The Independent View: Removing Gerrymandering with Geometry

Attempts to shape Voting Districts in ways that Unfairly favor a Political Party have provoked Legal Challenges across the Country. Creating Independent Redistricting Commissions is a start. But Courts still lack a practical Standard for Identifying Gerrymandered Districts.

In recent years Mathematics has stepped into the fray to develop Statistical Methods that courts can use to spot Manipulative Districting and to act as Experts inside and outside the Courtroom.

Gerrymandering

Gerrymandering is a practice intended to establish a Political Advantage for a particular Party or Group by Manipulating District Boundaries. The Two Principal Tactics used in gerrymandering:

"Cracking" - Diluting the Voting Power of the Opposing Party's Supporters across Many Districts.

"Packing" - Concentrating the Opposing Party's Voting Power in One District to Reduce their Voting Power in other Districts.

There are so many ways to District a State that Evaluation has become a massive Data Challenge for even the Fastest Computers. Courts are looking at Two Tools, "Efficiency Gap" and the "Markov chain Monte Carlo", that could stand up to the Task.

The Efficiency Gap

The Efficiency Gap has several Properties that make it ideal for Measuring the Extent of Gerrymandering.

First, it directly Captures the Packing and Cracking that are at the heart of every Biased Plan. Surplus Votes for Winning Candidates are the definition of Packing, and Lost Votes for Defeated Candidates the Essence of Cracking. All a Gerrymander is, in fact, is a Plan that Results in One Party Wasting many more Votes than its Opponent. The Efficiency Gap tells us exactly how Big the Difference Between the Parties’ Wasted Votes is.

Second, as an Arithmetical matter, the Efficiency Gap represents a Party’s Undeserved Seat Share: the Extra Fraction of Seats a Party Wins relative to a Neutral Plan. If Party A and Party B had each Wasted the same Number of Votes, the Party Winning number of Seats is expected. But if a Party Wins more Seats or a Party Losses more Seats, this then looks like a Gerrymandered District. This is precisely what the Efficiency Gap Reveals.

Third, the Efficiency Gap can be Calculated for any Election, no matter how Uncompetitive.

Fourth, the Efficiency gap is Computed using Actual rather than Hypothetical Election Results. When the Gap between Parties is over a Fixed Percent, you have a Gerrymandered District.

I am under No Illusion that the Court is in any Rush to Adopt a Gerrymandering Test with Real Teeth. But the Court wouldn’t have to do anything for our Approach to take Root. All that’s needed is for a Lower Court to Decide that the Efficiency Gap is Consistent with prior Court’s Comments. Then the Metric could Spread from Lower Court to Lower Court, much as many Doctrines Spread without Court Intervention. The Result would not be a National Bar on Gerrymandering, at least not at first, but it would still amount to a Redistricting Revolution.

CLICK HERE to read this Four page (pdf) on how the Efficiency Gap Works.

The Markov chain Monte Carlo

Markov chains are Random Walks around a Graph or Network in which the Next Destination is determined by a Probability, like the Roll of a Dice, depending on the current Position. Monte Carlo Methods use Random Samplings to Estimate a Distribution of Probabilities. Combined Markov chain Monte Carlo (MCMC) is a Powerful Tool for Searching and Sampling from a vast space of Scenarios, such as all the possible Districting Plans in a State.

CLICK HERE to read the 55 page (pdf) A New Automated Redistricting Simulator Using Markov chain Monte Carlo.

Two Mathematicians: Duke University's Jonathan Mattingly and Carnegie Mellon University's Wes Pegden, have recently testified about MCMC approaches for the Federal Case in North Carolina and the State-level Case in Pennsylvania.

Mattingly used MCMC to characterize the reasonable range one might observe for various metrics such as Seats Won, across ensembles of Districting Plans. His random walk was weighted to favor Plans that were deemed closer to Ideal, along the Lines of North Carolina State Law. Using his ensembles, he argued that the enacted Plan was an Extreme Partisan Outlier.

Pegden used a different kind of Test, appealing to a Rigorous Theorem that Quantifies how unlikely it is that a Neutral Plan would score much worse than other Plans visited by a Random Walk. His method produces p-Values, which constrain how improbable it is to find such Anomalous Bias by Chance. Judges found both Arguments Credible and Cited them Favorably in their respective Decisions.

Pennsylvania Governor Tom Wolf brought, Moon Duchin, an Associate Professor of Mathematics and a Senior Fellow at the Jonathan M. Tish College of Civic Life at Tuffs University, earlier this year as a Consulting Expert for the State's scramble to Draw New District Lines following it Supreme Court's Decision to Strike Down the 2011 Republican Plan. His Contribution was to use MCMC Framework to Evaluate New Plans as they were Proposed, harnessing the Power of Statistical Outliers while adding New Ways to take into account more of the varied Districting Principles in play, from Compactness to County splits to Community Structure. His analysis agreed with Pegden's in flagging the 2011 Plan as Extreme Partisan Outlier, and found the New Plan floated by the Legislature to be just as Extreme, in a way that was not explained away by its Improved Appearances.

As the 2020 Census approaches, the Nation is bracing for another wild round of Redistricting, with the promise of Litigation to follow. I hope the next steps will play out not just in the Courtrooms but also in Reform Measures that require Maps made with Open-Source Tools to be Examined before any Plan gets signed into Law.

Computing will never make Tough Redistricting Decisions for us and cannot produce an Optimally Fair Plan. But it can Certify that a Plan behaves as though Selected just from the Stated rules. That alone can rein in the Worst Abuses and start to Restore Trust in the System.