities with Capacity Transfers

In many real-world matching applications, there are restrictions for institutions either on priorities of their slots or on the transferability of unfilled slots over others (or both). Motivated by the need in such real-life matching problems, this paper formulates a family of practical choice rules, slot-specific priorities with capacity transfers (SSPwCT). These practical rules invoke both slot-specific priorities structure and transferability of vacant slots. We show that the cumulative offer mechanism (COM) is stable, strategy-proof and respects improvements with regards to SSPwCT choice rules. Transferring the capacity of one more unfilled slot, while all else is constant, leads to strategy-proof Pareto improvement of the COM. Following Kominer's (2020) formulation, we also provide comparative static results for expansion of branch capacity and addition of new contracts in the SSPwCT framework. Our results have implications for resource allocation problems with diversity considerations.

econ.TH↗

arXiv2020

Matching with Generalized Lexicographic Choice Rules

Motivated by the need for real-world matching problems, this paper formulates a large class of practical choice rules, Generalized Lexicographic Choice Rules (GLCR), for institutions that consist of multiple divisions. Institutions fill their divisions sequentially, and each division is endowed with a sub-choice rule that satisfies classical substitutability and size monotonicity in conjunction with a new property that we introduce, quota monotonicity. We allow rich interactions between divisions in the form of capacity transfers. The overall choice rule of an institution is defined as the union of the sub-choices of its divisions. The cumulative offer mechanism (COM) with respect to GLCR is the unique stable and strategy-proof mechanism. We define a choice-based improvement notion and show that the COM respects improvements. We employ the theory developed in this paper in our companion paper, Aygün and Turhan (2020), to design satisfactory matching mechanisms for India with comprehensive affirmative action constraints.

econ.TH↗

arXiv2020

Dynamic Reserves in Matching Markets

We study a school choice problem under affirmative action policies where authorities reserve a certain fraction of the slots at each school for specific student groups, and where students have preferences not only over the schools they are matched to but also the type of slots they receive. Such reservation policies might cause waste in instances of low demand from some student groups. To propose a solution to this issue, we construct a family of choice functions, dynamic reserves choice functions, for schools that respect within-group fairness and allow the transfer of otherwise vacant slots from low-demand groups to high-demand groups. We propose the cumulative offer mechanism (COM) as an allocation rule where each school uses a dynamic reserves choice function and show that it is stable with respect to schools' choice functions, is strategy-proof, and respects improvements. Furthermore, we show that transferring more of the otherwise vacant slots leads to strategy-proof Pareto improvement under the COM.

econ.TH↗