Reserve Design: Unintended Consequences and the Demise of Boston’s Walk Zones

Abstract

Admissions policies often use reserves to grant certain applicants higher priority for some (but not all) available seats. Boston's school choice system, for example, reserved half of each school's seats for local neighborhood applicants while leaving the other half for open competition. This paper shows that in the presence of reserves, the effect of the precedence order (i.e., the order in which different types of seats are filled) on distributional objectives is comparable to the effect of adjusting reserve sizes. Either lowering the precedence order positions of reserve seats at a school or increasing the number of reserve seats weakly increases reserve-group assignment at that school. Using data from Boston, we show that reserve and precedence adjustments have similar quantitative effects. Our results illustrate that policies about precedence, heretofore underexplored, are inseparable from other aspects of admissions policy. Moreover, our findings explain the puzzling empirical fact that despite careful attention to the importance of neighborhood priority, Boston's implementation of its 50-50 reserve-open seat split was nearly identical to the outcome of a counterfactual system without any reserves. Transparency about these issues-in particular, how precedence unintentionally undermined the intended admissions policy-led to the elimination of Boston's walk zones.JEL: C78, D50, D61, D67, I21

Lexicographic Choice Under Variable Capacity Constraints

“…On the other hand, variable capacities, and properties related to variable capacities, are at the heart of our study. We show that, one of our variable capacity properties, CWARP, is satisfied by only one of the four choice rules discussed in Dur et al (2013).…”

“…To achieve this goal, the Boston school district has been using a deferred acceptance mechanism based on a choice structure, where each school is endowed with a "capacity-wise lexicographic" choice rule, that is, at each capacity, the choice rule lexicographically operates based on a list containing as many priority orderings as the capacity, yet the lists for different capacity levels do not have to be related in any way. 11 Dur et al (2013) and Dur et al (2018) analyse how the order of the priority orderings in the choice rule of a school may cause additional bias for or against the neighbourhood students. 12 In Section 5, we consider a class of capacity-wise lexicographic choice rules discussed in Dur et al (2013) that are relevant for the design of the Boston school choice system and show that our analysis enables us to single out one rule from four plausible candidates.…”

“…11 Dur et al (2013) and Dur et al (2018) analyse how the order of the priority orderings in the choice rule of a school may cause additional bias for or against the neighbourhood students. 12 In Section 5, we consider a class of capacity-wise lexicographic choice rules discussed in Dur et al (2013) that are relevant for the design of the Boston school choice system and show that our analysis enables us to single out one rule from four plausible candidates.…”

“…Our analysis of the Boston school choice system is related to Dur et al (2018) and the working paper version Dur et al (2013). Dur et al (2013) compare alternative choice rules for schools in the Boston school district (one of which is the one used in the Boston school district) in terms of how much they are biased for or against the neighbourhood students. We consider these alternative choice rules from a different perspective.…”

“…In Section 5, we show that, although these choice rules are all based on a "lexicographic procedure" at each capacity, only one of them satisfies all the characterizing properties in Theorem 1, and therefore only one of them is actually a (capacity-constrained) lexicographic choice rule. The common feature of Dur et al (2018) and our Section 5 is that we both consider lexicographic choice procedures in the context of school choice in Boston. The main difference is that, although the choice rules that Dur et al (2018) consider have direct counterparts in a variable capacity context, their analysis pertains to the fixed capacity case.…”