Finding solutions for our democracy
I am a math major and policy geek, so you can just imagine my delight when I learned via my favorite Supreme Court news podcast that one of the cases on the docket for this year’s Supreme Court term is all about math.
The Supreme Court heard oral arguments for the case Gill v.Whitford on Oct. 3, whose goal was to determine whether a voting district in Wisconsin was politically gerrymandered, that is to say, whether the current district lines effectively disenfranchise voters based on their political party.
Maybe Gill is not entirely about math, but depending on the outcome of the case, math might come to play a central role in determining whether our country remains a representative democracy.
For those unfamiliar with the concept of gerrymandering, every 10 years, state legislatures are tasked with redrawing voting district lines based on population shifts uncovered by the census. The term “gerrymandering” was first coined in 1812 when a political cartoon published in The Boston Gazette likened the shape of one of the newly formed Massachusetts voting districts to a salamander. This particular district was clearly designed to help Massachusetts governor Elbridge Gerry’s party remain in power. Henceforth, the term gerrymandering—a combination of the governor’s last name and the word salamander—has been used to refer to any time a party in power draws new district lines to favor a particular party or group.
In the past, the Supreme Court has heard a number of cases in which the constitutionality of district maps have been challenged on the basis of political gerrymandering. The Equal Protection Clause of the Constitution stipulates that, within a state, voting districts must be roughly equal in population size so as to satisfy the one-person, one-vote principle.
However, the Supreme Court has never actually struck down a map based on partisan gerrymandering due to the lack of a manageable standard to test whether or not voters are being disenfranchised based on political party.
What’s so exciting about the Gill case is that the plaintiff has actually proposed a metric to tell us whether or not partisan gerrymandering has occurred. What’s even more exciting for math nerds like me is that the metric proposed boils down to an equation so simple that some might call it elegant. The “efficiency gap” metric, developed by Eric McGhee and Nicholas Stephanopoulos, is a measure of partisan symmetry, which is the principle that each political party should have roughly the same number of wasted votes in a given election.
A vote is “wasted” when it is cast for the losing candidate or for a candidate who would have won anyways. For example, imagine that we’re looking at a two-candidate race in a district of 100 voters. Let’s say 80 of the voters in a district vote for the Democratic candidate, while 20 voters vote for the Republican candidate. In this case, the 20 Republican votes are wasted since they were cast for the losing candidate. Additionally, 29 of the Democratic votes are wasted since the Democrats only needed 51 votes to win the district.
The efficiency gap for a state’s voting district map is found by dividing the difference between the number of Republican wasted votes and Democratic wasted votes by the total number of votes cast. In equation form:
Efficiency gap = |(# of GOP wasted votes – # of Dem wasted votes)| / (total # of votes cast)
An efficiency gap of zero would indicate that the parties have an equal number of wasted votes. The further the efficiency gap is from zero, the more it suggests that a state’s districts constitute an excessive partisan gerrymander.
It is my hope that I have shown my less mathematically-inclined readers that a complicated-sounding metric doesn’t have to be so intimidating. Furthermore, I think there is value in understanding the mechanisms by which our voting power as individuals might be determined for years to come.
Lastly, as a math tutor who is constantly plagued by the question “when is this used in real life?” This illustrates a concrete application of math in the “real world.” To be fair, the efficiency gap isn’t the sexy, made-for-Hollywood, “Moneyball” type of math used to win championships, but it presents a potential solution to a matter of critical importance for the future of our democracy.
Perhaps the efficiency gap isn’t the perfect standard for deciding whether or not gerrymandering has occurred, but we do need to find one, because otherwise there will be no way to challenge voting districts maps that disenfranchise people based on political party. I certainly don’t like the idea of my vote being systematically wasted due to a hyper-partisan district map, and I think it’s wonderful that mathematicians are currently hard at work to prevent this from happening.
