A Gerrymandering Metric

I’m trying to study for my Mathematics course and I need some help to understand this question.

Please see the attached pdf file for full requirement thx

As you found in Freedonia, drawing district boundaries can lead to dramatically different electoral outcomes based on the same votes, and that this process can be used to maximize political power. The process of drawing district boundaries to maximize political power is called gerrymandering . In this paper, you’ll attempt to measure its effects.

In October 2017, the Supreme Court heard arguments in Gill v. Whitford, concerning gerrymandering in Wisconsin during the redistricting process following the 2010 census. A lower court measured political gerrymandering in the Wisconsin legislative district map with a metric called the “efficiency gap,”[1] computed as the ratio of difference in “wasted votes” to the total votes cast. In June 2018, the Supreme Court decided the case on technical grounds without discussing the merits of the case. In a related case from Maryland and North Carolina, the Supreme Court decided in June 2019 that partisan gerrymandering is permissible unless state or federal legislatures decide differently.

1) Read the two articles written after the Supreme Court heard arguments in Gill v. Whitford.

> Here’s How the Supreme Court Could Decide Whether Your Vote Will Count By Darla Cameron, Washington Post, October 4, 2017 https://www.washingtonpost.com/graphics/2017/polit…

> How the New Math of Gerrymandering Works By Nate Cohn and Quoctrung Bui, New York Times, October 3, 2017 https://www.nytimes.com/interactive/2017/10/03/ups… gerrymandering-works-supreme-court.html

2) Return to the four maps you drew in Paper 1 – Redistricting in Freedonia. If you haven’t yet drawn those maps, now is a good time to do so. Measure the “efficiency gap” for each map.

3) Consider the second map, drawn by advocates for the Nationalist Party, which only a minority of Freedonians support. It’s possible to draw a map where the Nationalist Party wins elections for a large majority of the seats in the legislature. (If you haven’t yet drawn such a map, do so now.) This map is designed to waste as many Popular Front votes as possible, so it will have a large efficiency gap favoring the Nationalist Party. > While maintaining the maximum legislative majority in favor of the Nationalist Party, determine the minimum possible efficiency gap. What’s the smallest efficiency gap you can produce? Draw such a map. > While keeping the efficiency gap under 7% — the standard that the Supreme Court rejected as a measure of partisan gerrymandering — determine the maximum number of legislative seats that the Nationalist Party can win. Compare this number with the number of seats you’d expect the Nationalist Party to win based strictly on their proportion of voters in Freedonia.

4) Write a few paragraphs reflecting on your experience working with the efficiency gap as a measure of gerrymandering.