Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2511.19722

Individual and group fairness in geographical partitioning

Ilya O. Ryzhov·John Gunnar Carlsson·Yinchu Zhu
View original source ↗Read source document ↗Export metadata ↓

Abstract

Socioeconomic segregation often arises in school districting and other contexts, causing some groups to be over- or under-represented within a particular district. This phenomenon is closely linked with disparities in opportunities and outcomes. We formulate a new class of geographical partitioning problems in which the population is heterogeneous, and it is necessary to ensure fair representation for each group at each facility. We prove that the optimal solution is a novel generalization of the additively weighted Voronoi diagram, and we propose a simple and efficient algorithm to compute it, thus resolving an open question dating back to Dvoretzky et al. (1951). The efficacy and potential for practical insight of the approach are demonstrated in a realistic case study involving seven demographic groups and $78$ district offices.

Explore related subjects

econ.EMcs.LG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ilya O. Ryzhov, John Gunnar Carlsson, Yinchu Zhu. 2025-11-24. Individual and group fairness in geographical partitioning. https://arxiv.org/abs/2511.19722

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Conditional-Moment Estimation and Inference in the BLP Model

The random-coefficient demand model of Berry, Levinsohn, and Pakes (1995) is commonly estimated by the generalized method of moments (GMM), using an unconditional moment restriction with a fixed set of instruments. Identification of the model, however, rests on a conditional moment restriction. The two are not equivalent: the unconditional restriction may admit additional parameter values. We construct a counterexample in which the model is identified by the conditional restriction yet standard GMM is not, even with the optimal instrument. Building directly on the identifying restriction, we propose a two-step estimator, following Ai and Chen (2003), that first estimates the relevant conditional expectations nonparametrically and then selects the structural parameters by a conditional-variance-weighted minimum-distance criterion; standard GMM is recovered as the special case of a linear projection onto finitely many instruments. We establish root-T asymptotic normality for the proposed estimator, and we develop the theory for both kernel and series implementations of the first stage. The two implementations share a common limiting distribution, attaining the semiparametric efficiency bound. Simulation evidence illustrates the consequences of the identification gap and demonstrates that the proposed estimator outperforms standard GMM in finite samples.

econ.EM↗
arXiv2026

Generic Covariate Adjustment for Regression Discontinuity Designs

It is standard practice to include covariates in regression discontinuity designs (RDDs) and regression kink designs (RKDs), but the theoretical justification for doing so does not generally extend beyond linear estimands. This paper proposes a novel entropy balancing reweighting approach for covariate adjustment within a general framework of RDDs and RKDs. While conventional regression-based covariate adjustment methods generally fail to deliver consistent estimation for nonlinear estimands such as quantile treatment effects, our reweighting approach achieves consistency while improving efficiency. Moreover, even in settings where the regression-based covariate adjustment method already improves efficiency, our approach can deliver additional efficiency gains. Simulation studies corroborate these theoretical findings. We present an empirical application in which our covariate adjustment yields statistically significant results that would not be obtained without covariate adjustment.

econ.EM↗
arXiv2026

Kernel Balancing in Tree-based Methods

Studying heterogeneous treatment effects has become essential in experimental and observational studies. A critical assumption for obtaining reliable treatment effect estimates is overlap, which requires that treated and control units have sufficiently similar covariate distributions. Poor overlap may limit the effectiveness of estimators, especially those based on propensity scores, potentially leading to unreliable results. We investigate the effectiveness of kernel balancing (KBal) (Hazlett, 2020) as an alternative to propensity score methods for conditional average treatment effect (CATE) estimation, particularly in settings with overlap violations. Building on optimization-based balancing approaches, we integrate KBal weights into tree-based methods, specifically, causal forests (Athey et al., 2019) and the X-Learner (XRF) (Künzel et al., 2019), to assess their impact on bias reduction and estimation precision. Monte Carlo evidence shows that KBal achieves near-exact balance in a transformed feature space, thereby improving treatment effect estimation in cases where traditional reweighting methods struggle due to extreme weights, finite-sample bias, or insufficient removal of pre-existing confounding bias. We apply the proposed methods to the semi-synthetic IHDP benchmark dataset. Overall, the results indicate that KBal leads to performance improvements, especially in settings with nonlinear treatment effects and limited overlap, making it a useful alternative to propensity score methods.

econ.EM↗