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.
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