Bangia et al. 2017. “Redistricting: Drawing the Line”. Arxiv preprint: arXiv:1704.03360 [stat.AP].

Fun application of MCMC methods!

The first-past-the-post electoral systems (common in countries with electoral system that has common roots with the UK Westminster system, i.e. most of the Anglophone countries, most famously the US) are notoriously susceptible to effects of Gerrymandering (named after an ancient Bostonian electoral monstrosity of Governor Elbridge Gerry). However, while it’s often easy to intuitively spot if the electoral district boundaries have been drawn in a gerrymandered way, the evidence is seldom clearcut. For the legal purposes (preferably a court would order changes to be made to gerrymandered district boundaries), it would be beneficial to have a robust numerical measure that tells if a set of district boundaries are fair or not.

In the paper linked above, Bangia et al. generate (or sample1) 24 000 random but “reasonable”2 Congressional electoral district boundaries for the US state of North Carolina. Using the precinct-level data from the 2012 and 2016 Congressional elections, they compute the election results for each such obtained redistricting. This provides a Monte Carlo estimate of the pdf over the space of all possible redistrictings, on which various metrics can be based on.

Results: the real election results (with the real district boundaries) of North Carolina in 2012 and 2016 appear to be quite atypical.

Lately, there’s been lot of noise over the English-speaking Internet on computational / statistical methodology for evaluating how gerrymandered a particular set of district boundaries is. The main reason is that the US Supreme Court recently agreed to hear a case concerning Wisconsin districts, where the crux on the argument is based on a simple measure called efficiency gap. The efficiency gap score attempts to measure the number of wasted votes (underlying idea being that with gerrymandered districts the gap of votes wasted will be larger than with a natural district boundaries). See:

Stephanopoulos and McGhee. 2014. “Partisan Gerrymandering and the Efficiency Gap”. 82 University of Chicago Law Review, 831 (2015). link

And for critical analysis:

Bernstein, Duchin. 2017. “A formula goes to court: Partisan gerrymandering and the efficiency gap”. arXiv:1705.10812

Footnotes

1 :

With simulated annealing!

2 :

Using criteria such as even distribution of the population to districts and creating “geographically connected and compact” districts (in isoperimetric sense) and avoiding county splits and demographic representativeness.