# Was Gerrymandering the Culprit? — Part I

Results updated on November 23, 2012, with final Congressional results for 434 races; NC 7th is still undecided.

It is now time to put some of the findings from earlier postings together and try to determine the extent of gerrymandering in the 2012 Congressional Elections.

Three factors should influence the number of House seats a party wins in a state Congressional election:

I have taken two separate measurements of the first item, the relationship between seats and votes.  I have calculated both a longitudinal measurement using elections from 1942 on, and a cross-sectional measurement using state results for 2012.  In both approaches I estimate the coefficients α and β of this “logit” model:

The two models produce very different estimates for α, the seat “bias,” because it varies historically.  However the two estimates for β are nearly identical. The longitudinal estimate was 1.92; the cross-sectional estimate is 2.08.  For simplicity, I will just use two for the value of β.  (Mathematically, that implies that the ratio of Democratic to Republican seats varies in proportion to the square of the ratio of their votes.)

In this Technical Appendix, I explain why, if the Democrats win exactly half the vote, the only way they can win exactly half the seats is if the “bias” term α is zero. We can use this fact to create an “unbiased” distribution of seats.  I simply substitute two for β and apply it to the logit of the state-wide Democratic vote for Congress.  I will call this the “unbiased allocation.”  For each state I compare this estimate to the number of seats the Democrats actually won. Here are the results:

I have included all states where the difference between the predicted and actual number of Democratic seats was at least 0.7.  The state that gave us the word “gerrymander,” Massachusetts, shows the largest pro-Democratic deviation.  While the unbiased allocation model would award the Democrats only seven or eight of the nine seats in that state, not one Republican represents the Commonwealth of Massachusetts in Congress. The other state where Democrats did better than expected is Arizona, where they won a majority of the state’s Congressional seats with a minority of the popular vote.  Arizona had two of the closest races in the country, and they both fell to the Democrats by slim margins. All told, eight states including four New England states, have new Congressional delegations with an “extra” Democratic member in their numbers.

Many more states deviate from the unbiased allocation on the Republican side, with half-a-dozen states showing a pro-Republican bias of two, three, or, in the case of Pennsylvania, four seats. All told, sixteen states met our 0.7 criterion.  Compared to an unbiased allocation, the results in these sixteen states probably cost the Democrats 28 seats.  When we subtract out the eight extra seats the Democrats won in the pro-Democratic states, we get a net Democratic deficit in 2012 of some twenty seats compared to an “unbiased” allocation based solely on the popular vote for Congress in each state.

Before we start attributing all those seats to Republican gerrymandering, we first need to consider what other factors might influence the translation of Democratic votes to Democratic seats.  There is good reason to believe that the geographic distribution of Democratic voters by itself creates a pro-Republican bias when district lines are drawn.

Accounting for Geography