Mathematicians study gerrymandering

Stephen Ormes wrote an article for the Proceedings of the National Academy of Science titled Science and Culture: Math tools send legislators back to the drawing board. In it he talks about the various ways to mathematically detect gerrymandering.

The work in his area intensified in 2004 when Supreme Court Justice Anthony Kennedy in a ruling decried gerrymandering yet said there is no “workable standard” for judges to consistently and fairly determine if gerrymandering exists. Mathematicians and social scientists got to work and now have some answers.

The first test was developed in 1987. Political scientist Gary King of Harvard proposed the idea that the proportion of seats for each party should have the same ratio as the votes across the state. If each party gets 50% of the statewide vote, then each party gets 50% of the seats.

Another is the “Polsby-Popper test” which compares the perimeter of a district to the circumference of a circle of the same area. Alas, this doesn’t work well when the state boundary follows a river, such as the district in the western sliver of Maryland.

I’ve already discussed the efficiency gap, which counts the “wasted” votes of each party.

A recently devised test is from Carnegie Mellon University and University of Pittsburgh. Make small random tweaks to district boundaries and reapply the election results. If the tweaks consistently make the district less partisan, the district is gerrymandered.

The same team proposed a solution that doesn’t involve mathematical formulas. Party A draws districts. Party B gets to say “I’ll keep that one.” Party B redraws the rest of the map and Party A keeps one. Neither party gets an advantage. Both get a chance to protect their interests. This plan doesn’t work if both parties make an anti-democracy deal ahead of time.

Randomly create a suite of maps (10,000 to 24,000 should work). Apply the election data to those maps and compare the results to the official maps. If the official results are an outlier when compared to the random maps it is a “signature of gerrymandering.”

Mathematicians are, naturally, exploring other ideas to test for gerrymandering.

Now to get the courts to use these methods of measurement. Last fall Chief Justice John Roberts called such tools “sociological gobbledygook.” But mathematician Eric Lander, head of MIT’s Broad Institute says the courts don’t need mathematical details, only know that the tools provide a workable standard. So there needs to be work done to demonstrate the various measures hold up in a wide variety of circumstances, then work to teach judges about similar ways mathematics is used – such as distributions used to predict the path of a hurricane.

Alas, at least on the national level, this work of convincing justices will be on hold. Stephen Wolf of Daily Kos lists five ways a more conservative replacement for retiring Justice Kennedy is a catastrophe democracy.

1. Gut the rest of the Voting Rights Act and allow voter suppression.

2. Permit racial gerrymandering.

3. Permit partisan gerrymandering. With Kennedy gone the court could overturn that 2004 ruling by saying the Supremes (and any federal court) simply can’t get involved.

4. Invalidate redistricting commissions. These already exist in Arizona and California and I’m involved in trying to get one passed in Michigan. The Constitution’s “Elections Clause” says “the legislature” does the redistricting. In 2015 Kennedy was the key vote in saying a state constitution can designate who can make the laws, in this case a citizens commission. But Roberts strongly dissented, saying when the Constitution says “the legislature” it means the actual elected legislators.

5. Remove the last remaining caps on campaign spending by corporations.

There are ways to fight against this, at least at the state level. A state redistricting commission could still be used to draw districts for the state legislature.