The Limits of Gerrymandering

With the 2020 census approaching the United States will be in a position to redraw the political map. Most political junkies are familiar with the idea of gerrymandering and usually strongly opposed to it where it is a detriment to their party. I'll skip over most of the details of how this works as that has been covered in many articles from very popular sources. My question is not if gerrymandering exists, but if you took it to its extremes, how bad could it get?

So the two sentence explanation of gerrymandering before going into some simple models: it is the practice is drawing the lines of voting districts so you have an unfair chance of winning and get disproportionate amount of representation. It is named after a district that looked like a salamander and a guy named Gerry that did it (not kidding).

How Bad Can Gerrymandering Get?

So for a simple example, lets take 1,000 people. We'll call 50% red and 50% blue. There are 10 districts and thus 10 representatives representing this group. Each represents a group of 100. Logically, it seems like each group should get 5 representatives. Cool.

This could happen in three different ways:

• 5 districts are 100% red and 5 are 100% blue
• All 10 districts are 50% red and 50% blue, and a few people people or variations from the pure 50/50 split push the district to one side or the other
• Somewhere between the two extremes presented above

But with Gerrymandering, a simple model for stacking the deck would look like:

• 9 districts with 51 reds and 49 blues
• 1 district with 41 reds and 59 blues

Now red has 90% of the districts even though they have 50% of the population. This looks like cheating.

In The United States

But this is also a very theoretical and very obviously flawed example. So let's get some real numbers. Can a group representing 50% of the population actually be reduced to 10% of the governing legislature? Using the United States House of Representatives as an example:

• 435 representatives
• The US population is about 325 million
• There are 50 states with representation (plus DC and Puerto Rico, kind of...)

So on average

• Each representative has about 325,000,000/435 = ~750,000 constituents
• Each state has about 435/50 = ~9 representatives
• So each state is about 325,000,000/50 = ~6,750,000 people

(Yes, rounding makes this weird, but I wasn't going to use 8.7 delegates a state)

So if 50% of the people are from each party, then there are 3,375,000 in each party in a state. And to win a district you need over half the votes, or 750,000*1/2 +1 = 375,001.

So how many districts can we spread our 3,375,000 people over and still have 375,001 in each? Eight. 3,375,000 - 375,001*8 = 374,992, so you are just shy of stacking the last district.

In fact, you might see how if there were just 9 more of the party stacking the deck, they could win all the representatives. And if they convert from the other party, they just need to convert 5 people (because every vote they convert takes one away from the other group).

Final Thoughts on Gerrymandering?

So what is the conclusion? If you draw the lines to cheat, and have 50.01% of the population on your side, you can take over the entire US government in a legal way. Scary.

But at least this is a 50%+ group. What percent of people would need to be with you to just control over half the house of representatives? To win half of 435 we need 218 seats. To win each seat, we need 375,001 votes. So we need 218x375,001=81,750,218 people. This is only 25.06% of the population running over half the government. Representational democracy...Man, isn't freedom great?!?!