Affirmative action and school choice

• Date: 01 September 2014
• Author: Begoña Subiza,José Alcalde
• Published date: 01 September 2014
• DOI: http://doi.org/10.1111/ijet.12038

doi: 10.1111/ijet.12038

Affirmative action and school choice

Jos´

e Alcalde∗and Bego˜

na Subiza†

This paper studies a way of introducing affirmative action in the school choice problem to

implement integration policies. The paper proposes the use of a natural two-step mechanism.

The (equitable) first step is introduced as an adaptation of the deferred-acceptance algorithm

designed by Gale and Shapley, when students aredivided into two groups. The (efficient) second

step captures the idea of exchanging places inherent to Gale’s top trading cycle.

Key wor ds integration policy, school allocation, affirmativea ction

JEL classification C72, I28, J18

Accepted 25 October 2013

1 Introduction

Affirmative action policies can be seen, in a static setting, as discriminatory practices; whereas, from

a dynamic perspective, the existence of a certain degree of “historical discrimination” justifies the

use of affirmative action policies, as a necessary previous step, before concentrating on avoiding

discriminatory practices. In other words, policies against circumstantial discrimination are useless

if they are not accompanied by measures to reduce structural inequalities. Evidence suggests that

the “long run” arguments have prevailed, which is why, for instance, the OECD countries explicitly

implemented affirmative action measures to reach integration objectives.

The presentpaper deals w ith the debate on affirmativeaction measures versus non-discriminatory

practices. Our point is that these policies should cease to exist when the effects of “historic discrimi-

nation practices” are dissipated. Therefore, it is important to concentrate onhow these “everlasting”

inequalities could be reduced. In this sense, we believe that the educational training of “future gener-

ations” is one of the most relevant variables to take into account, as whenever childrenhave unequal

opportunities to achieve a comparable educational level, in the broadest sense, they will not be able

to compete fairly in the job market. Moreover, since there is empirical evidence to show the positive

correlation between school quality and housing prices in their “influence areas” (see, for instance,

Kane et al., 2006; Dougherty et al., 2009), and one of the two main factors for a student to be attached

to a certain school is to reside in its “influence area,” the main conclusion is that the non-application

of affirmative action measures, in favor of certain population groups, will lead to a more inequitable

income distribution in the long run.

This is why we analyze how to redesign school allocation procedures as a way to reduce certain

inter-group inequalities. To reach our objective we introducea two-step procedure. For the first step,

∗Department of Quantitative Methods and Economic Theory and IUDESP,University of Alicante, Alicante, Spain. Email:

jose.alcalde@ua.es

†Department of Quantitative Methods and Economic Theory and IUDESP,University of Alicante, Alicante, Spain.

We wish to thank Teodosia del Castillo, Josep E. Peris, PabloRevilla, Antonio Romero-Medina, the participants at the

MECA Seminar, and two refereesfor their useful comments.

International Journal of Economic Theory 10 (2014) 295–312 © IAET 295

International Journal of Economic Theory

Affirmative action and school choice Jos´

e Alcalde and Bego˜

na Subiza

we suggest a tentative allocation procedurewith a minimal segregation level.1Thesecondstepadopts

the idea of trading places, proposed by Alcalde and Romero-Medina (2011) to attain efficiency in

the allocation process.

Concerning the first step, we distribute each school quota among the different groups of agents2

in such a way that (if possible) each group has a number of “reserved places” and the share of

assigned places is equitable between groups. Note that such a division allows one isolated school

choice problem to be considered for each group.We then propose an initial distribution of its school

places for each group, satisfying “internal non-justified envy.”3This objective is reached by applying

(a modified version of) the classical “deferred-acceptance algorithm”introduced by Gale and Shapley

(1962). This algorithm is applied to each group separately.

Once this first step is finished, we can proceed toan “integr ate”second step, the main objective of

which is to achieve improvements,in terms of efficiency, related to the previous distribution without

increasing the segregation level.4

We wish to stress that by integration policies we do not necessarily mean racial policies for

integration. This term should be understood as widely as possible. For instance, some policy-makers

could be interested in gender integration by reducing the structural gap favoring men over women;

others might well be interested in income-based integration by helping children from low-income

families to access high-income district schools. What is important in this paper is that, once the

policy-makers have decided which specific integration policy they are interested in, the population

is partitioned into mutually exclusive groups; and therefore, no agent is free to decide which group

she belongs to. In this way we avoid certain types of strategic behavior.

The problem we study here can be viewed as a many-to-one, two-sided matching problem,

following the original model by Gale and Shapley (1962). Similar models have been used to study,

both from a positive and a normative point of view, how several specific markets work or would be

redesigned. For the case of school allocation, some recent papers explore the former Boston system

and propose modifications to reach a better allocation process (Abdulkadiro˘

glu et al., 2005b, 2006;

Ergin and S¨

onmez, 2006), while others suggest improvements to the current Boston system (Kesten,

2010; Alcalde and Romero-Medina, 2011); the New York City system for high schools has also been

explored in some papers (Abdulkadiro˘

glu et al., 2005; Abdulkadiro˘

glu et al., 2009).

Nevertheless, as far as we know, not many papers explore the school admission problem taking

into account the possibility of affirmative action ingredients. Abdulkadiro˘

glu (2005) deals with

college admissions, and considersthat the colleges are the only agents that decide how their affirmative

action policy should be implemented, and each college should respect a predetermined type-specific

quota. Then he proposes a strategic analysis for the student optimal stable matching mechanism.By

contrast, in the present paper, we considerthat schools do not have any capacity to influence the way

in which their places are ex ante distributed among the different groups of agents. Our interest is not

in global stability, as in Abdulkadiro˘

glu (2005), but internal stability plus inter-group fairness, which

1Frankel and Volij(2011) propose an exhaustive analysis for segregation indexes. Our approachdiffers from that of Frankel

and Volij (2011) as our aim does not considerthe different districts into which each municipality is divided, but rather

each municipality as a whole.

2Although our model, in Section 2, deals with two-group problems, our results are straightforwardly extended to any

number of population groups. What is important is that the number of available places at each school is high enough to

distribute them among the groups by guaranteeing some diversity representation at each school.

3The term non-justified envy was coined by Abdulkadiro˘

glu and S¨

onmez (2003) to reinterpret, in the framework of school

allocation, the classical notion of stability in matching problems.

4In an earlier version of this paper (Alcalde and Subiza, 2012), we also considerimprovements in terms of global efficiency

by allowing reductions of the integration level.

296 International Journal of Economic Theory 10 (2014) 295–312 © IAET