Related papers: The study of a new gerrymandering methodology
How to fairly apportion congressional seats to states has been debated for centuries. We present an alternative perspective on apportionment, centered not on states but "families" of state, sets of states with "divisor-method" quotas with…
Gerrymandering is the perversion of an election based on manipulation of voting district boundaries, and has been a historically important yet difficult task to analytically prove. We propose a Markov Chain Monte Carlo with Simulated…
We develop effective methods for constructing an ensemble of district plans via independent sampling from a reasonable probability distribution on the space of graph partitions. We compare the performance of our algorithms to that of…
In the context of modern sampling methods for redistricting, we define a natural measurement of the clustering of a political party, and we study how clustering affects the expected election outcome. We first prove general results and then…
Political districts may be drawn to favor one group or political party over another, or gerrymandered. A number of measurements have been suggested as ways to detect and prevent such behavior. These measures give concrete axes along which…
We explore the Declination, a new metric intended to detect partisan gerrymandering. We consider instances in which each district has equal turnout, the maximum turnout to minimum turnout is bounded, and turnout is unrestricted. For each of…
Redistricting practitioners must balance many competing constraints and criteria when drawing district boundaries. To aid in this process, researchers have developed many methods for optimizing districting plans according to one or more…
In parliamentary elections, parties compete for a limited, typically fixed number of seats. Most parliaments are assembled using apportionment methods that distribute the seats based on the parties' vote counts. Common apportionment methods…
This paper presents a graph bundling algorithm that agglomerates edges taking into account both spatial proximity as well as user-defined criteria in order to reveal patterns that were not perceivable with previous bundling techniques. Each…
We model the societal task of redistricting political districts as a partitioning problem: Given a set of $n$ points in the plane, each belonging to one of two parties, and a parameter $k$, our goal is to compute a partition $\Pi$ of the…
Map makers have long searched for a way to construct cartograms -- maps in which the sizes of geographic regions such as countries or provinces appear in proportion to their population or some other analogous property. Such maps are…
This article introduces the 50stateSimulations, a collection of simulated congressional districting plans and underlying code developed by the Algorithm-Assisted Redistricting Methodology (ALARM) Project. The 50stateSimulations allow for…
Individual fairness, proposed by Dwork et al., is a fairness measure that is supposed to prevent the unfair treatment of individuals on the subgroup level, and to overcome the problem that group fairness measures are susceptible to…
We introduce a non-partisan probability distribution on congressional redistricting of North Carolina which emphasizes the equal partition of the population and the compactness of districts. When random districts are drawn and the results…
This paper is part of an ongoing endeavor to bring the theory of fair division closer to practice by handling requirements from real-life applications. We focus on two requirements originating from the division of land estates: (1) each…
Assuming that partisan fairness and responsiveness are important aspects of redistricting, it is important to measure them. Many measures of partisan bias are satisfactory for states that are balanced with roughly equal proportions of…
Size uniformity is one of the main criteria of superpixel methods. But size uniformity rarely conforms to the varying content of an image. The chosen size of the superpixels therefore represents a compromise - how to obtain the fewest…
In a district-based election, we apply a voting rule $r$ to decide the winners in each district, and a candidate who wins in a maximum number of districts is the winner of the election. We present efficient sampling-based algorithms to…
Inverse optimization has received much attention in recent years, but little literature exists for solving generalized mixed integer inverse optimization. We propose a new approach for solving generalized mixed-integer inverse optimization…
Packing disjoint subgraphs in a given graph is a fundamental problem with many applications. Motivated by political districting, we focus on connected subgraphs that are compact (e.g., having constant radius from a single center vertex) and…