How can I employ Game Theory to better understand and identify the tactics used by mapmakers that create “Gerrymandered” Maps? Additionally, how can these game theory models inform those working to create legislation that assists in preventing Partisan Gerrymandering?


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During my sophomore year of high school, I had the opportunity to engage in a three week intensive course which examined the effects of Gerrymandering in United States government. In this course, we learned that throughout American history, Congressional district map makers have strategically used voting information to create congressional district maps that favor a particular party, or in some cases, even promote hateful ideology. One of these heinous gerrymanders actually occurred in my hometown of Chagrin Falls Ohio, where mapmakers during the 1950’s strategically drew map lines to exclude a predominantly black community from the Chagrin Falls school/ voting districts (this may also be classified as an example of “redlining”, but because school districts also have a direct effect on what is on a voting ballot, it also may be considered an example of “gerrymandering”). I realized during this course that gerrymandering poses a grave threat to the integrity of United States elections. Unfortunately, the United States constitution gives little insight into what constitutes a “fair” district, and many state legislators struggle to create legislation that properly addresses how to identify a “gerrymander”, and how to avoid them when creating maps. 

Guiding Question: 

How can I employ Game Theory to better understand and identify the tactics used by mapmakers that create “Gerrymandered” Maps? Additionally, how can these game theory models inform those working to create legislation that can assist in preventing Partisan Gerrymandering? 

A Case Study:

In order to better understand how Gerrymandering actually works, I have provided two examples that illustrate both a “Republican” and a “Democratic” gerrymander.

According to the 2020 CNN Election Results, Maryland voters elected 7 Democratic candidates to the House of Representatives, and 1 Republican candidate to the House of Representatives (2020 House Election Results). Although Maryland is a strong Democratic state (in the 2020 presidential election 65% of voters voted for the Democratic candidate), Maryland elected 87.5% Democratic candidates to the House of Representatives (2020 House Election Results). Similarly, in Ohio, voters elected 12 Republican candidates to the House of Representatives, and 4 Democrat candidates to the House of Representatives (2020 House Election Results). Although Ohio is considered my many to either be a swing state or lean Republican state (in the 2020 presidential election 53% of voters voted for the Republican candidate), Ohio nonetheless elected 75% Republican candidates to the House of Representatives (2020 House Election Results).

Despite both Maryland and Ohio having clear support for both parties within their states, their Congressional elections make it seem as if Ohio is a 75% Republican state, and Maryland an 87.5% Democratic state (2020 House Election Results). However, presidential election data reveals that this is clearly not the case. So why does this happen?

The answer to this dilemma- Gerrymandering. 

Gerrymandering occurs when map makers strategically draw Congressional district maps to favor a particular political party. Here are some examples of what these Gerrymanders look like in both Maryland and Ohio.

Ohio- 16 Seats, 12 Republican, 4 Democrat:

Maryland- 8 Seats, 7 Democrat, 1 Republican:

Notice how these Congressional districts look very odd. OH-4 looks almost like a snake, and MD 4 seems to wrap itself around another district. 
Gerrymandering- The Strategies/ Empathy Interview: 
For my empathy interview, I interviewed the instructor of the Gerrymandering course I took two years ago- Ms. Katie Scott. Ms Scott is an English/ Humanities teacher at Hawken School in Gates Mills Ohio. Here are a few of the questions I asked her along with her responses:
Q: What led to your interest in Gerrymandering/ teaching a course about it? 
A: A few things:
  • One person One Vote- Making sure that a voter in Ohio has the same say in Congressional Elections as a voter in California, Maryland, Kentucky, or any of the other 49 US states
  • Many people are unaware that local and state legislators are typically the ones behind these Gerrymanders, not federal legislators 
Q: What are some strategies map makers use to create partisan Gerrymanders? 
A: Here are a few: 
  • Packing and Cracking:
    • Map makers will pack the opposing voters into as few districts as possible and give their party a slight lead in the remaining districts
  • Contiguous Districts to the Extreme:
    • For many states, the only requirement for a Congressional district is that they be “contiguous”. There cannot be districts where one part of the district is not connected to another. Some map makers will create districts that are not compact, but are connected to each other to maximize their chances of winning
  • Nonvoting Residents:
    • Most states require that each Congressional district have the exact same population. In order to achieve a partisan Gerrymander without adding opposing voters, a map maker might add voters into their district that do not typically vote, or who are not allowed to vote. For example, if a Democratic map maker in Maryland did not want to add any new Republicans to a Democratic district, they could add a prison to increase the population of a particular district, but because prisoners cannot vote, they would not have any impact on the election
Q: Do you believe Federal legislation is the answer? (currently, each state has different legislation surrounding Gerrymandering). 
A: Yes, and:
  • The Federal Government should not step in and create new laws unless they absolutely have to
  • Partisan Gerrymanders violate the 14th and 15th Amendments, and any constitutional violation should be addressed by the federal government if states fail to uphold those amendments
  • Any legislation should be reactionary, and not make drastic changes to the constitution 
The Game Theory Connection:
Model 1- To Pack Or Not To Pack?
To better understand why map makers decide to employ the “packing and cracking” method despite its risks, I decided to create a Game Theory Model that would examine why it might be beneficial to “pack and crack”.

The Scenario: 


A map maker wants to know if they should “pack and crack” the opposing party, or create fair districts in a state with 16 congressional representatives. Although the state is split almost 50/50 in the presidential election the map maker believes that if they employ packing/ cracking, they can win up to 12 districts. However, the map maker also recognizes that if there is a higher voter turnout for the opposing party than expected, it could potentially hurt them (as the 12 “lean” districts all of a sudden turn into extremely competitive districts).


Player 1- The Map Maker

Strategy A- The Map Maker decides to pack/ crack

Strategy B- The Map Maker does not pack/ crack, and creates 16 fair districts (8 that are lean one way, and 8 that lean another way)


Player 2- Opposing Voters

Strategy C- Higher than expected voter turnout

Strategy D- Normal voter turnout


A,C (The map maker uses packing/ cracking, the voter turnout is higher than expected)

This is the most dangerous scenario for the map maker. If the opposition party has a higher turnout than expected, the “lean” districts could flip for the opposition party.

A,D (The map maker uses packing/ cracking, the voter turnout is normal)

This is the best scenario for the map maker, as their strategy of “packing” works perfectly. They just barely win in 12 districts (as the other 4 districts have mostly voters from the opposite parties “packed” into them).

B,C (The map maker does not pack/ crack, the voter turnout is higher than expected)

If the mapmaker decides not to pack and crack and the voter turnout is higher than expected, a map maker can expect evenly distributed districts (8 and 8).

B,D (The map maker does not pack/ crack, the voter turnout is lower than expected)

If the mapmaker decides not to pack/ crack, and the voter turnout is normal, this will likely help the mapmaker (as they are in a state which geographically favors their party, and a normal turnout will likely help them go over the top). 



After using movement diagrams to solve this non-zero sum game, it is revealed that there is no initial movement diagram solution to the game.

Instead, in order to find a solution, I first employed the Nash Equilibrium method:

Map Maker plays A 2/7 of the time, and B 5/7 of the time


Voters play C 2/3 of the time, and D 1/3 of the time



Using Nash Equilibrium, it can be concluded that the most common outcome of the “packing and cracking model” is for the map maker to create fair districts a majority of the time, and for the voters to have a higher turnout than expected a majority of the time. If this game is played multiple times, the most common outcome will likely be 16 competitive districts (8 each) with the map maker opting not to “pack and crack”.


If the mathematically “safest” result is for the mapmaker to avoid packing and cracking, then why is it an all too common practice among map makers? For starters, lets examine some things the above model might have left out:

  1. Player 2 (the voters) actually do not have much of a direct say over whether turnout is “high”, “low”, or “normal”. Because Player 2 is reflective of thousands of voters, they cannot simply decide to have a “high” turnout whenever they would like.
  2. As Ms. Scott eluded to, other factors (such as voter suppression or failing to uphold the 14th and 15th amendments) can impact voter turnout.
  3. Although there are associated risks with Packing and Cracking, there is much less of a risk in employing this strategy today compared to twenty years ago.  Whereas predicting voter turnout might have been extremely difficult twenty years ago, advanced data analysis technology makes predicting voter turnout, along with how people will likely vote much easier for map makers. There is much less of a “risk” today than this model likely reflects.

Ultimately, although this model might have some flaws, it does indicate one thing- if there is no external factors that make “packing and cracking” a “safe” option for a map maker (such as voter suppression), than the map maker will likely opt to create “safer” districts in order to avoid the major risks associated with “packing and cracking”.


Model 2- Map Makers Under Pressure

To better understand why map makers successfully pass “Gerrymandered maps”, I used a backward induction Game Theory model to analyze the process a map maker may go through when deciding how to approach creating their maps.

The Scenario:


A map maker is tasked by Political Party A with creating a map that will win them 12 congressional district seats out of the 16 available seats (even though the state is much closer to 50/50). Here are some of the things the map maker must consider when creating the map:

  • If the map maker fails to deliver 12 seats, Party A (which controls the state legislator) may never hire them again.
  • If the map maker creates districts that are not compact, the map maker/ Party A may be sued outside organizations (example- they look like Maryland District 4)
  • If the map maker fails to convince Party B that the map is fair, the map maker/ Party A might be sued by outside organization 
  • If there is clear evidence of “packing and cracking”, the map maker might be sued by outside organizations

The Game:

A map maker must create a map that abides as much of the above criteria as possible, while also delivering 12 seats to Party A, and convincing Party B that the map is competitive. The map maker wants the map to pass in the state legislator, which requires a majority of Party A (and some members of Party B) to support it.

There are three players in this game:

Player 1- The Map Maker

Player 2- Party A

Player 3- Party B

Typically, the map maker is the first person to “make a move” (as they are the ones proposing the map to Party A and Party B). Then, Party A (the majority party) will then “approve” or “disapprove” the map (if Party A does not believe the map is going to benefit them, then they will likely tell the mapmaker to redraw the map, or fire the mapmaker). Finally, Party B is usually the final party to have a say, as they are usually the deciding factor in if the map is approved in the state legislator.


A map maker wants to create a map that will pass in the state legislator and please Party A so they can keep their job as the map maker. Party A hopes to maximize the amount of seats they are awarded (they believe they can earn up to 12 of the available 16). Finally, Party B wants to pass the map and is willing to settle for 6.

If the map maker proposes a map that earns Party A 12 seats, they earn 6 points. If the map maker proposes a map that earns Party A 10 seats, they earn 10 points. However, if Party A vetoes their map and decides to go with another map, the map maker loses 5 points.

If Party A approves a map that earns them 12 seats, they earn 10 points. If Party A approves a map that earns them 10 seats, they earn 5 points.

If Party B approves a map that earns them 4 seats, they earn 0 points. If Party B approves a map that earns them 6 seats, they earn 6 points. If party B votes for a map that Party A did not recommend, they lose 10 points (as the map will likely go to a revote which will not be as favorable for Party B). 


(Payoffs as follows- Map Maker/ Party A/ Party B)

Outcome- 6 Points Map Maker, 10 Points Party A, 0 Points Party B

Ultimately, the result of the above Backward Induction chart reveals that the map maker(s) and Party A (the majority party) have the most say over the final  Congressional District Map. Because the map makers are for the most part, employed by the party in power (in this case Party A), they are most likely to create a map that favors benefiting the party in power, as opposed to compromising. While compromising might be the most beneficial outcome for the map maker, the risk of losing favorability in the party (or the in-game equivalent of losing points) far outweighs the prospect of giving Party A what they want. Then, when Party A inevitably decides to support the map that gains them the most congressional seats, the vote is then passed on to Party B. Party B must decide whether they vote for what they believe (a 10 seat map), and start the map making process all over again, or compromising and by giving Party A 12 seats. Unfortunately for Party B, if the process starts over again, they are likely to have less time to compromise, and risk having to vote for a map that might be even more “Gerrymandered” than before.

The Backward Induction Model reveals that the party in power, along with the map maker(s) have an extraordinary amount of power in drawing Congressional District Maps. Because these rules apply to both federal and state congressional maps, the maps that are approved are often favorable to the state legislators that are members of the party in power, thus allowing them to continue to remain in power, and draw/ pass gerrymandered maps.

Conclusion/ Reflection: 

After using Game Theory to analyze the process behind Gerrymandering, I drew two major conclusions: 

  1. If there is no “voter suppression”/ “external factors” that influence the results of an election in a state, then there is less of a chance that a map maker will “gerrymander” a Congressional District Map. 
  2. Map makers and the current party in power within a state have an institutional advantage that allows them to draw and pass gerrymandered maps. 

When reflecting upon Ms. Scott’s recommendation to pass “preventative” legation as opposed to creating new legislation, it becomes abundantly clear that the easiest way to prevent Gerrymandering has little to do with actually creating new Gerrymandering legislation. Instead, making sure that the 14th and 15th amendments are upheld, and ensuring that the principal of “one person, one vote” is upheld is the best way to prevent Gerrymandering. Although map makers/ the party in power have an institutional advantage, that institutional advantage weakens when the integrity of the election is upheld. 

Following the 2020 Presidential Election, a large nationwide debate ensued between Republicans and Democrats regarding the integrity of United States’ Elections. In response to this debate, some states (such as Georgia) have either considered, or actually passed legislation that aims to revise the procedures behind statewide elections (Cox). Unfortunately, many have criticized these laws for creating new voting inequities that will hinder the ability of certain groups to have their voice properly represented in the Untied States Government. If we are to properly address the issue of Gerrymandering in the United States, we must first carefully reexamine current and past state legislation that impacts voting equity. To prevent Gerrymandering, we must ask ourselves if our laws truly uphold “one person, one vote”.


Works Cited:

“2020 House Election Results.” CNN, Cable News Network,

Black, Shana. “Chagrin Falls Park, Black Neighborhood Next to Chagrin Falls, at Heart of Last Week’s Protest Controversy.” Cleveland Scene, Cleveland Scene, 19 Jan. 2021,

Cox, Chelsey. “Georgia Voting Law Explained: Here’s What to Know about the State’s New Election Rules.” USA Today, Gannett Satellite Information Network, 12 Apr. 2021,

Ingles, Jo. “Federal Court Says Ohio’s Congressional Map Is Unconstitutional.” The Statehouse News Bureau,

Ingraham, Christopher. “Analysis | How Maryland Democrats Pulled off Their Aggressive Gerrymander.” The Washington Post, WP Company, 27 Apr. 2019,

Ricci, David, and Katie Scott. “Gerrymandering Empathy Interview .”

“State-by-State Redistricting Procedures.” Ballotpedia,

“Who Draws the Maps? Legislative and Congressional Redistricting.” Brennan Center for Justice,



  1. Super interesting project! I have never heard of Gerrymandering before, but after reading I feel I have a better grasp on this idea, and how it effects our country’s politics!

    1. Thanks for the comment Braden! Unfortunately up until I took that course during my sophomore year, I had never heard of Gerrymandering either. Nonetheless I feel very lucky that I got to use GOA as a way to help spread awareness about the issue!

  2. Such a well thought out project by David! You could tell he is very passionate about the subject and is eager to teach others! I encourage everyone to read this and gain all the information it has to offer!

    1. Thanks Sarah- means a ton! I think you and I would both agree that learning about Gerrymandering is extremely important- and I am super glad that you thought I did a good job explaining it!

      1. Really interesting analysis David. I especially appreciate the explanations of the games to help me understand these larger more complex issues.

        1. I totally agree Thomas- observing a map maker’s thoughts and interactions through the lens of game theory definitely helped me to better understand why the often tend to lean toward gerrymandering when creating their maps- there are some inherent advantages to it.

  3. I learned what gerrymandering is.

    1. Thanks for checking this post our Grayson! Glad to hear that you learned about Gerrymandering- its a super important issue to me and I am super happy that you learned about it through this post!

  4. David, awesome project! Also very interesting about Chagrin Falls… definitely true implications on the culture and representation of the city due to gerrymandering.

    1. Thanks Syd! Definitely a sad example of Gerrymandering/ Redlining in our community, and I am glad it has now gotten some attention in our community.

  5. Very cool project! I have a better idea of how much gerrymandering impacts voting and the implications of the Supreme Court ruling of one person one vote on our country’s politics.

    1. Thanks for taking a look over this post Kaley! I didn’t even touch upon the Supreme Court in my post (specifically how they have largely stayed away from ruling on this issue). It is definitely something that needs to be addressed!

  6. This is an amazing project. I was personally unaware of gerrymandering and David’s project provided a thorough understanding. This is an important study for all Americans to review.

    1. Thank you so much for that comment! Totally agree that Gerrymandering is something that all Americans need to be aware of and review- I hope this will serve as somewhat of a step in educating about the issue

  7. This is so well thought-out and really intriguing!! It really shows your enthusiasm for teaching others about political issues such as gerrymandering. I like how you included many advanced facts and considered all of the outcomes!! Great job man!!

    1. Thank you so much for checking this post out Kate! The hardest part of the project was definitely coming up with the outcomes for my games- so I appreciate you noticing that- definitely required a lot of analytical thinking!

  8. This project was super interesting. I remember learning about gerrymandering, but I didn’t realize how prevalent it still is in American politics. You did a great job of showcasing why gerrymandering is still practiced and why it still works.

    1. Thanks for the comment Carli! It is easy to assume that gerrymandering might be harder in todays political system (given there are more voting rights laws today than there were at any point in American history), but there are still many ways to get around them and still gerrymander.

  9. hey!! loved how you explained how redlining and gerrymandering are related and effect each other, i think it’s a nuance that gets lost a lot.

    1. Thanks for the comment Alex! I agree that its easy to confuse gerrymandering and redlining (or forget one when talking about the other), but I think it is important to mention how by nature the two issues are similar and often intertwined.

  10. This is a really amazing and in depth project! I learned a lot reading through it and loved your incorporation of local examples. I learned about gerrymandering in my government class last year, but didn’t study a whole lot into it, so this was really interesting to read!

    1. Thanks for the comment Sarah! Definitely something that was studied super in depth during my personal government class, but I am glad I had the opportunity to learn more about it and realize how important of an issue it is (especially how prevalent it still is today).

  11. Great article, what an interesting way to look at the issue!

    1. Thank you for the comment! Definitely never thought I would be able to look at Gerrymandering through the lens of Game Theory, but I am very glad this class gave me the opportunity to branch out and do it!

  12. Very detailed and well thought out project David! I learned a lot about Gerrymandering that I did not know about before, and it was very interesting to hear the story about Chagrin Falls!

    1. Thanks so much Marie! I didn’t know the story about Chagrin Falls until just a couple years ago- and I’ve lived there my entire life. Definitely important to know the history behind the places you live, and how they relate to larger political issues.

  13. David is one of the brightest and most enthusiastic people I know, so I’m not surprised to see a collegiate-scholar level dive into such a complex and intimidating topic. Nicely done!

    1. Thank you so much for the comment Will! I feel like Gerrymandering is a topic rarely taught at the high school level (if it is taught it is usually just mentioned), and I am so happy to see people our age engaging with it!

  14. Awesome job David! The graphics really help the reader understand your study!

    1. Thank you so much Claire! Totally agree- seeing what a Gerrymander looks like definitely helps to better understand the topic.

  15. Such an amazing project David!! I have a much better understanding of Gerrymandering after reading and watching it. The idea of Gerrymandering in the context of game theory really highlights how strategic it is and how it impacts the American voting system.

    1. Thanks for the comment Chloe! It was definitely easier for me to understand Gerrymandering when I looked at it through the context of Game Theory- especially since there is a ton of strategy behind it. It also definitely helped me to have some empathy for the politicians involved (there has to be a ton of pressure to Gerrymander coming from outside sources).

  16. Wow, David! This project is truly an example of “good work” as it is engaged, ethical, and informative. Loved how you are shedding light on a poignant issue in our current political climate. I am so proud of you!

    1. Thank you James- means a ton! I am super excited to hear you found the project engaging- thank you so much for checking it out!

  17. Wow David this is super impressive! I have never heard of some of these terms before, but now I will definitely take an even closer look when I can vote one day! Thanks so much for sharing!

    1. Thank you Kennedy! I definitely agree that gerrymandering is something every voter should be aware of so that they can vote for candidates who commit to ending the practice

  18. David, it is clear that you put a lot of effort into this project, and the connection you drew between Game Theory and Gerrymandering is a powerful one. I especially enjoyed your analysis using the backward induction Game Theory model to conclude that the party in power (Party A) and the mapmaker (employed by the party) can hold power in a state using strategic mapping techniques, as well as the pressure that it puts on ‘Party B’ to either compromise, or risk having less time, resulting in a more “Gerrymandered” map. I do wonder what form of legislation may be able to help this issue. This was a very well thought out project, great job David!!

    1. Thank you so much for checking this out Christopher! Definitely would’ve loved to draft up some sample legislation myself following this project- might be a good next step for me (going through the process of creating this project totally made me want to continue my work on it).

  19. This is super interesting David! You did a great job with including graphics and explanations that make your readers better able to understand this topic. Gerrymandering and its effects are confusing and nuanced but you approached explain them in a very effective manner. This is super impressive–great job!

    1. Thank you so much Emma! I totally agree that Gerrymandering can be a complicated concept to understand (it certainly was for me when I first started learning about it). But graphics totally help when trying to understand it- once I saw an image of a “gerrymander” something clicked and I understood what it meant.

  20. This is awesome David!! Such a cool way to look at this pressing issue. I really enjoyed learning about this. Super important for students to talk about, especially as we become voters. Great work!

    1. Thank you so much for checking this post out Claire- means a ton! And yes- totally agreed that everyone who votes should be aware of this issue so they can combat it when they are in the voting booth if given the opportunity! (p.s.- best singer ever!)

  21. Great stuff David keep up the good work

  22. This is super interesting! I especially thought it was interesting to see the relationship between mathematical practicality and gerrymandering. It’s so important to learn how this issue still effects us – especially marginalized Americans – so thanks for sharing!

  23. David, this was such an interesting, effective way to present the issue of gerrymandering. I appreciate your layout, how you employed and applied the concepts and methods of Game Theory, and the clarity of your conclusion. Thank you for sharing!

  24. This is really impressive David! Awesome job – you can really see all the work and effort you put into this.

  25. I have a little background knowledge about gerrymandering because i enjoy learning about politics but this is much more in depth then anything else I’ve seen before. I never know you could use game theory to help find gerrymandering. Really fun read keep up the good work.

  26. I can tell you have so much knowledge on this topic and you are very interested in it as well. I think you did a great job applying game theory to your question and final product. Amazing work!

  27. This is really cool David! This is very different from anything I’ve seen and can apply to many past, modern, and future problems. Keep up the good work!

  28. Hello David,

    Amazing project, I didn’t know what gerrymandering was until I read your detailed explanations. Your application and knowledge of game theory have really shown well in this project which helped me realize how game theory can be used in various real-world scenarios. Keep up the great work.

    Please check out my project. I would really appreciate it-

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