The Geometry Of Gerrymandering.

 

The midterm elections are mostly over and a couple of cases on voting seem to head to the state court systems or the Supreme Court.  Often, the cases that make it to court deal with the way the area is divided up for voting.  States often want to redraw districts to favor the party in charge but did you realize how much of a role geometry plays in this whole situation?

It turns out that geometry provides a powerful tool for establishing the best division of area into voting districts for places that have at least two parties.  According to the constitution, the candidate who gets the most electoral votes wins but the way the districts are designed can have a huge impact on how the votes are distributed.

When governments rearrange the shapes of each district, they can encourage a favored candidate to win to keep them in power and to provide representation that may not be really representative of the district.  We'll use a small example of 50 voters who live in a 5 by 10 area, one person per square.  The voter distribution is 20 are red and 30 are blue, so if you divide the area into 5 districts, you have several possible results.  If you have two rows of red and 3 rows of blue and divide it so you have two districts of red and three districts of blue, the blue will provide more votes for their candidate so if this were the house, you'd have two red and three blue but what if you want the blue to win all the seats?  You would redesign the 5 districts so all 5 districts are set up so there are four red voters to every 6 blue voters and the blue would take all the seats but what if you wanted red to win the majority of seats.  You would have to redraw the districts so three of the districts had more red than blue and the red would get three votes.  The first few scenarios can be accomplished using regular districts but the last situation requires districts to be done in irregular shapes rather than standard shapes.

These examples are not all theoretical.  Back in 2012 in New York State when 58 percent of the voters voted democratic but the democrats got 21 out of the 27 available seats. On the other side, 51 percent of the voters in Pennsylvania only won 5 of the 18 available seats in the same year.  The practice of redrawing districts to give a certain party the advantage is referred to as gerrymandering which comes from Elbridge Gerry who was governor of Massachusetts in the early 1800's.  His party was good at redoing districts into strange shapes to give his partner the advantage.  A cartoonist noted that the districting looked like a salamander so the term gerrymandering was born.

It appears local and state governments change the lines of districts about every 10 years when a new census comes out.  Over the 10 year period people move and the number of red and blue voters change so the lines have to be redrawn to help a political party stay in power. Although intentional gerrymandering is illegal, most people find it difficult to establish rules for fair districting, and this includes mathematicians.  Every state has their own rules which makes it even more difficult.

The most fair criteria for districting is that the number of red and blue voters should be about equal, each district should contain about the same number of total voters, should not discriminate against any ethnic group, not cross county lines, and follow natural boundaries but in reality, it is hard to do this.  In addition, if one wants to keep compact districts, it can't always be done and doesn't always produce fair voting results.

One study looked at the presidential election in Florida in 2000 because the number of republican voters equaled the number of democratic voters but the republicans had the edge in results.  The scientists redrew district lines to meet the definition of compact districts while meeting Florida state rules but the results showed the republicans had the advantage. The skewed results came from the fact that most of the democrats lived in urban areas while republicans lived in rural areas. This leads to the republicans winning more. Others did more research and discovered you cannot prove the districts were drawn to give one party the advantage by just looking at the lines.

One set of scientists discovered that one has to look at the efficiency gap. The efficiency gap is calculated by subtracting the "wasted" votes of the two parties from each other and then the answer is divided by the total number of votes.  A wasted vote is defined as a vote cast in the district where the other party won or is above the margin needed to win. The smaller the efficiency gap, the more impartial the results.  Sometimes the efficiency gap isn't the best choice when all the voters of a party live in the same place.  So another group wrote a computer program to determine possible ways to set the districts based on state requirements.  They applied this to the state of Maryland in 2011 and the computer came up with 250 million possibilities.  They found the results gave the democrats an advantage.  In fact, 99.79 percent of the 250 million results favored the democrats. 

Many states have moved to using independent commissions to set up the districts and these commissions use computer programs to find the fairest way to set up the voting districts so the results are more fair to all but some states are still trying to adjust districts to give them an advantage.  So this is where math comes into play.  Have a great day and let me know what you think, I'd love to hear.