Student Workshop: Mathematics of Gerrymandering

Introduction

Each state of the U.S. is divided into a number of Congressional districts. The Congressional districts within a state must satisfy certain criteria, such as being of roughly equal population (though variances are permitted: e.g., geographic restrictions, not splitting a county between districts, etc.). But the district lines might also be drawn to give one party or minority group a majority in a district: this is a partisan or racial gerrymander. While the Supreme Court has ruled that these are unconstitutional, the Court has not yet identified a workable measure of whether or not a districting plan is a partisan or racial gerrymander.

The Problem

Suppose the supporters of each party are uniformly distributed throughout the region, and party supporters vote along party lines. Then, given any regular division of the region, one party wins all districts. Thus some distortion of the district lines is necessary to give all parties some chance of winning some seats. How much distortion should we allow?

Outline of Workshop

After an introduction to the basic parameters, participants will be divided into two or more groups and be given the same map of a “state” with voter partisan affiliations indicated. The groups will then be tasked with dividing the state into Congressional districts in a way that maximally benefits their party.

Part One

Ways to measure the level of gerrymandering will be discussed.

Part Two

Ways to set an allowable level of gerrymandering will be discussed.