Time series on Oregon State Rep and Senator

 So I have calculated the gerrymandering co-efficient for Oregon State Representatives and Oregon State Senate for the years from 2002 to 2018.  The co-efficient is stable for the State House of Representatives and does show that the re-districting resulting from the 2010 census had some effect in 2012.  The coefficient for the Oregon State senate is unstable.  One of the issues here is that approximately half of the senate seats are voted on every 2 years with possibly some special 2 year terms to replace vacancies.

More on gerrymandering

 I have done some analysis on the variance between the popular vote vs. seats held in a legislative body for a few states across the 2018 and 2016 elections.  I've tries to find if I can download the data in some format and while some of the states do provide some files that can be downloaded, it has been easier to create a spreadsheet and enter the values myself.  As a result it is rather slow to develop the data, but already, for comparison I have found a few interesting results.  See the graph below (made with matplotlib, let me know if you are interested in the code).  This plots a number of elections with the Kg coefficient that I have calculated on the x-axis and the number of seats in the legislature on the vertical axis.  For the state senates, I have used the number of seats in the senate even though generally only half the seats are up in any general election.  Then I plotted 2 lines.  The green line is where the marker would be if the overall Kg reflected a variance of 1 seat between the popular vote and the seats held.  The yellow line is where the marker would be if the Kg reflected a variance of 2 seats.

Some of the interesting things that we see here is that most legislative bodies seem to reflect some bias.  This does not identify which party benefits.  It just identifies if there is a bias.  Some bodies do have a pretty high level of bias.  For a number of these bodies I included a point for 2016 as well as 2018.  The direction of change cannot be predicted and seems to be a function of what motivates voters to go vote more than a function of the map.  While setting up a map overall can tilt the playing field, judging on the change in Kg from election to election, shows that migration, candidate quality and voter motivation can all influence the results, for example note the movement of the Idaho Senate and House between 2016 and 2018.  One moved in the direction of more gerrymandering and the other in the direction of less.  In compiling the statistics, I was struck by how many districts (about 20%) only had a single candidate.  This kind of situation clearly depresses voting based on the results that were reviewed.  In a district where there were multiple candidates, the number of votes cast was in some cases double.  For example, in Oregon, when there was only 1 candidate the number of "other" votes, typically write-ins and possibly spoilt ballots, was 10 times when a candidate from both the democratic and republican parties was on the ballot.

The next thing I am going to investigate is the change over time of the Oregon House and Senate, especially if I can see if there was a marked change as a result of the decennial redistricting.

Definition of a Gerrymandering coefficient using Oregon voting data 2012-2018

Abstract

Drawing of the lines of electoral districts is difficult work.  It is also one where an advantage can be built in systematically to favor a political party.  This systematic bias is called gerrymandering.  It creates a difference between the aggregate vote for each party and the number of seats held in a legislative body by each party.  It can be done in multi-party or two-party systems.  We will briefly look at some previous work that has been done to measure the level of gerrymandering.  This post introduces a way to quantitatively compare the level of gerrymandering by way of calculating a gerrymandering index [Kg] to be able to compare different jurisdictions.  In the USA, since district lines are drawn by a state body, it makes sense to look at this at the state level.  We will calculate the Kg for Oregon across a number of different elections and draw conclusions about the fairness of how the district lines are drawn.

Theortical considerations

An assumption of a fair electoral system is that the population, as a whole, gets a legislative body that closely mirrors the overall vote for the various parties that were running representatives.  This is represented by equation (1).

Where Vtotal is the total number of ballots cast in the election, Vi is the number of ballots cast for party i, Stotal is the total number of seats in the legislature, Si is the number of seats won by party i.

We can calculate the difference between the actual result in the proportion between parties and the theoretical result as shown in equation (2)

In the case where there is perfect agreement between the aggregate vote totals for each party and the number of seats won, this value is close to zero.  The maximum value is n, the number of parties.  One of the limitations is that the number of seats being considered is a small integer and as a result there is not a level of granularity to be able to get Kg smaller than n/2Stotal.

Previous work that has been done on this topic include:

https://www.washingtonpost.com/wp-srv/special/politics/gerrymandering/

http://www.svds.com/gerrymandering/

One of the metrics used in the previous research is "squiggliness" of the borders of districts where they are compared based on the variance from regular shapes.  I think this is unrealistic.  Borders and coastlines are ragged in many places and population density varies.

The Silicon Valley Data Science site has aged data and it is calculated for only the 2012 general election.  But it does use a similar methodology to determine the discrepancy between the number of seats vs. proportion of the vote on a state by state basis as overall nationally.  (It reports nationally, that for the US house of representatives, the republicans have 17 more seats than proportional representation would award them on a national scale but when considered on a state by state basis, the discrepancy is only 4 seats in favor of the republicans.)

Analysis of Oregon voting and results

I've calculated the Kg for the US house seats in Oregon, the Oregon Senate seats and the Oregon House seats based on data obtained from the Oregon Secretary of State for the 2012 through 2018 elections.  The total number of votes for Democratic candidates was summed.  Similarly for Republicans and finally, all of the other candidates as well as write-in votes was totaled for a third category.  Then the seat allocation by party was compared with the proportion of the overall vote.  From the difference in this comparison, the coefficient Kg was calculated.  The results are summarized in the graph below.

Conclusion and reflection

The US house races have the highest Kg values due to the small number of seats.  There isn't really any specific time trend in the values.  As you might imagine the imbalance was mostly in the Democrats favor, but in one case, the imbalance was in favor of the Republicans.  Comparing the US house vs. OR senate vs. OR house, it seems that the OR senate districts have the least amount gerrymandering since with 30 seats, you would expect higher values than the house, which has 60 seats.  More data needs to be gathered.  Analysis of years prior to 2012 will give insight as to whether the redistricting after the 2010 decennial census tilted the political field or not.  Analysis of other states will help calibrate the interpretation of Kg for the number of districts being considered.

In terms of seats, the US house of representatives is actually 1 seat in favor of the democrats.  The Oregon House of representatives is tilted 4 or 5 seats in favor of the democrats.  However the Oregon Senate has changed over time having 1 or 2 seats in favor of both parties at different times.

Having delved into this data so deeply has made me realize how simplistic the representation of Oregon as a Democratic haven is.  There are some areas that are have a large majority of supporters of one of the parties, but there are in fact a lot of areas which are quite close and the "Other" vote total was greater than the difference between the democrat and republican candidates.  Since the collapse of the center and the proliferation of litmus test issues, it does raise serious questions how government can be made to work to find compromises between the two factions and avoiding the tyranny of the majority.