Envy-Free School Redistricting Between Two Groups
Daisuke Shibatani, Yutaro Yamaguchi

TL;DR
This paper explores fair school redistricting between two groups, introducing a relaxed envy-freeness concept that guarantees a fair allocation with limited capacity violations, and provides a polynomial-time algorithm for finding such allocations.
Contribution
It introduces 1-relaxed envy-freeness for two-group redistricting and proves the existence and polynomial-time computability of such allocations.
Findings
Existence of 1-relaxed envy-free allocations for two groups.
Polynomial-time algorithm for finding these allocations.
Limited capacity violations at each school.
Abstract
We study an application of fair division theory to school redistricting. Procaccia, Robinson, and Tucker-Foltz (SODA 2024) recently proposed a mathematical model to generate redistricting plans that provide theoretically guaranteed fairness among demographic groups of students. They showed that an almost proportional allocation can be found by adding extra seats in total, where is the number of groups. In contrast, for three or more groups, adding extra seats is not sufficient to obtain an almost envy-free allocation in general, where is the total number of students. In this paper, we focus on the case of two groups. We introduce a relevant relaxation of envy-freeness, termed 1-relaxed envy-freeness, which limits the capacity violation not in total but at each school to at most one. We show that there always exists a 1-relaxed envy-free allocation, which can…
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Taxonomy
TopicsGame Theory and Voting Systems · Politics, Economics, and Education Policy · Economic Policies and Impacts
