If pro is the opposite of con, what’s the opposite of progress?
— widely circulated; attributed to Will Harvey
If you really want to understand the root cause of Washington’s dysfunction, start by trying to answer this simple multiple choice question: Among the 435 individual races for Congress that took place in the 2012 election, what was the average (mean) margin of victory?
a. less than 3 percentage points
b. 3 to 7 percentage points
c. 8 to 15 percentage points
d. 16 to 29 percentage points
e. more than 30 percentage points
You’re probably aware that we live in a country that is closely divided between those who lean Republican and those who lean Democratic. In 2012, for example, the national vote for Congress was 49.0% to Democratic candidates and 47.7% to Republicans. Most people therefore guess choice (a) for the multiple choice question, since it seems logical that individual races would also be closely contested. However, the correct answer is (e), because the average vote was about 66% to the winner and 34% to the loser, for a nearly 2-to-1 margin of victory. Indeed, many of the winners had such a clear path to victory that no serious candidate even bothered to challenge them, and only a few dozen of the 435 House races had outcomes that were even modestly in doubt before election day.
How can such a closely divided electorate produce such lopsided outcomes in individual races for Congress? The answer turns out to be the same one that explains why members of Congress (in both parties) generally hold much more extreme partisan views than do most voters, which in turn explains why they have such a difficult time reaching agreement even on critical issues like keeping the government running and avoiding a national default. In my many years of teaching about the mathematics of politics, I’ve found that most people know the common name of the answer — gerrymandering — but relatively few understand how it actually works. Fortunately, the basic ideas are very easy to understand.
Gerrymandering is the idea that it is possible to skew the outcomes of elections by drawing district boundaries with partisan goals in mind. It’s an idea that has been part of U.S. politics for a long time; the term “gerrymander” comes from an 1812 political cartoon that showed a district created under Massachusetts Governor Eldridge Gerry as having the shape of a salamander.
To understand how gerrymandering works, imagine that a state has a total of 4 million voters divided into 8 House districts (with 500,000 voters each), and that the state-wide Congressional vote is perfectly split with 2 million voters choosing a Republican candidate and 2 million choosing a Democrat. Most people guess that this would also lead to an evenly split Congressional delegation of 4 Democrats and 4 Republicans, but that is not the only possible outcome. To see why, imagine that the district boundaries were drawn by a Democratic legislature with the goal of maximizing Democratic seats in Congress. Let’s take an extreme case and assume that the legislature is somehow able to draw a district in which all 500,000 voters are Republican, so that the Republican candidate will win 100% of the vote in this district. For the rest of the state, then, all 2 million Democratic voters remain, while only 1.5 million Republican voters are still available. If the districts can be drawn to split these voters evenly among them, then the Democrats will win every one of the other 7 districts by a margin of 2 to 1.5, which is the same as about 57% to 43%. In other words, by drawing this set of boundaries, the legislature can create a situation in which the Democrats win 7 out of the 8 districts despite the evenly divided electorate. Moreover, none of the elections are even close. The Democrats’ margin of victory is 14 percentage points in their 7 wins, while the lone Republican victory is by a margin of 100 percentage points. The average (mean) margin of victory, then, is close to 25 percentage points.
While packing one district with 100% from one party isn’t really possible, the increasing sophistication of data collection and computer models has made it possible for real-world cases to get remarkably close. Consider North Carolina, which has 13 seats in the U.S. House of Representatives. In 2010, using district maps that had been created when Democrats controlled the legislature, Democrats managed to win 7 of the 13 seats — a majority — despite receiving only 45% of the statewide vote. In 2012, the Democrats improved their statewide showing to a majority of 51% — but with district boundaries having been redrawn by Republicans, the Democrats won only 4 of the 13 seats.
It may seem bad enough that the folks who draw the boundaries can skew election outcomes so far in their direction, but the real problems go even deeper. In an election that is likely to be close, both parties have an incentive to nominate candidates who will appeal to the broad political middle. But in an election that one party is almost guaranteed to win, the real contest occurs in the primary rather than in the general election. Primaries tend to draw much smaller numbers of voters than general elections, and the most highly partisan voters have an extra incentive to show up for a primary if they believe that their candidate is almost certain to win the general election. As a result, non-competitive districts tend to elect representatives with more extreme partisan views. Moreover, because this effect tends to bring out more extreme partisan voters in the primary, it can also affect nominations for Senate and other statewide offices, which is a major reason why we’ve seen a trend toward more highly partisan candidates for all offices.
So there you have it: the root cause of Washington’s current dysfunction is that our election process has been effectively commandeered for partisan purposes because we allow politicians to draw their own district boundaries. This suggests that the way forward should be to take the redistricting process out of partisan hands, but so far only a handful of states have attempted to do so. Still, the math is clear: Our current redistricting policies lead to a more highly polarized Congress, so if we really want to change the way Washington works, we have to start by changing the way district boundaries are drawn.
You’ll find more about redistricting and the mathematics of political polarization in Chapter 8 of my book, Math for Life.