James Allison

In a recent op-ed in the Washington Post Lee Hamilton, William S. Cohen and Alton Frye served notice: Although partisan gerrymanders may lie beyond the reformist reach of federal courts, and beyond the conscience of gerrymandering statehouse legislators, they are well within the grasp of Congress (July 17, 2020). Specifically, the House can “refuse to seat a state delegation achieved through excessive gerrymandering.” They propose to gauge the amount of gerrymandering in terms of the difference between the number of districts won by each party and its share of the statewide popular vote. They take the example of North Carolina’s 2018 elections, where Republicans won 50% of the popular vote for House members, but 77% of the state’s 13 seats. And the gerrymandering authors of those maps came right out and confessed proudly that their motive was to guarantee their party’s supermajority control.

The constitutional basis for direct Congressional oversight is in Article 1, Section 5, which says that “each House shall be the judge of the Elections, Returns and Qualifications of its own Members.” It has been used, albeit rarely, to exclude representatives chosen under questionable election procedures. And it was used after the Civil War against state intimidation of black voters and unconstitutional election laws.

But wait! What if the gerrymanderers, unlike those in North Carolina, don’t proudly confess? In North Carolina, for example, couldn’t that 50-77 difference just happen by chance? How big a difference does it take to arouse one’s suspicions? How much gerrymandering is “excessive”?

I can attest that these are not idle questions. After Indiana’s 2018 Congressional elections, where Republicans won 56% of the popular vote for House members but 78% of the state’s 9 seats, I asked a leading Republican legislator if we could agree that the state had been gerrymandered. He said “No,” and stalked off.

So, I repeat the question any member of Congress would have to face in deciding whether “a state delegation had been achieved through excessive gerrymandering,” in the words of Hamilton, Cohen and Frye. Absent a smoking North Carolina gun, how much gerrymandering is “excessive”? How do you know a real gerrymander when you see one?

The authors propose no specific decision rule the House might follow, but we can develop one from the basic principle of representative government: one person, one vote. This principle declares, loud and clear, that the representative value of my vote is neither more nor less than that of my neighbor. So, if my neighbor’s party has twice as many votes as mine, it deserves twice as many seats as mine, but no more. It would not be reasonable to insist on exact equality between those two numbers, the proportion of the the popular vote and the proportion of seats in the state legislature or the Congress. But it would be reasonable to insist on strict adherence to some previously specified objective standard. This is where inferential statistics can come to the rescue.

In the interest of bipartisanship let us take for example Maryland’s 8 Congressional districts in 2018, where Democrats won 66% of the popular vote but a whopping 88% of the 8 seats: Twice as many votes, but 7 times as many seats. How do Maryland’s 8 district maps look in terms of the average representative value of a Republican vote and that of a Democrat vote?

We find out by first calculating for each of the 8 districts one pair of numbers: The number of seats won/Republican vote, and the number of seats won/Democrat vote. These calculations give us two sets of numbers, 8 for Republican voters, and 8 for Democrat voters. We add up the 8 Republican numbers and divide by 8 to arrive at the average Republican seats/vote, and do the same with the 8 Democrat numbers. The two averages (multiplied by 100,000 to keep the reader from drowning in zeros), .068 and .450, look pretty different. But before we draw any conclusions, we want to know the probability that so big a difference could have happened by honest coincidence. To find out, we plug our 16 numbers into a statistical procedure called a t-test, which tells us that the chance of so big a difference by honest coincidence is extremely small, about one chance in a thousand. More likely, these two distributions arose by something other than luck, and Congress should therefore refuse to seat the Maryland delegation. Incidentally, courtesy of the internet the calculation of a t-test requires no great statistical expertise.

Similar analyses of 2018 Congressional elections reveal significant gerrymanders in Indiana and North Carolina, but not in Minnesota. This approach is not new: See Robert X. Browning and Gary King, “Seats, Votes and Gerrymandering: Estimating Representation and Bias in State Legislative Redistricting.” Law and Policy, Vol. 9, No. 3, July, 1987. But if adopted by Congress, its potential threat alone could create a powerful driving force toward nationwide redistricting reform.