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The Gerrymandering Problem in America and Solution to It

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The Census has been a staple in the United States Government since Washington’s presidency. The sixth line of The Constitution introduces the idea of counting the population to better create a fair representative government, “​The actual Enumeration shall be made within three Years after the first Meeting of the Congress of the United States, and within every subsequent Term of ten Years, in such Manner as they shall by Law direct.” ​Ever since, the census has been used not only to choose amount of representatives for states, but to also redistrict and determine the borders of counties. Redistricting is a necessary process which is needed for our government to work smoothly and to ensure equity throughout the states of different populations. Redistricting should therefore be a nonpartisan matter, and should be conducted by a third party whose sole interest is creating fair districts. The power of redistricting resides in the hands of the state legislature, which is then approved by the governor. If one party holds power, it is very easy for that party to redistrict the state such that the one party can win votes and in turn, future elections. 

As the population of the United States grew, certain individuals determined that it was in the parties’ best interest to do what is now called Gerrymandering, the redistricting of a state in a partisan manner such that one party can be in control. While the name Gerrymandering may seem random it is named after Elbridge Gerry, the Governor of Massachusetts in 1812. In 1812, Elbridge Gerry was in control of the redistricting of Massachusetts. Gerry redistricted counties surrounding Boston such that it created a bizarre shape of South Essex, which in turn allowed for the Democratic-Republican Candidates to hold power over the Federalists. Certain Federalist writers were quick to call his new creation a monster, some even calling it what appeared to be a Salamander. Quick to their pens, these Federalist deemed the new creature a Gerrymander, a portmanteau of the Governor’s last name and the word salamander.

While Gerrymandering seems to just be a partisan way to gain votes, many in charge have also used it to also gain social and racial power. It is human nature to group with those who are similar to themselves and, in addition to socio-economic pressure, ethnicities and races tend to live together. This made it very easy for certain individuals to disadvantage minorities. But in the Voting Rights Act of 1960, it became law that legislators could not use the power of redistricting to suppress black voters. An example of this was Shaw vs. Reno in 1993, when a North Carolina legislator put all cities into one district, thus packing all minority and urban voters into one district and minimizing their votes. This is a difficult matter when you ask a Political Scientist, as it is important to redistrict in a way such that minorities are represented by those who have similar experiences to them, while also making it such that districts do not suppress them. This is why, when redistricting, we cannot create square counties or states. By creating arbitrary lines, minorities’ voices become silenced and therefore there would become a tyranny of the majority. A key example of this is given below. While the district appears to be Gerrymandered, which typically has a bad connotation, instead, the green are two Latino communities and the space in between them is a heavily African American community. If it was possible to redistrict a country so that each county and district are perfect squares, without social or political pushback, I believe it would have been done already. However, people do not live in boxes, and communities in this country are filled with a diverse group of people and geographical locations. Before it is possible to determine what is wrong with our current system, as well as propose new ways to redistrict our country, we must first understand how legislatures divide communities presently. 

As I stated before, it is illegal to Gerrymander to suppress racial groups. However, it is not illegal to Gerrymander to suppress voters of opposing parties. To advantage one’s own party, legislatures either crack or pack. By cracking, one spreads out the minority group so that they do not have any representatives. By packing, legislatures put all political minorities in a compact district, and in turn gives them as little representatives as possible. A key example of packing was when Michigan was Gerrymandered in 2010. Even though the voting percentage of Democrats and Republicans were approximately the same over the four year period, due to the redistricting Democrats were condensed into districts, giving Republicans power in elections. To create a fair system, one must allow for there to be representatives that equally represent each individual in their state. For example, if a state has a 40% blue population and a 60% red, representatives should be 40% blue and 60% red. 

To create an even fairer system, one must also include racial, cultural, and economic representatives. By looking at the issues with the republic, many mathematicians have taken to geometry and graph theory to determine proper ways to mathematically fix the system. While there is a diverse amount of solutions presented, one that has merit in proving that there is a better mathematical way is the graph partitioning method. To understand how to graph-partition, we must understand the different vocabulary and variables. While for graph-partitioning we will be using vertices, these vertices, v, will be representing census block groups. Census Block groups are a way that the government splits the country into smaller groups. These Census Block groups are small communities, and districts are made up of Block Groups, which are made up of Census Block groups. 

To figure out how to make equally weighted groups, we must combine Census Block groups and connect them in graphs, G. Each vertex will be given a specific rank or weight determined by how many live in the area. We will connect these vertices together through edges. (Doyle, 42) Census Block groups are the smallest political grouping of an area, and therefore census block groups are typically one party. This is why for each vertex we can denote either blue or red, representing either democratic or republican. For the sake of explaining how to complete this process, I will be looking at a small area. After we accomplish this, we will be able to show it, through computer programs, on a nationwide scale. Given an area, drawn in figure 4, due to population distribution, the government has deemed that it is composed of 7 census blocks. 

We are given the task of changing this map into 2 districts. The block shown is split 50% democratic and 50% republican, which means we must then split the census blocks in the same percentage to have a fair division. ‘So that it is simpler, there has already been coarsening performed this graph. Originally, we would have each individual be represented by a vertex, which is then turned into this weighted graph. Although, in real maps, there will be a decent amount of people living in each census block, for our explanation we will give each census block a weight of either 1-7, each census block having the weight of their number. This map can then be turned into a graph. Due to the fact that in our original graph there is only one edge in between every different cell block, and we are ignoring the weighting of the original graph, the weight of each edge is therefore 1. 

To get the smallest amount of edge cutting, we must find the maximum matching. (Soberon) In our graph above, we can find matchings with 1 & 2, 3 & 4, and 5 & 6, leaving 7, our most weighted vertex, out of the matching. By completing this, we can then make a minimum amount of Democratic and Republican groupings. By adding the weights of the new vertices together, we can then look at better ways to divide this section up into Republican and Democratic districts. If we denote 1 &2 and 5 & 6 as a republican district, and 3 &4 and 7 as a Democratic district, as 1 + 2 + 5 + 6 = 3 + 4 + 7, then we can create two split districts. 

Next, we can uncoarse the graph, and go back to our original graph, now with red and blue Census block groups. The red lines are edges that are connecting like colored vertices. However, when we create two districts, there is no way to connect them to create contiguous district. To make sure they are continuous, we can do something called local refinement. To accomplish local refinement, we must calculate the edge cut size, which is “sum of edge weights in an edge cut”. To keep the ratio, we must also keep the weight of the districts. We can do this by switching 3 and 4 with 1 and 6. Now, while the red has 4 census block groups and blue has three, they are equal in weight and therefore it is a fair system. While this method might seem to work perfectly in theory, in reality it comes with many flaws. In the beginning of this paper I introduced the delicate balance between racial representation and racial oppression when it comes to redistricting. Although there are ways to create weights for block groups, it is not foolproof and many minorities, specifically in pockets in the midwest, will be spread out among white majority communities. 

There are ideal ways to solve the Gerrymandering issues without the need of computer algorithms. Graph-partitioning methods just show how by breaking down counties into sections, we can create fair lines politically. If one wanted to change the percentage of colors, or split the weights to represent race or economic stature rather than party and density then one could do that. However, it would be very difficult, even with computers, to create a system with weighted towns that encompass every criteria we need to create a fair system. 

Although the graph partitioning method is an interesting mathematical take on how to solve our Gerrymandering issue, it isn’t feasible. A simple response to our Gerrymandering problem would be to look at what some states, such as California, are already attempting; Rather than having partisan legislatures create boundaries they are turning to non-partisan and bipartisan groups to divide up the state. Yes, it is impossible to create a bipartisan map. Even math, which is the the least partisan method, still has faults with creating fair lines due to the fact that it can in some instances hurt minorities which also means hurting democrats. However, by gathering intelligent educated citizens with no strong loyalty to their party, they can use methods such as the graph partitioning method as well as their intuition to create fair redistricting. 

Works Cited

  • “A Commissioner’s Guide to Redistricting in Michigan.” ​Princeton University​, The Trustees of Princeton University,
  • Gerrymandering Over Graphs. In Proc. of the 17th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2018), Stockholm, Sweden, July 10–15, 2018, IFAAMAS, 9 pages.
  • Austin, James Trecothick. ​The Life of Elbridge Gerry: with Contemporary Letters​. Wells and Lilly, 1828.
  • Bazelon, Emily. “The New Front in the Gerrymandering Wars: Democracy vs. Math.”
  • Cavell, Nic. “Gerrymandering Is Even More Infuriating When You Can Actually See It.” Wired​, Conde Nast, 3 June 2017,
  • Doyle, Shawn (2015) ‘A Graph Partitioning Model of Congressional Redistricting,’
  • Rose-Hulman Undergraduate Mathematics Journal: Vol. 16 : Iss. 2 , Article 3.
  • Gerrymandering Group. “Metric Geometry and Gerrymandering Group.” ​Metric Geometry and Gerrymandering Group​,
  • Griffith, Elmer C. ​The Rise and Development of the Gerrymander​. Sagwan Press, 2015.
  • Miller, Greg. “The Map That Popularized the Word ‘Gerrymander’.” ​This Is the Map That Popularized the Word ‘Gerrymander’​, 6 Nov. 2018,
  • Prokop, Andrew. “Who Actually Does the Gerrymandering?” ​Vox​, Vox, 14 Nov. 2018,
  • Schulz, Christian. ​Graph Partitioning and Graph Clustering in Theory and Practice​. Institute for Theoretical Informatics Karlsruhe Institute of Technology, 2016.
  • Soberón, Pablo. “Gerrymandering, Sandwiches, and Topology.” ​Notices of the American Mathematical Society​, vol. 64, no. 09, 2017, pp. 1010–1013., doi:10.1090/noti1582.
  • Supreme Court. ​Shaw v. Reno​. 20 Apr. 1993.

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