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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.


Introduction
The landmark Supreme Court judgment Indra Sawhney and others v. Union of India (1992) 1 formulates a number of affirmative action provisions built into the Constitution of India. Allocation of seats in the country's legislative bodies, public employment, and publicly funded educational institutions are governed by the principles outlined in this ruling. Equity is embedded within a merit-based system under these principles through two types of affirmative action policies called vertical reservations (VR) and horizontal reservations (HR). In order to operationalize these principles in practical applications, merit is typically determined with entrance exams (or the number of votes for legislative seat allocation), and the two affirmative action policies are implemented by reserving a fraction of positions for each of a number of protected groups. Of the two policies, the VR policy is envisioned as the main and higher-level affirmative action policy, and thereby it is mandated to be implemented on an "over-and-above" basis. This means that if a member of a VR-protected class is "entitled" to receive an open (or unreserved) position based on merit, then she must be awarded an open position and not use up a reserved position. Therefore, the protected positions are exclusively awarded to eligible individuals who do not merit an open position under the VR policy. This primary reservation policy has largely been intended for historically oppressed classes, most notably Scheduled Castes (SC), Scheduled Tribes (ST), and Other Backward Classes (OBC). The HR policy, on the other hand, is envisioned as a secondary and lower-level affirmative action policy, and thereby it is mandated to be implemented on a "minimum guarantee" basis. This means that any position awarded to a member of an HR-protected group counts towards HR protections. Also known as the interlocking reservations in India, the HR policy is typically implemented separately within open positions and each category of VR-protected positions.
As they are stated in Indra Sawhney (1992), the formulation of VR and HR policies becomes airtight under the following three conditions: (1) Homogeneity: All positions are identical.
(2) Stand-alone implementation: Only one of the reservation policies is implemented.
(3) Non-overlapping protected groups: No individual belongs to multiple protected groups. 2 However, this landmark judgment, which serves as the primary reference for India's reservation system, has not provided detailed guidance when any combination of the three conditions fail, a scenario that holds for a vast majority of field applications in the country.
For the last three decades this lack of precision not only resulted in adoption of numerous flawed allocation mechanisms in India, but also in countless litigations and inconsistent rulings at all three levels of the country's judicial system.
In an effort to eliminate the above-described imprecision for field applications where positions are identical but the other two restrictive conditions are dropped (i.e., when the two policies are implemented together and protected groups potentially overlap), a procedure was formulated and enforced countrywide in a subsequent judgement Anil Kumar Gupta, Etc vs State Of Uttar Pradesh & Ors (1995) of the Supreme Court. 3 However, a key flaw in this procedure has further aggravated the crisis for the next twenty five years. We documented the crisis due to the flawed Supreme Court procedure (henceforth the SCI-AKG choice rule) in Sönmez and Yenmez (2021), and formulated a remedy through a mechanism we refer to as the two-step meritorious horizontal (2SMH) choice rule. Parallel to our analysis and policy recommendations in Sönmez and Yenmez (2021), the flawed SCI-AKG choice rule is recently rescinded and the 2SMH choice rule is endorsed 4 by a three-judge full bench 5 of the Supreme Court in Saurav Yadav vs The State Of Uttar Pradesh (2020). 6 While Saurav Yadav (2020) has finally resolved the legal inconsistencies and provided Indian institutions with a well-behaved mechanism when all positions are identical, to the best of our knowledge no mechanism has ever been endorsed or mandated to this date by any court in the country when the positions are heterogenous. 7 This lacuna has forced local agencies to design their own mechanisms, 8 which have subsequently been challenged in court and resulted in numerous inconsistent decisions at all three tiers of the Indian Judicial System. 9 In this paper, we aim to fill this gap by formulating a mechanism that satisfies the core principles outlined in Indra Sawhney (1992) for the most general version of the problem 3 The ruling is available at https://indiankanoon.org/doc/1055016/ (retrieved on 12/25/2021). 4 Strictly speaking the endorsement in Saurav Yadav (2020) assumes away any possible overlap in HRprotected groups. The 2SMH choice rule takes a simpler form referred to as the two-step minimum guarantee (2SMG) choice rule in this case. 5 Typically, the cases filed at the Supreme Court of India is decided by two judges through what is referred to as a division bench. For example, Anil Kumar Gupta (1992) was decided by a division bench. Deviating from this norm, larger benches may be formed in some important and potentially controversial cases. A bench consisting of three or four judges is known as a full branch and a bench consisting of five or more judges is known as a constitution bench. The landmark case Indra Sawhney (1992) was decided by a nine-judge constitution bench of the Supreme Court. 6 The ruling is available at https://indiankanoon.org/doc/27820739/ (retrieved on 12/25/2021). 7 This more general version of the problem is important in India, because, not only it covers allocation of some of the most prestigious public jobs (e.g., the Indian Administrative Service positions), but also the assignment of public college seats. 8 To the best of our knowledge, no institution in India has been able design a mechanism that abides by the principles outlined in Indra Sawhney (1992) when the positions are heterogenous. 9 See Section 5 for some of the main decisions with important flaws.
where all three restrictive conditions are dropped, and prove that it is the unique "plausible" mechanism that is in line with the recent and more precise mandates of the Supreme Court in Saurav Yadav (2020). School choice mechanisms using the celebrated individual-proposing deferred acceptance (DA) algorithm by Gale and Shapley (1962) as their core engines have been adopted by numerous jurisdictions worldwide in the last two decades following the formulation of this approach in Abdulkadiroglu and Sönmez (2003). Under this approach, schools are endowed with exogenously specified choice rules that typically capture various objectives of the central planner. Following the same tradition, our proposed mechanism 2SMH-DA is based on extending the 2SMH choice rule to the general version of problem with heterogenous positions across multiple institutions (or different departments of a single institution) through a joint implementation of the DA algorithm with the 2SMH choice rule for each institution. While our proposal is admittedly mainstream, its significance is in the constitutional basis we provide to 2SMH-DA by relating it to desiderata formulated in the Supreme Court's milestone ruling Saurav Yadav (2020). As such, we argue that our paper not only provides a potential lead for the Supreme Court and the high courts in India with a precise instrument that can be used to remove the inconsistencies in the legal system which are partially documented in Section 5, but also provides the institutions in India with a mechanism to implement their reservation policies without any risk of generating controversial outcomes vulnerable for litigation.
Key for our advocacy for 2SMH-DA, Saurav Yadav (2020) brings clarity to two principles on joint implementation of VR and HR policies, elaborated in Section 2.5. While the judgment itself concerns a litigation for allocation of identical positions, the legal language that is used to describe these principles is suggestive that they are more broadly intended for the general version of the problem with heterogenous positions. 10 Postulating that the principles clarified in Saurav Yadav (2020) also reflect the Supreme Court's position more broadly for allocation of heterogenous positions, we argue that 2SMH-DA is the only "plausible" mechanism for the country. That is because, not only 2SMH-DA Pareto dominates any other mechanism that complies with the Saurav Yadav (2020) principles (Theorem 1), but it is also the only strategy-proof mechanism that complies with these principles (Theorem 2). Therefore, either one of the two fundamental principles in economic theory directly implies the 2SMH-DA mechanism when combined with Saurav Yadav (2020) formulation of the principles in Indra Sawhney (1992). Hence we argue that 2SMH-DA is the only natural mechanism to address numerous legal challenges faced by public institutions in India due to their flawed allocation mechanisms. 11

Root Cause of the Failures: A System Based on Migrations and Adjustments.
As a secondary contribution of our paper, we identify the root cause of the inconsistencies between major court rulings on implementation of reservation policies in Section 5. As we have already emphasized, the VR policy was developed as the primary affirmative action policy to correct years of discrimination and to give a boost to groups historically discriminated against on the basis of caste in India. Since no individual can belong to more than a single caste (i.e., the protected groups cannot overlap), stand-alone implementation of the VR policy is straightforward with the over-and-above choice rule for the basic version of the problem with identical positions: First open positions are allocated based on merit, and then VR-protected positions of each reserved category are allocated to remaining members of the category based on inter se merit (i.e., merit within category members). Under this benchmark procedure, positions at each category is processed one-at-a-time, and starting with the open category.
In India, the legal language does not differentiate between categories for individuals and categories for positions. While individuals who do not belong to any VR-protected category are mainly referred to as general-category candidates, they are often referred to as open-category candidates as well. We find this terminology to be highly misleading and believe that it likely contributes to the confusion in India, because, unlike the positions in VR-protected categories which are exclusively set aside for the members of these categories, open-category positions are not exclusively set aside for the general-category candidates. Likely as a technical tool to avoid potential confusion in this and related issues, the concept of a migration has emerged in India. When a VR-protected individual receives an open-category position based on merit, she is considered to have migrated to the open or general category. In this way, just as positions set aside for the VR-protected categories are awarded to members of these categories, open-category positions also become awarded to members of the open category.
When the HR policy was later included in the system as a secondary reservation policy, in Anil Kumar Gupta (1995), the Supreme Court responded by introducing a second technical concept of an adjustment. The idea is based on first determining a tentative assignment of positions at each category via the traditional over-and-above choice rule, and of any institution in other countries which implements the VR and HR policies concurrently. However, either one of these policies are implemented on a stand-alone basis in several applications worldwide. For example for the version of the problem with heterogenous positions, the VR policy is implemented for allocation of seats at Chicago's elite high schools (Dur et al., 2020) and the HR policy with overlapping protected groups is implemented in all cities of Chile for allocation of K-12 public school seats (Correa et al., 2019). For the version of problem with identical positions and overlapping protected groups, the Jordanian House of Representatives use a reservation system with 15 of the 130 seats reserved for women and 12 reserved for minorities (see https://data.ipu.org/content/jordan?chamber_id=13434, retrieved on 12/31/2021) and the National Assembly of Pakistan use a reservation system with 60 of the 342 seats reserved for women and 10 reserved for minorities (see https://na.gov.pk/en/content.php?id=2, retrieved on 12/31/2021). subsequently making any necessary adjustments within each category to accommodate the minimum guarantees provided with the HR policy. However, until recently the adjustments for the open category positions were denied for the VR-protected individuals, thus resulting in the crisis documented in Sönmez and Yenmez (2021). This failure is recently corrected in Saurav Yadav (2020), where the Supreme Court justices have clarified that VRprotected individuals are entitled for adjustments for open-category positions (just as they are eligible for them in the absence of HR protections). 12 The tradition of relying on the concepts of migration and adjustment also persisted for the more general version of the problem with heterogenous positions. In a typical mechanism in the field, open positions across all institutions are tentatively allocated in a first phase through a serial dictatorship which assigns the highest merit individual her top choice, the second highest merit individual her top choice among the remaining open positions, and so on. Next, the VR-protected positions are tentatively allocated to eligible individuals in a similar way in a second phase. Since a VR-protected individual can receive two distinct tentative assignments in each of the first two phases, she migrates to the institutioncategory pair associated with her more preferred position. Adjustments for HR protections may be made at any stage. Subsequently, vacated positions have to be reallocated in a way that still respects merit for open positions and inter se merit for VR-protected positions. Key for our purposes, this equity objective is no longer feasible solely relying on the concepts of migration and adjustment, unless the underlying process indirectly captures them through an iterative procedure such as the DA algorithm. 13 For the simpler version of the problem with identical positions, relying on the concepts of migration and adjustment is not necessary to implement the 2SMH choice rule. That being the case, this choice rule does have an alternative (albeit more complicated) formulation which utilizes these concepts, and, therefore, it is feasible to use them in this framework. 14 However, for the general version of the problem with heterogeneous positions, relying on these concepts to derive an outcome precludes ones that reflect the principles in Indra Sawhney (1992), unless an arbitrary number of rounds of migrations and adjustments are allowed. In our view, this methodological failure is at the core of the legal inconsistencies and ongoing litigations in India. 15 In Section 5, we show that the Supreme Court's main rulings for this version 12 See paragraphs 24, 25, 31 and 32 in Saurav Yadav (2020), given in Appendix C.1. 13 The reason is analogous to the necessity of iterative procedures to find stable matchings in two-sided matching markets.
14 In particular the formulation of the 2SMH choice rule endorsed in Saurav Yadav (2020) relies on the concepts of migration and adjustment. In contrast, Sönmez and Yenmez (2021) use a simpler formulation which does not rely on these concepts, and establishes its equivalence to the Saurav Yadav (2020) formulation in an Online Appendix. 15 An especially detrimental aspect of this flawed methodology pertains to the reallocation of the open positions which are tentatively allocated to VR-protected individuals in the first phase earning them each a status called meritorious reserved candidate, but subsequently vacated when they migrate to a VR-protected of the problem suffer from fundamental inconsistencies, both internally and also between themselves.

Related Literature.
To the best of our knowledge, our paper is the first one to propose a mechanism to implement VR and HR policies in India concurrently for applications with heterogeneous positions (either at a single institution or across multiple institutions). As we have elaborated earlier in depth, our analysis builds on Sönmez and Yenmez (2021) where a simpler version of the problem with identical positions is considered. Apart from this paper, our motivation is closest to Ehlers and Morrill (2020) where the analysis is also based on legal desiderata, although our formulation is more direct in its reliance on explicit mandates in the judgments Indra Sawhney (1992) and Saurav Yadav (2020). Our theoretical results generalize characterizations in Sönmez and Yenmez (2021) derived for identical positions only, and the basic characterizations in Alcalde and Barberà (1994), Balinski and Sönmez (1999) derived in the absence of any form of reservation policy.
Our paper is not the first one to suggest a mechanism based on the DA algorithm for practical applications of job matching or college admissions in India. Thakur (2018) adopts a similar approach for allocation of government positions by the Union Public Service Commission, whereas Baswana et al. (2019a) and Aygün and Turhan (2022) adopt similar approaches for allocation of seats at engineering colleges. However, unlike our paper, none of these papers properly accounts for the HR policy. Since HR protections for persons with disabilities is mandated throughout India by the full-bench Supreme Court judgement Union Of India vs National Federation Of The Blind (2013), 16 inclusion of these provisions is essential for implementation of reservation policies. Two of these papers, Thakur (2018) and Aygün and Turhan (2022), assume away the HR policy altogether. 17 In Baswana et al. (2019a), the authors report their design and implementation of a large scale seat allocation process for some of the technical universities in India. 18 While the authors incorporated both VR-protected and HR-protected groups in their design, they have not differentiated between the two policies under their mechanism. As such, their design is in direct violation of Indra Sawhney (1992). 19 category to receive a more-preferred position. A simple search via Indian Kanoon, a free search engine for Indian Law, reveals that as of January 2022, there were 28 cases at the Supreme Court and 670 more at the high courts which relate to the migration of meritorious reserved candidates. 16 The ruling is available at https://indiankanoon.org/doc/178530295/ (retrieved on 12/30/2021). 17 See Section 4.1 for a more in-depth discussion of Aygün and Turhan (2022). 18 Implemented in the period 2015-18, their system allocated approximately 39,000 seats at around 100 institutes in 2018 (Baswana et al., 2019b). 19 HR protections are implemented as if they are VR protections under the mechanism designed and implemented by Baswana et al. (2019a,b). In particular, the specification of their mechanism treats persons with disabilities (PwD) as if they are a VR-protected group, even though they are explicitly awarded with HR protections by the Supreme Court judgement National Federation Of The Blind (2013). For example, a generalcategory candidate with a disability is first considered for a regular open-category position, and only then Abstracting away from the legislative requirements in India, there is a large literature on priority-based resource allocation mechanisms using the DA algorithm as their core engine. A few papers in this literature are especially related to our paper since they include various forms of reservation policies. These include Dur

Model
There exist a finite set of individuals I and a finite set of institutions J referred to as "jobs" throughout this section. 20 Each job j ∈ J has q j identical positions. Each individual i ∈ I has a strict preference ranking ≻ i over all jobs and the outside option denoted by ∅, which could be being unemployed. We denote the set of all preference rankings for agent i by P i . A job j ∈ J is acceptable to individual i ∈ I if it is stricty more preferred to the outside option, that is, j ≻ i ∅. We denote the corresponding weak order by i and the indifference relation by ∼ i . For any set of individuals I ⊆ I, we denote the profile of individual preferences by ≻ I = (≻ i ) i∈I . In addition, we denote the set of all preference profiles by P = (P i ) i∈I .
Each individual i ∈ I has a distinct merit score σ j (i) ∈ R + for any given job j ∈ J . While individuals with higher merit scores have higher claims for a job in the absence of affirmative action policies, disadvantaged populations are protected with two types of affirmative action policies, (i) the vertical reservation (VR) policy providing the primary VR protections, and (ii) the horizontal reservation (HR) policy providing the secondary HR protections.

VR Policy.
There exist a set of VR-protected categories R and a general category g ∈ R. 21 Each individual belongs to a single category in R ∪ {g}. Individual memberships to VR- that individual i is ineligible for VR protections, and thus she is a member of the general category g. 22 At any given job j ∈ J , there are r c j ≥ 0 positions set aside exclusively for the members of category c ∈ R. We refer to these positions as category-c positions or (VR-protected positions for category c). We assume that ∑ c∈R r c j ≤ q j . 23 In contrast, members of the general category do not have any positions set aside for them under the VR policy. Therefore, r o j = q j − ∑ c∈R r c Given a category v ∈ V, let I v ⊆ I denote the set of individuals who are eligible for category-v positions.
The defining characteristic of the VR protections is stated as follows in the landmark Supreme Court judgement Indra Sawhney (1992): It may well happen that some members belonging to, say Scheduled Castes get selected in the open competition field on the basis of their own merit; they will not be counted against the quota reserved for Scheduled Castes; they will be treated as open competition candidates.
When there is a single job and the VR policy is the only affirmative action policy, the interpretation of this statement becomes airtight: If a VR-protected individual deserves an open position on the basis of her merit score only, she should be awarded an open position and not use up a VR-protected position set aside for her category. In this sense, VR protections are implemented on an "over-and-above" basis, a feature which makes this policy the "higher level" affirmative action policy. Unfortunately, Indra Sawhney (1992) formulation of the VR policy given above loses its clarity when it is implemented jointly with the HR policy which is formally introduced next in Section 2.2. 22 To keep the notation at a minimum, we assume that (i) the set of VR-protected categories R, (ii) the general category g, and (iii) the category-membership function ρ are all independent of a job. This assumption is without any loss of generality and all these primitives can be made job-dependent by a simple inclusion of a job index without interfering with any aspect of our analysis. 23 In India, the total number of VR-protected positions cannot be more than half of the positions at any given job by the Supreme Court judgement Indra Sawhney (1992), although this upper bound is not followed in some states such as Tamil Nadu.

HR Policy.
In addition to the categories in R that are associated with the higher level VR protections, there is a finite set of traits T associated with the lower level HR protections. Each individual has a (possibly empty) subset of traits, given by the trait function τ : I → 2 T . HR protections are provided in the form of minimum guarantees within each vertical category v ∈ V. 24 For any job j ∈ J , VR-protected category c ∈ R, and trait t ∈ T , subject to the availability of qualified individuals, a minimum of r c,t j category-c positions are to be assigned to individuals from category c with trait t. If there are not enough individuals from category c with trait t to fill these positions, then the remaining empty seats are to be allocated to other individuals from category c. We refer to these positions as category-c HR-protected positions for trait t. Similarly, for any trait t ∈ T and subject to the availability of individuals with trait t, a minimum of r o,t j open-category positions are to be assigned to individuals with trait t. If there are not enough individuals with trait t to fill these positions, then the remaining empty seats are to be allocated to other individuals. We refer to these positions as open-category HR-protected positions for trait t.
For each job j ∈ J and vertical category v ∈ V, we assume that the total number of category-v HR-protected positions is no more than the number of positions in category v. That is, for each job j ∈ J and category v ∈ V, In contrast to VR protections which are provided on an "over-and-above" basis, HR protections are provided within each vertical category on a "minimum guarantee" basis. This means that positions obtained without invoking any HR protection still accommodate the HR protections.

Primary Assignment of Individuals to Jobs and Vertical Categories.
In India, each position is classified by its job, vertical category (including the open category), and the associated trait (or its absence). Therefore, in order to describe an outcome, it may be compelling to assign individuals to a triple consisting of a job, a vertical category, and a trait or its absence. We will, however, take a slightly different approach for the reasons we elaborate below. An outcome needs to indicate the job assignments of individuals because they have strict preferences over jobs. While the category assignment is not important for individual preferences, it is important for the implementation of the VR policy. That is because, the laws clearly specify who should receive the open positions and who should 24 Provision of HR protections within each vertical category is not a federal mandate in India but rather a formal recommendation by the Supreme Court judgment Anil Kumar Gupta (1995). The vast majority of the institutions in India follows this recommendation and implement the HR policy in this form, which is also referred to as interlocking reservations or compartmentalized horizontal reservations. receive the VR-protected positions. Therefore, at a minimum, an outcome needs to specify the job assignment and the category assignment of each individual who receives a position. Specification of a trait assignment (or its absence), on the other hand, offers some flexibility in terms of modeling an outcome. While an outcome can explicitly specify the trait (or its absence) for a position that is received, this modeling choice results in immaterial multiplicities under our axioms which formulate affirmative action legislation in India. For example, if there is a minimum guarantee of two positions for women in the open category of a given job while there are five women who receive open-category positions, under Indian laws there is no meaningful way to specify which two of these five women receive the HR-protected positions. Therefore, in order to avoid any arbitrary conditions that fail to capture the Indian legislation, in our model an outcome simply assigns individuals to job-vertical category pairs or leaves them unassigned. An implicit trait assignment will still be important to verify that the HR protections are honored to the extent it is possible, and it will be captured in our model through a secondary assignment introduced in Section 2.4. 25 Definition 2. An assignment is a function α : We denote the set of all assignments by A.
For each individual, an assignment specifies which job offers the position she receives, if any, and the vertical category through which she receives it. Given an assignment α, let denote the set of individuals who receive a position at job j.
Since individual preferences are originally defined over J ∪ {∅} rather than over J × V ∪ {∅}, we trivially extend the domain P of the preferences to J × V ∪ J ∪ {∅} as follows: For any preference profile ≻ I ∈ P, individual i ∈ I, job j ∈ J , and category v ∈ V, we have Therefore, an individual has preferences over jobs only and is indifferent between categories of the same job.
Definition 3. A mechanism ϕ : P → A is a function that selects an assignment ϕ(≻ I ) ∈ A for each preference profile ≻ I ∈ P.
Given a mechanism ϕ and and profile of reported preferences ≻ I , the assignment for individual i ∈ I is denoted by ϕ(≻ I )(i). Likewise, the set of individuals assigned to job j ∈ J and category v ∈ V is denoted by ϕ −1 (≻ I )(j, v), and the set of individuals assigned to job j is denoted by ϕ −1 (≻ I )(j).

Secondary Assignment of Individuals to Traits within their Primary Assignments.
In this section, we briefly discuss a technical tool we refer to as a trait-matching (Sönmez and Yenmez, 2021). Given an assignment α ∈ A, a trait-matching can be thought as a secondary assignment of the HR-protected individuals to traits within any given pair (j, v) ∈ J × V, and its size provides us with a natural metric to assess to what extent the HR protections are honored at pair (j, v).
Fix an assignment α ∈ A, a job j ∈ J , and a category v ∈ V. Consider the set of individuals I ⊆ I who receive category-v positions at job j under assignment α. That is, First, consider a simpler version of the problem where each individual has at most one trait (i.e., the HR-protected groups do not overlap). For any trait t ∈ T , the set of individuals in I who have trait t is given by {i ∈ I : t ∈ τ(i)}. Therefore, within category v of job j, • HR protections for trait t are fully honored if |{i ∈ I : t ∈ τ(i)}| ≥ r v,t j , whereas • r v,t j − |{i ∈ I : t ∈ τ(i)}| of the trait-t HR-protected positions are left dishonored, otherwise.
For the latter case, an individual i ∈ I v \ I can object to the allocation of category-v positions at job j under assignment α, provided that she has trait t and desires to receive a position at job j. Also observe that the total number of HR-protected positions that are honored within category v at job j by the set of individuals I is given by Hence, any individual i ∈ I v \ I can object to the allocation of category-v positions at job j under assignment α, provided that n v j I ∪ {i} > n v j (I) and she desires to receive a position at job j. This observation plays a key role in several of our formal axioms, later introduced in Section 2.5.
The same idea can also be extended to the more general version of the problem when individuals can have multiple traits (i.e., the HR-protected groups may potentially overlap). However, the secondary assignment of individuals to traits require additional care in this case. For example, if there is a single HR-protected position for women and a single HR-protected position for persons with disabilities, a disabled woman can receive positive discrimination for either one of the two HR-protected positions. However, if the only other individual who has either one of the two traits is a disabled man, it would be implausible to award the HR-protected position for persons with disabilities to the disabled woman and consequently deny an HR-protected position to the disabled man. Both of the HRprotected positions can be honored by awarding the HR-protected position for women to the disabled woman and the HR-protected position for persons with disabilities to the disabled man. We next build on this simple observation to extend the above-given function n v j to the general version of the problem. Fix a job j ∈ J , a category v ∈ V, and a set of individuals Definition 4. Given a job j ∈ J , a category v ∈ V, and a set of individuals (2) for any i, j ∈ I, Definition 5. Given a job j ∈ J , a category v ∈ V, and a set of individuals I ⊆ I v , a trait-matching µ of individuals in I with the HR-protected positions in H v j has maximum cardinality in the HR graph if there exists no other trait-matching that assigns a strictly higher number of HR-protected positions to individuals. statistics on the compliance with the HR policy, 28 reflected in three of our formal axioms introduced next in Section 2.5.

Desiderata on Assignments and Mechanisms.
In this section, we introduce our formal axioms on assignments and mechanisms.
Our main objective in formulation of these axioms is giving a mathematically precise meaning to the mandates of the Supreme Court of India on the reservation policy. We will organize our axioms into three groups.
(1) In the first group, we have two axioms which are so benign that they are not explicitly discussed in the court rulings.
(2) In the second group, we have three core axioms which formulate the Supreme Court's explicit mandates on concurrent implementation of VR and HR policies.
As far as we can tell, the inability to design mechanisms which satisfy these axioms, and the legislative confusion on their formulation are the primary reasons for the challenges in India. We argue that the formulation of these three axioms in Sauram Yadav (2020) finally clears the second of these reasons; i.e., the legal confusion on their formulation. This landmark judgment of the Supreme Court also offered a mechanism for the simplest version of the problem with identical positions and non-overlapping HR-protected groups. In Section 3.3, we propose a mechanism for the problem in its full generality.
(3) When all positions are identical, the axioms in the first two groups uniquely characterize a mechanism (Sönmez and Yenmez, 2021). As we present in Example 2 below, this is not the case when positions are heterogenous. The role of the two axioms in the last group, namely the Pareto principle and strategy-proofness, is closing this modest gap. Together with the axioms that formulate the mandates of the Supreme Court, either one of these foundational principles in economic theory uniquely characterize our proposed mechanism 2SMH-DA presented in Section 3.3.
Our first axiom states that no position should be awarded to an individual who has no desire to receive this position. Definition 6. An assignment α ∈ A satisfies individual rationality if, for every i ∈ I, A mechanism ϕ satisfies individual rationality if its outcome ϕ(≻ I ) satisfies individual rationality for each ≻ I ∈ P.
Our second axiom states that, a position can be left idle only if no individual who desires to receive it is eligible for the position.
Definition 7. An assignment α ∈ A satisfies non-wastefulness if, for every j ∈ J , v ∈ V, and i ∈ I, A mechanism ϕ satisfies non-wastefulness if its outcome ϕ(≻ I ) satisfies non-wastefulness for each ≻ I ∈ P.
Our third axiom formulates the positive discrimination given to HR-protected individuals. It states that an individual cannot be denied a position at any job-category pair (j, v) ∈ J × V, if her recruitment increases the number of HR-protected positions that are honored at pair (j, v).
Definition 8. An assignment α ∈ A satisfies maximal accommodation of HR protections if, for every j ∈ J , v ∈ V, and i ∈ I v , A mechanism ϕ satisfies maximal accommodation of HR protections if its outcome ϕ(≻ I ) satisfies maximal accommodation of HR protections for each ≻ I ∈ P.
Our fourth axiom formulates the following equity principle given in the paragraph 31 of the Supreme Court judgment Saurav Yadav (2020): [...] Subject to any permissible reservations i.e. either Social (Vertical) or Special (Horizontal), opportunities to public employment and selection of candidates must purely be based on merit.
Any selection which results in candidates getting selected against Open/General category with less merit than the other available candidates will certainly be opposed to principles of equality. There can be special dispensation when it comes to candidates being considered against seats or quota meant for reserved categories and in theory it is possible that a more meritorious candidate coming from Open/General category may not get selected. But the converse can never be true and will be opposed to the very basic principles which have all the while been accepted by this Court. Any view or process of interpretation which will lead to incongruity as highlighted earlier, must be rejected.
Definition 9. An assignment α ∈ A satisfies no justified envy if, for every i ∈ I, j ∈ J , v ∈ V, and i ′ ∈ I v , A mechanism ϕ satisfies no justified envy if its outcome ϕ(≻ I ) satisfies no justified envy for each ≻ I ∈ P.
That is, if an individual i receives a category-v position at job j while another individual i ′ receives a less-desired assignment, it is either because individual i has a higher merit score under σ j than individual i ′ or because replacing individual i with individual i ′ decreases the number of HR-protected positions that are honored.
When applied for the open-category positions where every individual is eligible, our no justified envy axiom morphs into a condition that is known as the principle of merit in India. Similarly, when applied for the positions of a VR-protected category c ∈ R where only category-c individuals are eligible, our no justified envy axiom morphs into a condition that is known as the principle of inter se merit in India. While these principles were originally laid out in the landmark Supreme Court judgment Indra Sawhney (1992), the precise role of the HR protections for open positions under the principle of merit only became airtight with the recent judgment Saurav Yadav (2020). 29 Failure of this axiom is one of the primary reasons for litigations In India on implementation of the VR and HR policies.
Our fifth axiom formulates the defining characteristic of VR protections as the "higher level" reservation policy. It states that, VR-protected positions shall not be awarded to individuals who deserve an open-category positions based on the principle of merit, and thus be left for VR-protected individuals who are truly in need of positive discrimination. 30 Definition 10. An assignment α ∈ A satisfies compliance with VR protections if, for every j ∈ J , c ∈ R, and i ∈ I c , the following three conditions hold whenever α(i) = (j, c): . A mechanism ϕ satisfies compliance with VR protections if its outcome ϕ(≻ I ) satisfies compliance with VR protections for each ≻ I ∈ P.
Observe that, both of the following two assignments satisfy all five axioms: While both individuals receive their first choices under assignment α, they receive their second choices under assignment β.
Example 2 reveals that, in the absence of additional considerations, the HR policy may be detrimental to the very groups it is supposed to help. In particular, if assignment β is chosen by a central planner (which may be motivated by maximizing the number of HRprotected positions that are honored), the positive discrimination given to individual a for the position at job x due to her trait t 1 not only ends up hurting individual b, but also individual a herself. Indeed, having the highest merit score for both jobs, individual a is 31 The role of the third condition in formulation of VR protections is due to Saurav Yadav (2020). See Sönmez and Yenmez (2021) for additional details. 32 Below we present the simplest possible example which makes this point, not one that is realistic. Modifying the example to make it realistic is straightforward. not in any need of positive discrimination. Therefore, an excessive effort to honor the HRprotected positions without considering individual preferences can be detrimental to the very groups the HR policy is supposed to protect. Fortunately, there is another assignment, which not only satisfies all five axioms representing the Supreme Court's mandates, but also is in better interests of all individuals despite not honoring any of the HR-protected positions. This observation motivates the axioms in our third group. While these axioms do not correspond to any desiderata formulated by the Supreme Court, they are among the most fundamental principles in economic theory.
(1) the assignment ϕ(≻ I ) either Pareto dominates or is equal to the assignment φ(≻ I ) for each ≻ I ∈ P, and (2) the assignment ϕ(≻ I ) Pareto dominates the assignment φ(≻ I ) for some ≻ I ∈ P.
A mechanism ϕ is Pareto efficient if its outcome ϕ(≻ I ) is Pareto efficient for each ≻ I ∈ P.
Our final axiom is a highly sought-after incentive compatibility condition, defined only for mechanisms (and not for assignments).
Truthful preference revelation is always weakly more preferred than reporting any other preference ranking for every individual under a strategy-proof mechanism.

Proposed Mechanism: 2SMH-DA
In this section, we extend a mechanism proposed in Sönmez and Yenmez (2021) for the version of the problem with identical positions to the general version with heterogenous positions through the celebrated individual-proposing deferred acceptance algorithm by Gale and Shapley (1962).

Single-Job Solution Concepts.
We next formulate a number of single-job solution concepts. Assuming individual rationality and a mechanism only relies on preferences over acceptable positions, the set of applicants contains all the necessary information that is given in a preference profile when all positions are identical. That is because, individuals who prefer remaining unmatched over receiving a position can be ignored, and the remaining individuals all have the same preference relation. Therefore, the domain of single-job solution concepts can be given as 2 I rather than P.
Definition 14. Given a job j ∈ J and a category v ∈ V, a single-category choice rule is a function C v j : 2 I → 2 I v such that, for any I ⊆ I, A single-category choice rule is simply the inverse mapping of a single job and singlecategory mechanism.
Definition 15. Given a job j ∈ J , a multi-category choice rule is a multidimensional function (2) for any two distinct categories v, v ′ ∈ V, A multi-category choice rule is simply the inverse mapping of a single job mechanism.
Definition 16. For any multi-category choice rule C j = (C v j ) v∈V , the resulting aggregate choice rule C j : 2 I → 2 I is such that, for any I ⊆ I, For any set of individuals, the aggregate choice rule yields the set of chosen individuals across all categories.

2-
Step Meritorious Horizontal Choice Rule. In Sönmez and Yenmez (2021), we introduced the following single-category choice rule. Consider a job j ∈ J and a category v ∈ V. Let I ⊆ I v be a set of individuals who are eligible for category v.

Meritorious Horizontal Choice Rule
Step 1.1 Assuming such an individual exists, let i 1 be the the highest merit-score individual (with respect to σ j ) in I who has a trait for an HR-protected position.
Choose individual i 1 for an HR-protected position. Let I 1 = {i 1 }, and proceed with Step 1.2. If no such individual exists, proceed to Step 2.
Step 1.k (k ∈ {2, . . . , ∑ t∈T r v,t j }) Assuming such an individual exists, let i k be the the highest merit-score individual (with respect to σ j ) in I \ I k−1 with Choose individual i k for an HR-protected position. Let I k = I k−1 ∪ {i k }, and proceed with Step 1.(k+1). If no such individual exists, proceed to Step 2.
Step 2. For unfilled positions, choose unassigned individuals with highest merit scores (with respect to σ j ) until either all positions are filled or all individuals are selected.
The following multi-category choice rule uses the meritorious horizontal single-category choice rule multiple times; first, to allocate open-category positions, and next for each VRprotected category to allocate VR-protected positions.

2SMH-DA Mechanism ϕ 2s M
For each preference profile ≻ I ∈ P, the outcome ϕ 2s M (≻ I ) of the 2SMH-DA mechanism is obtained as follows: Step 1. Assuming such a job exists, each individual i ∈ I applies to her most preferred acceptable job under ≻ i . Let I 1 j be the set of individuals who apply to job j ∈ J . Each job j ∈ J tentatively assigns individuals in C 2s M ,j (I 1 j ) to its categories based on C 2s M ,j (I 1 j ), and (permanently) rejects any remaining applicants. If there is no rejection by any job, then the procedure is terminated and the tentative assignments are finalized. Otherwise, proceed to Step 2.
Step k. Assuming such a job exists, each individual i ∈ I who is rejected in Step (k − 1) applies to her next preferred acceptable job under ≻ i . For any job j ∈ J , let I k j be the set of new applicants in Step k along with individuals who are tentatively assigned to categories of job j in Step (k − 1). Each job j ∈ J tentatively assigns individuals in C 2s M ,j (I k j ) to its categories based on C 2s M ,j (I k j ), and (permanently) rejects any remaining applicants. If there is no rejection by any job, then the procedure is terminated and the tentative assignments are finalized. Otherwise, proceed to Step (k+1).
Since there is a finite number of jobs and individuals, this mechanism terminates at a finite round for every preference profile.

Main Results
We next present our main results. The general message of our results is, while the five axioms formulated in Saurav Yadav (2020) do not single out a mechanism when positions are heterogenous, they come pretty close, and either one of two fundamental axioms in economic theory completes this gap.
The primary objective of the Indian reservation system is to enhance the social and educational status of underprivileged communities and thus improve their lives. Given Theorem 1 we believe 2SMH-DA is the only plausible mechanism to pursue that objective.
Observe that, Theorem 1 does not imply that the mechanism 2SMH-DA is Pareto efficient. Our next example shows that, Pareto efficiency is incompatible with the Supreme Court's axioms even when all institutions have the same merit ranking of individuals. 33  Consider the following two assignments: Since (i) all individuals prefer either of the two jobs to remaining unmatched, (ii) individuals b and c each have trait t 2 , and (iii) the only position at job y is HR-protected for trait t 2 , individual a cannot receive his first choice position at job y under any assignment that satisfies the axiom of maximal accommodation of HR protections. Therefore, assignment α is the only assignment that satisfies all five axioms, even though it is Pareto dominated by assignment β.
While it is perhaps the most fundamental axiom in economic theory, the Pareto principle is not the only condition that closes the gap between the Saurav Yadav (2020) axioms and our proposed mechanism 2SMH-DA. Our final result shows that strategy-proofness also achieves the same task, further strengthening the case for 2SMH-DA.
We next relate our contributions to a slight variant of the problem in elite engineering colleges in India, and to a recent paper Aygün and Turhan (2022) for this application.

Significance of VR-Protections as Hard Reserves, and the Relation between Theorem 2 and Theorem 4 in Aygün and Turhan (2022).
Throughout the paper we assume that, for any VR-protected category c ∈ R, an individual i ∈ I is eligible for a category-c position if and only if individual i is a member of category c. That is, the VR-protected positions are hard reserves which are exclusively set aside for their beneficiaries, and as such they cannot be awarded to other individuals. This assumption holds for most field applications in India, and typically any unused VR-protected positions are carried over to next allocation period by legislation. Unlike the VR-protected positions, however, the HR-protected positions are soft reserves. Given any category v ∈ V and trait t ∈ T , an individual i ∈ I v with trait t merely has higher priority for each trait-t HR-protected position over an individual i ′ ∈ I v who lacks trait t.
The assumption that the VR-protected positions are hard reserves is important for the uniqueness part of Theorem 2. Indeed, unless additional structure included in the procedure, the 2SMH choice rule is not even well-defined if the VR-protected positions are implemented as soft reserves for some (or all) of the VR-protected categories. In that case, the outcome (in general) depends on the processing sequence of VR-protected categories in Step 2 of the procedure when the meritorious horizontal choice rule is implemented for these categories. Once the processing sequence of VR-protected categories is fixed (at each institution), however, the resulting mechanism satisfies all of the six axioms in Theorem 2. It is only the uniqueness part of Theorem 2 which no longer holds.
Aygün and Turhan (2022) observe that, for a specific field application in India-the allocation of seats at some elite engineering colleges-the VR-protected positions for the category OBC should not be implemented as hard reserves. 34 Instead, based on the Supreme Court judgment Ashoka Kumar Thakur vs Union Of India (2008), 35 members of OBC are each given (up to) a 10 points of advantage in their merit scores for allocation of the VR-protected seats for OBC. More precisely, the final decree of the judgment is the following: 11. Would it be reasonable to balance OBC reservation with societal interests by instituting OBC cut-off marks that are slightly lower than that of the general category?
It is reasonable to balance reservation with other societal interests. To maintain standards of excellence, cut off marks for OBCs should be set not more than 10 marks out of 100 below that of the general category.
Therefore, at any college j ∈ J , all individuals are eligible for the VR-protected positions for OBC, although members of OBC receive a 10 points of advantage over other individuals. In our view the proper generalization of the choice rule 2SMH for this variant of the problem is based on the following two simple adjustments: (1) For allocation of category-OBC positions with the meritorious horizontal choice rule in the second step of the procedure, keep all individuals eligible, but modify the vector of merit scores by increasing the merit score of each member of OBC by 10 points.
(2) Provide a specific processing sequence of VR-protected categories in Step 2.
The first adjustment is needed to accommodate the Supreme Court's decree in Ashoka Kumar Thakur (2008), while the second one is needed to assure that the procedure is welldefined. Analogous to the effect of the processing sequence of VR-protected categories on the outcome when the VR-protected positions are implemented as soft reserves, the outcome (in general) of the generalized procedure too depends on the processing sequence of the VR-protected categories. Therefore the second adjustment assures that the procedure is well-defined.
In response to the decree in Ashoka Kumar Thakur (2008), Aygün and Turhan (2022) take a different approach. Prior to declaring its ruling, justices provide the following policy recommendation in paragraph 278 of the judgment: 278. To this end, the Government shall set up a committee to look into the question of setting the OBC cut off at nor more than 10 marks below that of the general category. Under such a scheme, whenever the non-creamy layer OBCs fail to fill the 27% reservation, the remaining seats would revert to general category students.
Based on the second sentence of the paragraph, Aygün and Turhan (2022) interpret the suggested deviation from the general norm as a decree to implement the VR-protected positions for OBC in the form of soft reserves. 36 In addition to above-given out of context interpretation of the Supreme Court's decree, Aygün and Turhan (2022) also assume away the HR-protections altogether. While this restriction simplifies their analysis considerably, it is critical for the application they study, because there are (court-mandated) HR-protections for persons with disabilities for allocation of seats at engineering colleges. 37 However, even for the simplified version of the problem with only VR protections, the uniqueness part of our characterization in Theorem 2 fails to hold as we have emphasized earlier in this section. To bypass this limitation, Aygün and Turhan (2022) formulate a variant of our compliance with VR protections axiom which requires the following: In addition to open positions which should be allocated before the VR-protected positions, the surplus OBC positions which cannot be awarded to members of OBC should also be allocated before the VRprotected positions at other categories. Just as our compliance with VR protections axiom forces open positions to be allocated prior to VR-protected positions, this extra technical requirement forces the VR-protected positions for OBC to be allocated prior to VR-protected positions from other categories. They refer to the resulting choice rule as backward transfers choice rule. It is simply a slight modification of the over-and-above choice rule where positions for OBC are allocated prior to other VR-protected categories and with soft reserves 36 Aygün and Turhan (2022) do not explicitly indicate that their formulation is equivalent to soft reserves.
Instead they introduce a concept of "de-reservation" of leftover positions to be allocated to remaining individuals based on the original merit scores. The two formulations are identical. 37 The first two versions of Aygün and Turhan (2022), both available at https://arxiv.org/abs/2103.05899v4, also acknowledge that their application has HR protections (also called special reservations in India) in footnote 5 of each version. rather than hard reserves. 38 Referring to the mechanism that implements their backwards transfers choice rule at each institution under the individual-proposing deferred acceptance algorithm as the DA-BT mechanism, they present a counterpart to our Theorem 2 in their Theorem 4.

Legal Inconsistencies within and between Supreme Court Judgements
In this section we present the legal inconsistencies that emerged in several important judgments of the Supreme Court, and identify a methodological flaw that is largely responsible for these inconsistencies. 39 In all judgements presented in this section, the VRprotected categories are SC, ST, and OBC.

Meritorious Reserved Candidates.
While the specific mechanism differs in most applications, the initial step of mechanisms employed by various institutions in India often consists of tentatively allocating the ∑ j∈J r o j open-category positions to candidates using a mechanism known as the serial dictatorship in the literature: The highest merit ranking candidate tentatively receives his top choice job, the second highest merit ranking candidate tentatively receives his top choice job among the remaining open positions, and so on. Each reserved category candidate who tentatively receives an open position at this step is referred to as a meritorious reserved candidate (MRC).
Consider an individual i who is an MRC from a VR-protected category, say from SC. Observe that, while candidate i tentatively receives an open-category position on his own merit without using the benefits of VR protections, this position is not necessarily at his first choice job. Therefore, he would rather receive an SC-category position at a more-preferred job. At this point, the following important questions emerge, where the answers guide the mechanics of the rest of the mechanism: (1) Shall an MRC who is tentatively assigned an open-category position be allowed to migrate to a higher choice job, and receive a position set aside for his VR-protected category? 38 Since Aygün and Turhan (2022) instead use their concept of "de-reservation" to describe this choice rule, their description is considerably more complex. 39 These inconsistencies often result in litigations, interruption of the recruitment processes, and reversals of recruitment decisions in India. For example, a March 2017 The Times of India story reports the likely consequences of a ruling by the High Court of Gujarat as follows: " The advertisement was issued in 2010 and recruitment took place in 2016 amid too many litigations over the issue of reservation . . . With the recent observation by the HC, the merit list will now be changed for the third time. Those already selected and at present under training might lose their jobs, and half a dozen new candidates might find their names on the new list. However, all appointments have been made by the HC conditionally and subject to final outcome of these multiple litigations." The story (retrieved on 01/06/2022) is available at https://tinyurl.com/995xykym.

(2) If the answer to the first question is in the positive, then what is to happen to the open-category position that is vacated by the MRC?
These two questions and their answers are at the heart of countless lawsuits in India. We next present three Supreme Court cases in this context. Through these cases we argue that the methodology of using migrations and adjustments through meritorious reserved candidates is fundamentally flawed, and it is the main source of the legal conflict and confusion in all of these cases and countless others. All these difficulties can be avoided with our proposed mechanism 2SMH-DA, presented in Section 2. 40

Anurag Patel vs U.P. Public Service Commission (2004). The Uttar Pradesh Public
Service Commission (UPPSC) conducted an examination in 1990, merit ranking all candidates, and used the following mechanism to allocate 358 positions at various jobs: Step 1. Allocate the ∑ j∈J r o j units of open-category positions using the serial dictatorship induced by the given merit ranking: The highest merit ranking candidate receives his top choice, the second highest merit ranking candidate receives his top choice among the remaining open positions, and so on.
All assignments in this step are final.
Step 2. For each VR-protected category c ∈ {SC, ST, OBC}, consider only category-c candidates who have not received an assignment in Step 1, and allocate the ∑ j∈J r c j units of category-c positions to these candidates using the serial dictatorship induced by the given merit ranking. All assignments in this step are final.
At least one of the shortcomings of this mechanism is immediately apparent: MRC candidates who receive their assignments in Step 1 are not given an opportunity to migrate and be considered for any of the VR-protected positions for their categories, and as such they often receive positions at less-preferred jobs compared to lower merit ranking candidates from their own categories. Therefore, the UPPSC mechanism fails to respect inter se merit, an important principle that plays a key role in all Supreme Court cases we discuss 40 Each Supreme Court case in Sections 5.2-5.4 involves the handling of MRC candidates under a litigated mechanism in India. The descriptions of the mechanisms we present in these sections are based on their descriptions in these court cases. Not all aspects of the actual mechanisms are relevant for these cases, and they only provide details that relate to the case. In particular, all the cases focus on VR protections to SC/ST/OBC and none of them gives details on the handling of HR protections as they are not focal to these cases. This means that the mechanisms we present may correspond to a simplified case, abstracting away from HR protections. In actual implementation HR protections are likely accommodated through adjustments at various steps of the procedures, as it is traditional in India. Since we present failures of these mechanisms in this section even in the absence of HR protections, the details provided in the cases are sufficient for our purposes. in Sections 5.2-5.4. This shortcoming of the UPPSC mechanism resulted in a lawsuit at the High Court of Allahabad, and consequently the UPPSC was ordered to come up with a reallocation that respects inter se merit. This reallocation, in turn, resulted in an appeal at the Supreme Court by a candidate who was adversely affected by the high court's decision. The appeal was dismissed by the Supreme Court, and the high court's decision was sustained, reaffirming that the mechanism has to respect inter se merit. The following quote is from this important judgement: In the instant case, as noticed earlier, out of 8 petitioners in writ petition No. 22753/93, two of them who had secured ranks 13 and 14 in the merit list, were appointed as Sales Tax Officer-ll whereas the persons who secured rank Nos. 38, 72 and 97, ranks lower to them, got appointment as Deputy Collectors and the Division Bench of the High Court held that it is a clear injustice to the persons who are more meritorious and directed that a list of all selected backward class candidates shall be prepared separately including those candidates selected in the general category and their appointments to the posts shall be made strictly in accordance with merit as per the select list and preference of a person higher in the select list will be seen first and appointment given accordingly, while preference of a person lower in the list will be seen only later.
Anurag Patel (2004) is best known for reaffirming that any mechanism used for allocation of government jobs or seats at public educational institutions has to respect inter se merit. 41 Therefore, an MRC is entitled by law to migrate to a higher choice job claiming a position vertically reserved for his reserved category, answering the first question in Section 5.1 in the positive.

Union of India vs Ramesh Ram & Ors (2010). Selection to three All India Services
(Indian Administrative Service, Indian Foreign Service, and Indian Police Service), and eighteen other services in various government departments is made by the Union Public Service Commission (UPSC), by conducting Civil Service Examinations periodically. Given the merit ranking produced by the Civil Service Examination along with the submitted preferences of the candidates over the set of jobs, the following UPSC mechanism is used to allocate the positions.
Step 1. Tentatively allocate the ∑ j∈J r o j units of open-category positions using the serial dictatorship induced by the given merit ranking. Promote the VR-protected candidates who secured tentative positions at this step to the status of an MRC. 41 Anurag Patel (2004) also supports our position that, the principles on implementation of VR and HR policies clarified in Saurav Yadav (2020) is not limited to applications with identical positions, but they apply more broadly for applications with heterogenous positions as well.
Finalize all tentative assignments, except those received by VR-protected candidates who are promoted to the status of MRC.
Step 2. For each VR-protected category c ∈ {SC, ST, OBC}, consider all category-c candidates (including MRCs who each received a tentative assignment in Step 1), and tentatively allocate the ∑ j∈J r c j units of category-c positions to these candidates using the serial dictatorship induced by the given merit ranking.
Finalize all tentative assignments except those received by the MRCs.
Step 3. Step 4. Finalize the assignment of each MRC with the more-preferred one of the (at most) two tentative assignments received in Steps 1 and 2. In case the two tentative assignments correspond to the same job, finalize the open-category position received in Step 1.
Step 5. For each MRC, (at most) one position may be vacated at Step 4 and become available for reassignment. Allocate them to waitlisted candidates as follows: (1) An MRC is allowed to migrate to a preferred job, claiming a VR-protected position for his category.
(2) An open-category position tentatively assigned to an MRC in Step 1 is awarded to a waitlisted candidate from the general category once the MRC receives a morepreferred position that is VR protected. Of course, the petitioners' position is against the principle of inter se merit and in direct conflict with the Supreme Court judgement in Anurag Patel (2004) discussed in Section 5.2. Despite the unsustainable position taken by the petitioners, their case was not dismissed by the Tribunal. The Tribunal instead ruled that, while the MRCs can be allowed to migrate to a higher choice job claiming positions that are vertically reserved for their categories, this shall not be done at the expense of consuming away the VR-protected positions for categories SC, ST, and OBC. In other words, while the petitioners' challenged Step 1 of the UPSC mechanism, the Tribunal required the UPSC to change Steps 2, 3, and 5 of its mechanism. This ruling was challenged by the Union of India at the Madras High Court. Not only did the Union of India lose their appeal in a judgement upholding the Tribunal's decision, the High Court ruled the following aspect of the UPSC mechanism to be unconstitutional: This corresponds to ruling Steps 2, 3, and 5 of the UPSC mechanism to be unconstitutional. Consequently, the High Court directed the Government of India and UPSC to repeat the allocation in the absence of their Rule 16(2).
The judgement of the Madras High Court, in turn, was challenged by the Union of India at the Supreme Court in Ramesh Ram (2010). In a decree that became a main reference for the allocation of government positions, the appeal was allowed, the judgement of the Madras High Court was set aside, and the UPSC mechanism was ruled to be constitutional. The following statement is from the conclusion of this historical decree: We sum up our answers-: i) MRC candidates who avail the benefit of Rule 16 (2) and adjusted in the reserved category should be counted as part of the reserved pool for the purpose of computing the aggregate reservation quotas. The seats vacated by MRC candidates in the General Pool will be offered to general category candidates.
ii) By operation of Rule 16 (2), the reserved status of an MRC is protected so that his/ her better performance does not deny him of the chance to be allotted to a more-preferred service.
iii) The amended Rule 16 (2) only seeks to recognize the inter se merit between two classes of candidates i.e. a) meritorious reserved category candidates b) relatively lower ranked reserved category candidates, for the purpose of allocation to the various Civil Services with due regard for the preferences indicated by them.
iv) The reserved category candidates ''belonging to OBC, SC/ ST categories'' who are selected on merit and placed in the list of General/Unreserved category candidates can choose to migrate to the respective reserved category at the time of allocation of services. Such migration as envisaged by Rule 16 (2) is not inconsistent with Rule 16 (1) or Articles 14, 16 (4) and 335 of the Constitution.
Therefore, in the context of allocation of government jobs, the Supreme Court judgement Ramesh Ram (2010) provides the following answers to the questions posed in Section 5.1: (1) An MRC is entitled to migrate to a higher choice job claiming a VR-protected position for his category.  a 1 , a 2 , a 3 , b 1 , b 2 . Candidates b 1 , b 2 are members of category-c and hence they are eligible for the VR-protected position. Candidates a 1 , a 2 , a 3 are members of the general category, and therefore ineligible for the VR-protected position. All candidates have the same preferences where x is their first choice, y is their second choice, z is their third choice, and remaining unmatched is their last choice. All jobs have the same merit ranking of the candidates based on the merit function σ as follows: We next find the outcome of the UPSC mechanism: Step 1. The highest merit ranking candidate a 1 tentatively receives an open position at job x, the second highest merit ranking candidate b 1 receives an open position at job y, and the third highest merit ranking candidate a 2 receives an open position at job z.
Candidate b 1 is given the status of an MRC. Assignment of candidate a 1 is finalized as an open position at job x, assignment of candidate a 2 is finalized as an open position at job z.
Step 2. Candidates b 1 and b 2 are the only ones eligible for the category-c position at job x. Having higher merit ranking than candidate b 2 , candidate b 1 tentatively receives this position.
Step 3. A waitlist each is prepared for the general category and category-c. Since there is only one MRC candidate, there is a single candidate in each waitlist. Candidates a 3 and b 2 are waitlisted at the general category waitlist and category-c waitlist respectively.
Step 4. Having the status of an MRC, the assignment of candidate b 1 is finalized as the more-preferred position he tentatively received from Steps 1 and 2. He receives the category-c position at his first choice job x.
Step 5. The position vacated by candidate b 1 is an open-category position at job y. It is assigned to candidate a 3 as the only individual in the general category waitlist. Therefore, the final assignment is given as follows: Observe that this assignment does not respect inter se merit. Candidate a 2 receives a lesspreferred assignment than candidate a 3 , despite being a member of the same category (i.e., the general category) and having a higher merit score.
Indeed, a close inspection of Example 3 reveals a number of additional issues with the judgement in Ramesh Ram (2010). The Supreme Court ruled that: The seats vacated by MRC candidates in the General Pool will be offered to general category candidates.
This decision would be plausible only if candidates from the general category are more meritorious than those in the VR-protected categories. As it is seen in Example 3, this may not always be the case. In our view, offering the vacated position to the lowest merit ranking candidate a 3 is not justified when the higher merit ranking candidate b 2 remains unassigned simply because he is a member of a VR-protected category. A system that is intended as positive discrimination for candidate b 2 results in his discrimination. Equivalently, the cut-off score, the minimum score needed for a position, is higher in this example for the category-c candidates than for the general category candidates. 43 These types of scenarios result in some other related anomalies as well. In the absence of affirmative action, the outcome of the UPSC mechanism would have been a 1 a 2 a 3 b 1 b 2 x y ∅ x z , and the sole VR-protected candidate b 2 would have been better off. Or, alternatively, had candidate b 2 not claimed his VR protections, he would have received a position at job z.

Tripurari Sharan & Anr. vs Ranjit Kumar Yadav (2018). The judgement in Ramesh
Ram (2010), discussed in Section 5.3, is now considered a main reference for allocation of government jobs when positions are heterogeneous. Based on this reference judgement, open-category seats vacated by MRC candidates are to be offered to general-category candidates for allocation of government jobs. We emphasize government jobs, because the Supreme Court has taken a contrary position for the allocation of seats at medical colleges. While the main reference for this application is considered to be Shri Ritesh R. Sah vs Dr. Y.L. Yamul & Ors (1996), we instead discuss the more recent Supreme Court case Tripurari Sharan (2018), 44 for it is more illuminating for our purposes. Citing the judgement in Ramesh Ram (2010), the petitioners appealed in Tripurari Sharan (2018) an earlier decision by the Patna High Court, which ruled: In case of admission to medical institutions, an MRC can have in, for the purpose of allotment of institutions, of his choice, the option of taking admission in a college, where a seat in his category is reserved. Though admitted against a reserved seat, for the purpose of computation of percentage of reservation, he will be deemed to have admitted as an open category candidate, rather he remains an MRC. He cannot be treated to have occupied a seat reserved for the category of reservation he belongs to. Resultantly, this movement will not lead to ouster of the reserved candidate at the bottom on the list of that reserved category. While his/her selection as reserved category candidate shall remain intact, he/she will have to adjusted against remaining seats, because of movement of an MRC against reserved seats, only for the purpose of allotment of seats.
Aware of the contradictory judgement in Ramesh Ram (2010), the judges of the Patna High Court justified their decision as follows: (i) There is an obvious distinction between qualifying through a common entrance test for securing admission to medical courses in various institutions vis-a-vis a common competitive examination held for filling up vacancies in various services. (ii) This distinction arises because all candidates receive, in a case of common entrance test held for securing admission in medical institutions, the same benefits of securing admission in one of the medical institutions, in a particular course, whereas in the case common selection process adopted for filling up vacancies in various services, there are variations, which accrue to the successful candidates, because the services may differ in terms of status and conditions of service including pay scale, promotional avenues, etc. Consequence of migration of an MRC to the concerned reserved category shall be, therefore, different in case of the admission to various medical institutions vis-a-vis selection to various posts.
According to the judges, while the benefits from securing different jobs may vary, the benefits from securing admission to different medical institutions are uniform. We do not agree with this assessment; however, even if that is the case, then why bother migrating an MRC to a higher choice medical institution?
The appeal was declined by the Supreme Court in Tripurari Sharan (2018), reaffirming the Patna High Court's decision. Furthermore, the Supreme Court judgement also specified the exact manner in which the open-category seats vacated by MRC candidates are to be filled in allocation to medical institutions: i) An MRC can opt for a seat earmarked for the reserved category, so as to not disadvantage him against less meritorious reserved category candidates. Such MRC shall be treated as part of the general category only.
ii) Due to the MRC's choice, one reserved category seat is occupied, and one seat among the choices available to general category candidates remains unoccupied. Consequently, one lesser-ranked reserved category candidate who had choices among the reserved category is affected as he does not get any choice anymore.
To remedy the situation i.e. to provide the affected candidate a remedy, the 50th seat [intended as the last reserved position] which would have been allotted to X-MRC, had he not opted for a seat meant for the reserved category to which he belongs, shall now be filled up by that candidate in the reserved category list who stands to lose out by the choice of the MRC.
So an MRC is allowed to migrate to a VR-protected seat at a higher choice college in order to respect inter se merit, and the open-category seat vacated by the MRC is to be awarded to the VR-protected candidate who is displaced due to this migration. There are numerous issues with this judgement, including its contradiction with Ramesh Ram (2010). But perhaps the most striking one is, the following inconsistency in the final judgement quoted above: While the judges justify part (i) above on the basis of inter se merit, they fail to observe that their mandate in part (ii) results in a potential compromise of inter se merit! As such, this judgement contradicts with Anurag Patel (2004) as well. This is the main point made in our next example. Preferences of the candidates are are given as follows.
Both schools have the same merit ranking of the candidates, given by the merit function σ as follows: While the mechanisms of various medical colleges may differ, they all produce the same assignment in this example, provided that they comply with the judgement in Tripurari Sharan (2018). The three open-category seats are allocated to the highest merit score candidates, where the general category candidates a 1 , a 2 each receive an open-category seat at college x, and the category-c candidate b 1 tentatively receives an open-category seat at college y. Receiving a seat on his own merit, category-c candidate b 1 is promoted to the status of an MRC. The two category-c seats at college x are tentatively allocated to the two remaining candidates b 2 and b 3 from category c. At this stage, the court decision in Tripurari Sharan (2018) kicks in. Candidate b 1 who is promoted to the status of an MRC prefers a seat at college x to his tentative assignment at college y. Therefore, he is assigned one of these seats at the expense of the lowest merit ranking category-c candidate b 3 . Again, by Tripurari Sharan (2018), category-c candidate b 3 receives the open-category seat at college y that is vacated by b 1 , ironically profiting from this adjustment. The assignment dictated by the Supreme Court's decision is: This outcome fails inter se merit, because category-c candidate b 2 receives a less-preferred assignment than the assignment of the lower merit ranking category-c candidate b 3 . In doing so, the respondents also would notice that the steps taken by them in accordance with the Rules 16 (3)(-)(5) are redundant once they issue the result of recruitment in one phase, instead of two as they have become primary cause for the litigation and avoidable confusion in the minds of the candidates seeking recruitment.

The Case
Therefore, the judges have directed the Union of India to announce their outcome in one phase in a manner that respects inter se merit, without relying on the artificial concept of migration. 46 However, despite being spot on, this ruling was ignored by the Union of India, and the case moved all the way to the Supreme Court. One possible explanation for the refusal of the Union of India to follow the decision of CAT-CB may be their technical inability to construct a mechanism that complies with the court's order. As we have argued in Section 2, our proposed mechanism 2SMH-DA is uniquely suited for this task.

Consequences of the Constitution (103rd Amendment) Act, 2019
In a highly debated reform on the reservation system, the One Hundred and Third Amendment of the Constitution of India provides ten percent reservation to the economically weaker sections (EWS) in the general category. 47 While the language of the act is not clear about 46 See Appendix C.2 for a comprehensive quote from this case. 47 The bill of the One Hundred and Third Amendment of the Constitution of India was introduced in the Lok Sabha-the lower house of the Parliament of India-on 01/08/2019 as the Constitution (One Hundred and whether the EWS reservation is intended as a VR policy or an HR policy, a government memorandum dated 01/31/2019 specifies it as the former: 48

ADJUSTMENT AGAINST UNRESERVED VACANCIES:
A person belonging to EWS cannot be denied the right to compete for appointment against an unreserved vacancy. Persons belonging to EWS who are selected on the basis of merit and not on account of reservation are not to be counted towards the quota meant for reservation.
If the One Hundred and Third Amendment survives the Supreme Court challenge and, implemented as a vertical reservation, it will likely amplify the legal challenges in India due to limitations of MRC-based mechanisms presented in Section 5.5.
It is estimated that, around 26% of the population in India does not belong to the VRprotected categories SC, ST, and OBC. 49 Therefore, in the absence of the new amendment, about 26% of the population belongs to the general category. While the amendment is intended for the economically weaker sections of the general category, according to most estimates more than 80% of the members of this group satisfy the eligibility criteria for the EWS reservation. 50 This means, with the introduction of the EWS reservation, the fraction of the population who are ineligible for VR protections reduces to roughly 5-6% of the population. Therefore, the "new general category," those members of the society who are ineligible for VR protections, shrinks to approximately 5-6% of the whole population. This observation, by itself, is not very important. Indeed, inclusion of another VR-protected category has no impact on the analysis of our proposed mechanism 2SMH-DA, presented in Section 3.3. However, the situation is very different for the MRC-based mechanisms discussed and criticized in Sections 5.2-5.5. The reason is that, with the inclusion of EWS to VR-protected categories, the number of VR-protected individuals who are promoted to the status of MRC will increase significantly. Indeed, the fraction of open positions linked to the MRC candidates will likely change from being a minority to a large majority. 51 Therefore, all the problems we emphasized in Section 5.5 can be expected to be amplified, adding to the legal challenges due to these flawed mechanisms.
This observation can be made most clearly for the UPSC mechanism, analyzed in Section 5.3. In Example 3, we have shown that the cut-off score needed for a VR-protected category can be higher under the UPSC mechanism than it is under the general category. The high number of EWS candidates who are expected to be promoted to the status of an MRC candidates, and the ineligibility of EWS candidates for open positions that are vacated from other EWS candidates under Ramesh Ram (2010), means that the minimum cut-off score could easily be higher for EWS candidates than the "new general category" candidates under the UPSC mechanism. Interestingly, this observation has already been made by the officials, who seem to be in search of a solution. The following quote is from a January 2019 The Hindu story: 52 While ideally the non-reserved 40% open seats should be open seats based on merit, there are complexities here too. For example, the UPSC accepts a reserved candidate in the civil services examination making it in the general merit list as general only if she has not benefited from reservation in the preliminary, mains, service choice (if one gets a better service, say IAS or IPS, due to reservation, one is counted as reserved irrespective of one's overall rank) and State cadre choice (if a reserved candidate is in the general merit list but is getting a cadre of her choice as a reserved candidate, she is counted as reserved), say bureaucrats. So, many who are above the general cut-off may still occupy this 10% quota, as they get a better service or cadre in it.
A senior IAS officer told The Hindu that it is possible that a provision will be made for accommodating those who fall below the 10% EWS quota -in case its cut-off is above the general cut-off due to fewer seats -in the open, or general, seats, but this can give rise to litigation.
We believe our proposed mechanism 2SMH-DA also serves as a natural remedy for this dilemma.

Conclusion
Public institutions in India has long struggled with implementing its constitutionally protected VR and HR policies, when either Many field applications in India such as the allocation of positions for the prestigious All Indian Services (the Indian Administrative Service (IAS), the Indian Police Service (IPS) and the Indian Forest Service (IFS)), and assignment of seats at public educational institutions have both features.
The main challenge for the first complication has been an ambiguity in the legal formulation of the VR policy, originally given in the landmark Supreme Court judgment Indra Sawhney (1992). This ambiguity-which resulted in countless litigations and disruption of recruitment policies in India for the last three decades-has finally been resolved by another important Supreme Court judgment Saurav Yadav (2020). The same judgment also endorsed a mechanism for the joint implementation of VR and HR policies; one that was earlier proposed in Sönmez and Yenmez (2021).
The challenges for the second complication are technically deeper, although a resolution that relies on implementing VR policies across multiple institions with the celebrated deferred acceptance algorithm is straightforward when VR policy is implemented in isolation. 53 However, persons with disabilities is HR protected in India at the federal level, 54 and hence it is vital to implement VR and HR policies together. To the best of our knowledge, no mechanism has been proposed or implemented in India for this general version of the problem.
In this paper we argue that, even though the recent Supreme Court judgment Saurav Yadav (2020) directly concerns applications where all positions are identical, the clarification it has provided for the more general principles originally given in Indra Sawhney (1992) offers a natural resolution for the more general version of the problem with heterogenous positions as well. We propose the 2SMH-DA mechanism, which is a refinement of the celebrated individual-proposing deferred acceptance mechanism (Gale and Shapley, 1962) where each institution is endowed with the choice rule 2SMH (Sönmez and Yenmez, 2021). Not only the 2SMH-DA mechanism Pareto dominates any other mechanism that satisfies the Supreme-Court mandated principles in Saurav Yadav (2020), it is the only strategy-proof mechanism that satisfies all these principles. Hence, we believe, 2SMH-DA mechanism is uniquely suited to implement VR and HR policies when positions are heterogenous.

Appendix A. Additional Terminology and Auxiliary Results
In this appendix, we provide additional terminology and auxiliary lemmas that we use in the proofs.
A.1. Additional Terminology. In this section, we define some terminology to use in the rest of the appendix.
Definition 17. A job matching µ : I → J ∪ {∅} is a function such that, for every j ∈ J , If µ(i) = ∅ for some individual i ∈ I, then the individual is unmatched.

Definition 18.
A choice rule is a function C : 2 I → 2 I such that, for any I ⊆ I, Note that, any single-category choice rule (introduced in Definition 14) is a choice rule. Similarly, any aggregate choice rule (introduced in Definition 16) is also a choice rule.

Definition 19.
A job matching µ is stable with respect to a profile of choice rules (C j ) j∈J if the following three conditions hold: (1) Individual rationality: For each i ∈ I, µ(i) i ∅, (2) Job rationality: For each j ∈ J , C j (µ −1 (j)) = µ −1 (j).
(3) No blocking pairs: There exist no i ∈ I and j ∈ J such that j ≻ i µ(i) and i ∈ C j (µ −1 (j) ∪ {i}).
Definition 20. An assignment α is stable with respect to a profile of multi-category choice rules ( C j ) j∈J if the following three conditions hold: (1) Individual rationality: For each i ∈ I, α(i) i ∅, (2) Job rationality: For each j ∈ J and v ∈ V, C v j (α −1 (j)) = α −1 (j, v).
(3) No blocking pairs: There exist no i ∈ I and j ∈ J such that j ≻ i α(i) and i ∈ C j (α −1 (j) ∪ {i}).
Given an assignment α ∈ A, the job matching µ induced by assignment α is constructed as follows: For each i ∈ I, It is easy to check that µ is a job matching given that α is an assignment. Likewise, for an assignment mechanism, there is an induced job matching mechanism where, for every preference profile of individuals, the outcome of the matching mechanism is the matching induced by the outcome of the assignment mechanism for the preference Definition 24. A choice rule C satisfies the law of aggregate demand if, for every I, I ′ ⊆ I I ′ ⊇ I =⇒ |C(I ′ )| ≥ |C(I)|. Lemma 6. The aggregate choice rule C 2s M ,j satisfies the law of aggregate demand.
Definition 26. Let I ⊆ I be a set of individuals such that, for every i ∈ I, job j is acceptable to individual i. A multi-category choice rule C j = (C v j ) v∈V satisfies maximal accommodation of HR protections for I, if for each v ∈ V, and i ∈ (I ∩ I v ) \ C j (I), Definition 27. Let I ⊆ I be a set of individuals such that, for every i ∈ I, job j is acceptable to individual i. A multi-category choice rule C j = (C v j ) v∈V satisfies no justified envy if, for , which establishes that assignment α satisfies maximal accommodation of HR protections.
Proof. Fix a preference profile ≻ I = (≻ i ) i∈I ∈ P. Let assignment α = ϕ 2s M (≻ I ) be the outcome of mechanism 2SMH-DA for ≻ I . Consider i ∈ I, j ∈ J , v ∈ V, and i ′ ∈ I v such that α(i) = (j, v) and j ≻ i ′ α(i ′ ). To prove that 2SMH-DA satisfies no justified envy, we need to establish that, (2) for each i ′ ∈ I with α(i ′ ) = (j, o), we have with respect to ( C 2s M ,j ) j∈J , we need to show job rationality and the absence of blocking pairs when each job j ∈ J is endowed with the multi-category choice rule C 2s M ,j . For each j ∈ J , defineĨ j = {ĩ ∈ I : j ĩ α(ĩ)}. Since α is individually rational, for everyĩ ∈Ĩ j , job j is acceptable to individualĩ. Claim 1. For each j ∈ J and v ∈ V, , and, for each j ∈ J , C 2s M ,j (Ĩ j ) = α −1 (j).
Proof. Given a job j ∈ J and category v ∈ V, construct a single-category choice rule C v j as follows. For each I ⊆ I, Since α is an assignment and C 2s M ,j is a multi-category choice rule, C j = (C v j ) v∈V is also a multi-category choice rule. We next show that, for each job j ∈ J , C j satisfies non-wastefulness forĨ j , maximal accommodation of HR protections forĨ j , no justified envy forĨ j , and compliance with VR protections forĨ j .
Maximal accommodation of HR protections forĨ j : Let v ∈ V and i ∈ (Ĩ j ∩ I v ) \ C j (Ĩ j ).
By construction, we have j ≻ i α(i). Since α satisfies maximal accommodation of HR protections and function n v j is monotone, we have Therefore, C j satisfies maximal accommodation of HR protections forĨ j .
Compliance with VR protections forĨ j : Let c ∈ R and i ∈ C c j (Ĩ j ). By construction, i ∈ α −1 (j, c). Since α satisfies condition (1) of the axiom compliance with VR protections, we have |α −1 (j, o)| = r o j , or equivalently Furthermore, for each i ′ ∈ C o j (Ĩ j ), we have α(i ′ ) = (j, o), and since α satisfies condition (2) of the axiom compliance with VR protections, we have ∪{i} .
Hence, C j complies with VR protections forĨ j .
We have established that, for any job j ∈ J , the multi-category choice rule C j satisfies non-wastefulness forĨ j , maximal accommodation of HR protections forĨ j , no justified envy forĨ j , and compliance with VR protections forĨ j . By Lemma 9, C v j (Ĩ j ) = C 2s,v M ,j (Ĩ j ) for each v ∈ V. Therefore, for each j ∈ J and v ∈ V, α −1 (j, v) = C v j (Ĩ j ) = C 2s,v M ,j (Ĩ j ), and, so, for each j ∈ J , α −1 (j) = v∈V α −1 (j, v) = v∈V C 2s,v M ,j (Ĩ j ) = C 2s M ,j (Ĩ j ), completing the proof of Claim 1.
(I) At the initial stage when the ''Open or General Category'' seats are to be filled, the claim of all reserved category candidates based on merit must be considered and if any candidates from such reserved categories, on their own merit, are entitled to be selected against Open or General Category seats, such placement of the reserved category candidate is not to affect in any manner the quota reserved for such categories in vertical reservation.
(II) However, when it comes to adjustment at the stage of horizontal reservation, even if, such reserved category candidates are entitled, on merit, to be considered and accommodated against Open or General Seats, at that stage the candidates from any reserved category can be adjusted only and only if there is scope for their adjustment in their own vertical column of reservation.
Such exercise would be premised on following postulates: -(A) After the initial allocation of Open General Category seats is completed, the claim or right of reserved category candidates to be admitted in Open General Category seats on the basis of their own merit stands exhausted and they can only be considered against their respective column of vertical reservation.
(B) If there be any resultant adjustment on account of horizontal reservation in Open General Category, only those candidates who are not in any of the categories for whom vertical reservations is provided, alone are to be considered.
(C) In other words, at the stage of horizontal reservation, Open General Category is to be construed as category meant for candidates other than those coming from any of the categories for whom vertical reservation is provided.
25. The second view may lead to a situation where, while making adjustment for horizontal reservation in Open or General Category seats, less meritorious candidates may be adjusted, as has happened in the present matter. Admittedly, the last selected candidates in Open General female category while making adjustment of horizontal reservation had secured lesser marks than the Applicants. The claim of the Applicants was disregarded on the ground that they could claim only and only if there was a vacancy or chance for them to be accommodated in their respective column of vertical reservation.
[...] 31. The second view is thus neither based on any authoritative pronouncement by this Court nor does it lead to a situation where the merit is given precedence. Subject to any permissible reservations i.e. either Social (Vertical) or Special (Horizontal), opportunities to public employment and selection of candidates must purely be based on merit.
Any selection which results in candidates getting selected against Open/General category with less merit than the other available candidates will certainly be opposed to principles of equality. There can be special dispensation when it comes to candidates being considered against seats or quota meant for reserved categories and in theory it is possible that a more meritorious candidate coming from Open/General category may not get selected. But the converse can never be true and will be opposed to the very basic principles which have all the while been accepted by this Court. Any view or process of interpretation which will lead to incongruity as highlighted earlier, must be rejected.
32. The second view will thus not only lead to irrational results where more meritorious candidates may possibly get sidelined as indicated above but will, of necessity, result in acceptance of a postulate that Open / General seats are reserved for candidates other than those coming from vertical reservation categories. Such view will be completely opposed to the long line of decisions of this Court. and complete the select list for 457. Having done this exercise, the respondents should apply Rule 16 (2) to ensure that allocation of the service is in accordance with rank-cum-preference with priority given to meritorious reserved candidates for service allocation by virtue of Rule 16 (2) which is as per para 5 of Anurag Patel order. The entire exercise, as directed above, should be completed as per the order.
(iii) Applying the ratio of Anurag Patel decision of Hon'ble Apex Court (Paras 6 & 7), if there is need for re-allocation of services, the respondents will take appropriate measures to that extent and complete this process also within two months from the date of receipt of a copy of this order." The CAT had also issued the following direction as to how the results of the UPSC examinations (2005) should have been announced: ''If the UPSC had followed the decision of the Hon'ble Apex Court cited supra and released the select list in one go for all the 457 vacancies then it would have ensured that the select list contained not only 117 OBCs but also an additional number of OBC candidates by this number, in additional to 117 under 27% reservation, while simultaneously be number of general candidates recruited will be less to the extent of OBCs recruited on merit and included in the general list in the result of Civil Services Examination, 2005. Once this order is met, the successful candidates list will include 242 candidates in the General Category which is inclusive of all those Reserved Category candidates coming on merit plus 117 OBC, 57 SC and 41 ST exclusively from these respective reserved categories by applying relaxed norms for them.. If such a list is subjected to Rule 16(2) of Civil Services Examination, 2005 in present form for making service allocation only and then services are allotted based on Rule 16(2) in this context, then the announcement of recruitment result and allocation services will be both in accordance with law as per various judgments the Hon'ble Apex Court and in accordance with the extent orders issued by the Respondent No.1 and also in keeping with spirit of Rule 16 (2) so that, the meritorious reserved candidates get higher preference service as compared to their lower ranked counter parts in OBC, ST,SC. In doing so, the respondents also would notice that the steps taken by them in accordance with the Rules 16 (3)(-)(5) are redundant once they issue the result of recruitment in one phase, instead of two as they have become primary cause for the litigation and avoidable confusion in the minds of the candidates seeking recruitment.''