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Improving Community Cohesion in School Choice via Correlated-Lottery Implementation
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Improving Community Cohesion in School Choice via Correlated-Lottery Implementation
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Improving Community Cohesion in School Choice via Correlated-Lottery Implementation
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Journal Article
Improving Community Cohesion in School Choice via Correlated-Lottery Implementation
2014
Overview
In school choice, children submit a preference ranking over schools to a centralized assignment algorithm, which takes into account schools’ priorities over children and uses randomization to break ties. One criticism of existing school choice mechanisms is that they tend to disperse communities, so children do not go to school with others from their neighborhood. We suggest improving community cohesion by implementing a
correlated lottery
in a given school choice mechanism: we find a convex combination of deterministic assignments that maintains the original assignment probabilities, thus maintaining choice but improving community cohesion. To analyze the gain in cohesion for a wide class of mechanisms, we first prove the following characterization, which may be of independent interest: any mechanism that, in the large market limit, is nonatomic, Bayesian incentive compatible, symmetric, and efficient within each priority class is a “lottery-plus-cutoff” mechanism. This means that the large market limit can be described as follows: given the distribution of preferences, every student receives an identically distributed lottery number, every school sets a lottery cutoff for each priority class, and a student is assigned to her most preferred school for which she meets the cutoff. This generalizes liu-pycia-2012 to allow arbitrary priorities. Using this, we derive analytic expressions for maximum cohesion under a large market approximation. We show that the benefit of lottery-correlation is greater when students’ preferences are more correlated. In practice, although the correlated-lottery implementation problem is NP-hard, we present a heuristic that does well. We apply this to real data from Boston elementary school choice 2012 and find that we can increase cohesion by 79% for kindergarten 1 (K1) and 37% for kindergarten 2 (K2) new families. Greater cohesion gain is possible (tripling cohesion for K1 and doubling for K2) if we reduce the choice menus on top of applying lottery correlation.
