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The Journal Gazette

Tuesday, April 18, 2017 1:00 am

By the numbers

Researchers craft mathematical formula to determine degree of gerrymandering

Christer Watson

The Supreme Court soon will hear a gerrymandering case from Wisconsin, Whitford vs. Gill. The state lost the case in federal district court, where the judges ruled that its election district boundaries were unconstitutional. The basic idea is that when Republicans drew voting boundaries in 2010, they discriminated against voters based on their political preferences. I am especially interested in this ruling because the plaintiffs have included a straightforward, numerical method of measuring gerrymandering. If it is successful, it is a nice demonstration of how a clear, mathematical description of a problem can help courts find a solution.

Gerrymandering is drawing voting district boundaries to favor one party. It occurs almost constantly and, honestly, is to be expected when elected officials are in charge of drawing the boundaries. However, it also clearly undermines some basic principles of democracy. Equal representation depends on each vote having basically an equal influence.

The courts should be a natural check on gerrymandering. However, they have struggled to limit the practice. In a 2004 Supreme Court decision, for example, Justice Anthony Kennedy was explicit is stating that there was a “lack of comprehensive and neutral principles for drawing electoral boundaries. No substantive definition of fairness in districting seems to command general assent.”

Two academics, Nicholas Stephanopoulos and Eric McGhee, treated this opinion as a request. They developed a direct, simple measure of gerrymandering. To understand the method, it helps to put yourself in the perspective of a party wanting to divide its reliable votes among districts. In practice, this is basically done by knowing where voters live and drawing boundaries either to include or exclude them.

From a drawing-the-boundaries-perspective, there are two goals.

First, when you win a district, you want to win it with as few votes over 50 percent as you can.

Second, when you lose a district, you want to have as few votes in that district as possible. If you draw the district boundaries with only these two goals in mind, a party can win significantly more districts than you would estimate based on overall vote counts.

For example, there were seven states that were heavily gerrymandered in 2010: Florida, Michigan, North Carolina, Ohio, Pennsylvania, Virginia and Wisconsin. In 2012, the House election results, averaged statewide, were (voting Republican) 50 percent, 47 percent, 49 percent, 50 percent, 49 percent, 51 percent and 49 percent. The fraction of House seats, however, was 63 percent, 64 percent, 69 percent, 75 percent, 72 percent, 73 percent and 63 percent, respectively.

The authors have measured the two gerrymandering goals. That is, they measure how many wasted votes (the authors' term, not mine) above the 50 percent in winning districts and how many wasted votes in losing districts each party has. If one party has significantly fewer wasted votes than the other, the districts are gerrymandered.

This measurement is great for several reasons. First, it is a direct measurement of what gerrymandering is. I cannot think of a way to gerrymander a district without it showing up in this measurement. Second, it can be measured in any state, even ones that lean heavily Republican or Democratic. Third, we can quantify how much gerrymandering is acceptable. The Supreme Court already has a general principle that congressional district populations should be within 10 percent of the average. It is easy to imagine a similar criterion for party imbalance of wasted votes. The authors suggest 7 percent based on historical data, although they admit that number is soft.

Hopefully with this clear measurement, the courts will be willing to place stricter limits on gerrymandering. It will mean a healthier democracy for everyone.


Christer Watson, of Fort Wayne, is a professor of physics at Manchester University. Opinions expressed are his own. He wrote this for The Journal Gazette, where his columns appear the first and third Tuesday of each month.