Miller's point is that, by just about any measure of "compactness," one can imagine highly gerrymandered districts that still score pretty well. He and his co-authors prefer the term bizarreness for his measurement. Basically, it's an easily quantifiable standard that could contain gerrymandering without punishing legitimate districts that are funny-looking by necessity.
Still, how much does the shape of a district really tell us about the degree of political monkey business? If a district has to take a few odd turns to encompass a diverse, competitive group of voters, is that a bad thing?
Part of the difficulty of this debate is that no one can agree on the definition of a "perfect distribution"—that is, what the demographics of a district's population should be. Should they match the demographics of the whole state? Probably not; this would require slicing up urban areas like a pizza into different districts and would award a highly disproportionate number of seats to the majority party in the state. But the goal isn't necessarily to have the distribution of seats match the distribution of Democrats and Republicans in the state. If that were the idea, we could just hold elections the way many European countries do it. (One of the presenters said he gave a similar talk in Bulgaria, where the audience was totally perplexed at how complicated we make it here.)
The best idea of the session, which was arranged by Scientists & Engineers for America, came from Sam Hirsch, who is not a mathematician but a lawyer. He thinks redistricting should be a public contest that uses the law and the metrics developed by mathematicians as a scoring system. It's kind of like a Netflix Prize for redistricting.
Under the Hirsch plan, any public proposal would have to comply with the law and current standards for equal population, continuity, and so forth. For all the plans that passed this threshold, there would be three further metrics:
- County integrity (matching district lines with county lines when possible);
- Partisan fairness (roughly half the districts should be more Democratic than the state as a whole, while the other have should be more Republican—the system doesn't include third parties);
- Competitiveness (a little more complicated, but recalculating previous election data according to the new districts).
The advantage of a plan like Hirsch's, which draws heavily on a lot of the mathematicians' research, is that it's quantifiable. Once plans start rolling in, any future proposal would have to score higher on those three metrics to be considered. And it would be fairly easy to substitute metrics if a particular state wanted, say, to value compactness (or nonbizarreness) over county integrity.
Hirsch is realistic about the odds that many states would adopt his plan wholesale (though his plan includes a sample constitutional amendment just in case), and it would take years for today's computers even to run the numbers on every possible plan. But the basic idea that districts can be rigorously quantified as to their competitiveness, bizarreness, congruity with media markets, racial enfranchisement—or any number of other metrics—is a potent one. Once plans can be evaluated according to measures that everyone can agree with, at least in principle, one needs only some form of competition to find the one that satisfies all parties reasonably equally. Screw the algorithms: Let the people do the heavy lifting.