The following is a guest post from Greg Warrington and Jeff Buzas, which may be relevant to the upcoming Supreme Court partisan gerrymandering case:

I am grateful to Rick Hasen for the opportunity to post here about my recent preprint with Jeff Buzas.

Quantitative research into partisan gerrymandering serves at least two important ends. One is the goal of identifying partisan gerrymander and quantifying how extreme they are. Measures such as the compactness of an electoral district and the efficiency gap of an election can help do this. These measures can, and do, play a supporting role in litigation. Another is the goal of evaluating the impact of gerrymandered districts on people and their representative bodies. While there are many questions one could ask about the effects, we will focus here on one question in particular: To what extent does partisan gerrymandering influence the partisan composition of the US House?

In a February 2017 post on this blog, Rick Pildes describes a 2016 paper by Jowei Chen and David Cottrell that tries to answer this question. Their conclusion in the paper is that the Republicans only benefited from partisan gerrymandering by a single extra seat (net) in the US House in 2012. (In a follow-up to Rick Pildes’s post, Justin Levitt explores what this study does not tell us as well as some of the limitations of the Chen-Cottrell approach.) But as Rick Pildes presciently noted, "[a]ny complex study of this sort poses many methodological issues." In our preprint, Jeff Buzas and I identify one such methodological problem in their paper. We believe it is serious enough to invalidate their conclusion.

The Chen-Cottrell approach consists of two main parts. The first is the generation of simulated district plans that provide a basis to which enacted district plans can be compared. There are many challenges to generating appropriate distributions of districts (and even defining what one means by "appropriate"). Even so, we view the general approach of utilizing simulations as fundamentally sound. The flaw in their methodology occurs in the second part of their approach. There, they compute the expected number of democratic seats associated to a given district plan (whether real or simulated). Our critique of Chen-Cottrell lies in the particular way in which they approach this second part. Chen and Cottrell are not the only ones to compute the number of seats each party wins in a simulated district plan. But they are the only ones we know of who make this computation using a logistic regression. Unfortunately, a logistic regression is not sensitive to the packing and cracking by which partisan gerrymanders occur. Fortunately, our critique does not apply to any other papers we know of.

We will not attempt to give a detailed explanation in this post of why the logistic regression should not be used in this way. However, we can sketch the problem. What Chen and Cottrell do is assign a probability that each district elect a Democrat based solely on the presidential vote in that district. They determine this probability by fitting a logistic regression using historical data. In this context, such a model will generate probabilities that change gradually. For example, if the presidential vote in a district is 45%, the probability of electing a democratic legislator as determined by their logistic regression model will only be moderately lower than if the presidential vote there had been 55%. These probabilities are not wrong, they are merely the natural consequences of determining a probability from hundreds of historical races, each with its own idiosyncrasies.

The problem faced by the model is that map drawers are concerned not with what happens on average, but what will happen in a few particular districts of which they know a lot about. A gerrymander they create may fade in potency over time and may be susceptible to wave elections. But in the short term, reducing the democratic presence in a district from (say) 55% to 45% can be enough to effectively guarantee that what was a democratic district becomes a republican one. This substantial change in probabilities simply isn’t captured by Chen and Cottrell’s application of a logistic regression.

In our preprint, we offer our own computation of the net influence of partisan bias on the composition of the House using the declination introduced in this preprint. Our conclusion is consistent with that of a report from the Brennan Center authored by Michael Li and Laura Royden: the Republicans won more than 20 extra seats in 2012. But since our preprint does not utilize simulations, it is unable to distinguish between extra seats due to partisan gerrymandering and extra seats due to inherent geographic advantages. The very limited investigations we have done suggest that little is due to geography, however further investigation on this point is certainly warranted.