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# Extreme gerrymandering and the purpose of elections

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There’s an interesting article on the math of extreme gerrymandering — and of detecting it — at a magazine, Qanta, that I’ve never head of before. The quotation that I’ve seen circulating concerns, first, how simulations can now produce compact districts that are still heavily gerrymandered, and, the math of addressing that.

Util recently, gerrymandered districts tended to stick out, identifiable by their contorted tendrils. This is no longer the case. “With modern technology, you can gerrymander pretty effectively without making your shapes very weird,” said Beth Malmskog, a mathematician at Colorado College. This makes it that much harder to figure out whether a map has been unfairly manipulated.

Without the telltale sign of an obviously misshapen district to go by, mathematicians have been developing increasingly powerful statistical methods for finding gerrymanders. These work by comparing a map to an ensemble of thousands or millions of possible maps. If the map results in noticeably more seats for Democrats or Republicans than would be expected from an average map, this is a sign that something fishy might have taken place.

But making such ensembles is trickier than it sounds, because it isn’t feasible to consider all possible maps — there are simply too many combinations for any supercomputer to count. A number of recent mathematical advances suggest ways to navigate this impossibly large space of possible simulations, giving mathematicians a reliable way to tell fair from unfair.

The piece is partially built around Allen v. Milligan, a case where I assume the Court will de facto extend its principled position that a) it’s unconstitutional to design districts based on race unless b) the aim is to elect more Republicans to Congress. If it does so, it may point to the same kind of mathematical simulations it previously dismissed on the grounds that “math is hard.”

But what caught my attention was the following:

Colorado has an unusual requirement beyond the typical constraints of contiguity and compactness: Colorado law also requires that districts be “competitive.”

The law only vaguely defines competitiveness, so the independent commission in charge of drawing Colorado’s state legislative district map decided to define a competitive district using historical data. For a hypothetical district to be “competitive,” the vote total for selected races over the previous three election cycles, for both Democrats and Republicans, had to be between 46% and 54%.

The commission then turned to DeFord, Malmskog and Jeanne Clelland, a mathematician at the University of Colorado, Boulder, along with Flavia Sancier-Barbosa, a colleague of Malmskog’s at Colorado College. The four researchers used the ReCom algorithm to generate ensembles of millions of maps that followed the state’s redistricting criteria; they then used those ensembles to figure out a “range of values for how many districts you might expect to fall into that competitive range,” Clelland said. Then, as the commission drew new plans, the mathematicians determined where they fell within the statistical analysis. In the end, the legislative redistricting commission selected a map that had more competitive districts than the average that the mathematicians saw in their ensembles, Clelland said.

Clelland noted that while competitive districts might sound fair, in practice they can conflict with proportionality, the goal that the number of representatives from either party should match the number of voters in that party statewide. “If you have a whole lot of districts where the result is really close to 50%, then a very small change in the fraction of the vote share could make a very big change in the fraction of the seat share.”

We don’t talk about it very much, but arguments against extreme gerrymandering rest on different, and not necessarily compatible, theories of electoral politics.

When Clelland references “proportionality,” she’s invoking the principle that the best electoral outcomes are ones that most closely resemble (see Arrow’s Impossibility Theorem) the distribution of preferences among voters. For example, if the electorate splits 30-20-50 between different parties, then elections should produce a 30-20-50 distribution of power. If this is what we care about, we probably want some form of proportional representation. In the context of designing districts in a two-party system, highly uncompetitive districts are just fine so long as they best represent the distribution of preferences across the electorate.

If we think the point of elections is to constrain government officials by holding them accountable to voters, then we probably want more competitive elections even if those violate principles of proportionality. This might not be true in all political contexts, but it seems like it’s the case in ones that combine a) high levels of partisan polarization and b) primary systems that empower more the most partisan voters. We might prefer competitive elections over proportionally if we think that:

• Politicians who don’t fear being tossed out of office in general elections tend to become more corrupt and less sensitive to the effects of their policies on ordinary people;
• They encourage norms and habits of democratic citizenship insofar as they increase the stakes of participating in elections and electoral politics.

So far I’ve made the implicit assumption that parties are the best way to aggregate interests, but one reason to favor “compact districts” is the argument that geographic proximity can create strong, shared preferences that transcend parties. I honestly don’t know how much that remains true as even local elections become increasingly nationalized.

There are a lot of other electoral options than single-member districts or the party-primary-followed-by-general-election model that predominates in U.S. politics. They have their own advantages and drawbacks.

The important point is that how we understand those pros and cons, and how we weigh them, depends on often implicit (or at least unarticulated) wagers about the purpose(s) of elections in liberal republics (aka representative democracies).

That’s easy to forget, though, because extreme gerrymandering in places like Wisconsin and North Carolina satisfies none of the arguments about why elections matter. Not proportionality. Not accountability. Not the representation of geographically specific interests. It doesn’t even satisfy a strictly majoritarian theory of democracy. That’s why, as Scott likes to point, Roach, despite some very stiff competition, is likely the worst SCOTUS decision in decades.