Hmm. This is interesting because I've always wondered about using mathematics to generate a "gerrymandering-ness metric" from a given population/boundary distribution. The idea being that instead of having the supreme court scratch their heads wondering if a boundary assignment was unfair, you could just compute the metric.
But this article seems to imply that this metric can't exist.
Ok so now I wonder about the corollary: use an algorithm to generate the boundaries. If the article has a proof that all boundary assignments are unfair, then presumably an algorithmic boundary generator can be made to be randomly unfair one way or the other, balancing out the unfairness overall.
I think the "gerrymandering-ness metric" you are looking for is called the "Efficiency gap". The problem, of course, is getting everyone to agree what the acceptable range is for this value, and to make it the law.
But this article seems to imply that this metric can't exist.
Ok so now I wonder about the corollary: use an algorithm to generate the boundaries. If the article has a proof that all boundary assignments are unfair, then presumably an algorithmic boundary generator can be made to be randomly unfair one way or the other, balancing out the unfairness overall.