It is NP complete in determining to an absolute degree that a redistricting plan is excessively unfair, as the number of possibly districts grows exponentially. Demonstrating to a quantitative degree is more clear (eg stop drawing more maps after a few billion).

I highly recommend anyone interested read at least the summary of the above brief, but relevant details from page 4 are reproduced:

"With modern computer technology, it is now straightforward to (i) generate a large collection of redistricting plans that are representative of all possible plans that meet the State’s declared goals (e.g., compactness and contiguity); (ii) calculate the partisan outcome that would occur under each such plan, based upon actual precinct-level votes in one or more recent elections; (iii) display the distribution of the outcomes across these plans; and (iv) situate the State’s chosen plan along that continuum to reveal the degree to which that plan is an outlier. One can analyze outcomes for a statewide plan as a whole, or for an individual district within a plan. In this way, it is now straightforward to measure the quantitative degree to which a partisan gerrymander is excessive."

I had the privilege of sitting in on an Election Law class last year at YLS. The topic was gerrymandering, with a discussion of the legal arguments presented in Vieth v. Jubelirer.

For non-lawyers, the plaintiffs arguments for what should constitute illegal gerrymandering is technically complex, using statistic concepts, graphs (computer science), and even np-completeness. In essence, the argument was to use computers to draw all possible congressional districts, score them on the basis of discarded votes, and if the scoring of the drawn districts is greater than two standard deviations from the mean district, determine it is unfairly drawn. I found particularly striking an audio recording the professor shared of a lawyer struggling to answer John Robert's questions on technical topics. The professor used this as an example to be prepared to answer questions that you may not have a background in, even if the expert witnesses had already explained the concepts. Unfortunately, the court rejected the proposed determination of unfair gerrymandering in a 5-4 decision, with the dissent stating that the presented way to determine unfair gerrymandering was clever, correct, and should be revisited.

As we continue to push the frontiers of what we can do with computers, we need informed lawyers who can clearly present deep technical topics, and we need judges who are capable of understanding them.

This SO post is a great guide for where to look: https://stackoverflow.com/questions/388242/the-definitive-c-...

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