Gary King, along with Bernard Grofman, Jonathan Katz, and myself, wrote an amicus brief for a Supreme Court case involving the Texas redistricting. Without making any statement on the redistricting itself (as noted in the brief, I’ve never even looked at a map of the Texas redistricting, let alone studied it in any way, quantitative or otherswise), we make the case that districting plans can be evaluated with regard to partisan bias, and that such evaluation is uncontroversial in social science and does not require any knowledge or speculation about the intent of the redistricters.
The key concept, as laid out in the brief, is to identify partisan bias with deviation from symmetry. I’ll quote briefly from the brief (which is here; see also Rick Hasen’s election law blog for more links) and then mention a couple additional points which we didn’t have space there to elaborate on. I’m interested in this topic for its own sake and also because Gary and I put a lot of effort in the early 90s into figuring this stuff out).
Here’s what we wrote on partisan symmetry in the amicus brief:
The symmetry standard measures fairness in election systems, and is not specific to evaluating gerrymanders. The symmetry standard requires that the electoral system treat similarly-situated political parties equally, so that each receives the same fraction of legislative seats for a particular vote percentage as the other party would receive if it had received the same percentage. In other words, it compares how both parties would fare hypothetically if they each (in turn) had received a given percentage of the vote. The difference in how parties would fare is the “partisan bias” of the electoral system. Symmetry, however, does not require proportionality.
For example, suppose the Democratic Party receives an average of 55% of the vote total across a state’s district elections and, because of the way the district lines were drawn, it wins 70% of the legislative seats in that state. Is that fair? It depends on a comparison with the opposite hypothetical outcome: it would be fair only if the Republican Party would have received 70% of the seats in an election where it had received an average of 55% of the vote totals in district elections. This electoral system would be biased against the Republican Party if it garners anything fewer than 70% of the seats and biased against the Democratic Party if the Republicans receive any more than 70%.
A couple of other things we didn’t have space to include
1. To measure symmetry, both parties need to be in contention. For example, there’s no way to determine if the districting system is “fair” to a third party that gets 20% of the vote, since it’s unrealistic to extrapolate to what would happen if the Democrats and Republicans get 20% of the vote. This connects to the idea that the “ifs” needed to evaluate partisan bias are based on extrapolation rules that are extensions of uniform partisan swing. If one party is always getting 70% of the statewide vote, our symmetry measure isn’t so relevant.
2. Our measure (and related measures) are not about “gerrymandering” at all (in the sense that “gerrymandering” refers to deliberate creation of wacky discricts) but rather are measures of symmetry (and, by implication, fairness) of the electoral system.
Thus, one could crudely imagine a 2 x 2 grid, defined by “gerrymandering / no-gerrymandering” and “symmetric / not-symmetric”. It’s easy to imagine districting plans in all four of these quadrants. We’re saying that the social-science standard is to look at symmetry, not at gerrymandering–thus, at outcomes, not intentions, and in fact, at state-level outcomes, not district-level intentions. This is a huge point, I think.
Very interesting topic. I read through the brief and found it to be frustratingly vague or even misleading about the way in which this "objective" symmetry measure must necessarily depend on imposing a specific statistical model about how votes shift between parties. The brief says:
I find that very surprising, and actually quite hard to believe. How can you claim to know what would happen if the Democratic share of votes in Texas went from 40% to 60%? Wouldn't it depend quite a bit on what was causing this gigantic shift? Are you really claiming that any differences in this prediction would be too small to matter?
Perhaps you could recommend one or two papers on the topic that would adress this concern.
Reading further, I find this in Andrew's 1994 APSR paper with Gary King:
If this is true, then I fail to see how it is possible to measure the "symmetry" of the Texas redistricting, since the prospect of Texas becoming majority Democrat now seems even more remote than the prospect of Alabama becoming Republican might have seemed back in 1994. I still think the idea of "partisan bias" is a nice one, but perhaps this is not the best court case to try to get it adopted as a standard by the court.
Ed,
Thanks for the comments. It's up to the courts to decide what hypotheses about vote shifts are feasible, given historical patterns. I'm no expert on Texas and so have nothing useful to add in that area. Our brief points out that objective standards of partisan bias (as defined based on symmetry) do exist in the social science literature. The symmetry standard is important, I believe, in going beyond the simple, and not particularly useful, benchmark of proportional representation.
An interesting idea, but I think this may be a situation where statistical analysis rather misses the point.
The whole problem can be avoided by just instituting a system of proportional representation on a state-wide basis using party lists. If that's not how they do things in Texas, it's presumably becuase they regard something else as more important than "fairness". The only thing that occurs to me (apart from a desire to cheat) that might justify not using proportional representation is a desire to have legislators who represent coherent communities. This is promoted by having geographically compact districts (perhaps modified a bit to produce more cultural homogeneity). I don't see how one can argue that such a policy is "unfair" just because it doesn't satisfy this rather abstract symmetry condition.
In any case, the other comments about the difficult counterfactual basis of the symmetry condition seem strong to me. It's basic to democracy that the people get to change their minds, drastically if they wish. Imposing a condition that assumes that they don't seems dubious, even if in fact they usually don't.
Radford,
Proportional representation is one way to get symmetry but not the only way. This is actually a topic that has been studied by statisticians for over 100 years.
Regarding districting in the U.S., it is a political process with many different goals–there have been several books written about the topic! Compactness is far from the only concern. It's an evolving process, and I think it is a worthy goal of social scientists to study it, and even study it quantitatively.
Regarding your other comment, I agree that any model should allow for the possibilities that people will change their minds, especially since, historically, vote swings do occur.
The more I think about this, the more dissatisfied I become. "Symmetry" is simply *not* a charactersitic of the "election system," it's a characteristic of a system *combined* with an assumed model of how votes shift between parties. In fact, I assert that *any* system can be made symmetric by imposing a suitable vote-shifting model. (Proof: just pick the model where everyone switches her vote.) Conversely, I conjecture (without proof) that most district-based systems can be made "non-symmetric" by some vote shift pattern (as opposed to strict proportional representation, or one big at-large district, or random districting not connected to geography, which are necessarily symmetric.) And in the real world, there is not just a single way for votes to shift, but many, so whatever model you pick, it's wrong.
BTW, I agree that studying this stuff formally and quantitatively is a worthy goal. In fact, political/social choice models are perhaps my favorite example of formal modelling in all the social sciences. These types of models have profoundly affected my intuition about everything having to do with democracy. So I hope Andrew keeps up the good work! (And Radford should explain why he's so sure that proportional representation=fairness.)
I realize this is mostly disagreeing with the rhetoric in the brief, rather than the basic idea. Including "symmetry" in court's analysis of redistricting would probably be a big improvement. If nothing else, making them more aware of this literature might avoid a lot of nonsense.
ed writes: …Radford should explain why he's so sure that proportional representation=fairness.
I'm not trying to argue that. I'm saying that there is a certain judgement about "fairness" implicit in the idea that symmetry is a good thing, but if you have that idea of fairness, it would be better obtained with proportional representation. So if Texans don't want proportional representation (and if they do, why don't they have it?), they must not share this idea of what is a "fair" electoral system, and so the symmetry condition is irrelevant. What I
think is fair isn't at issue.
Andrew – When you say that gerrymandering and symmetry are not the same thing I think you are using the classical definition of a gerrymander — oddly shaped districts. In my mind, the term has evolved to mean a districting plan, irrespective of the compactness of the districts, that leads to bias (or asymmetry). I do agree that it is possible to fill all four cells of 2×2 table if you define gerrymandering only as the refering to the shape of districts (i.e. there can be "fair" plans that have very oddly shaped districts), but I suspect that most folks now think of gerrymandering as an effective non-symetrical district plan (which could contain very pretty compact districts).
Radford,
Your view is that symmetry is "better obtained with proportional representation." It's fine to have that view, but many people do not share it. Symmetry is a more general condition than proportinality, and there are good reasons for using symmetry as a baseline even when proportionality is out of the question. See our 1994 paper and also much of the literature on this topic (dating back at least to 1898!). The courts in the U.S. have in fact ruled that certain districtings violate people's rights, and they do sometimes require that districts be redrawn.
Tom,
What I meant is that it's possible for completely "innocent" plans to have partisan bias (asymmetry). It's also possible, of course, to get partisan bias on purpose. And we did find that the plans created by partisan redistricters tended to have more bias than those created by bipartisan redistricters.
A lot depends on the geography of the voters in the state. Or, in your terms, it's possible to gerrymander without trying to do so.
Phil Henshaw sent some interesting thoughts. I'm posting it here for comments.
Redistricting for better debates
I also don’t think the objective of redistricting should be to have
elections produce party representation to match voter affiliation.
Glaring asymmetry is just a symptom. I would more favor having
districts drawn so every community would have good debates leading up to
elections. Removing the need to debate the issues is what I see as the
real crime of politicians drawing safe districts for themselves. It’s
been cited by the reformist state senator Eric Schneiderman, among
others, as a main source of New York’s perennial political gridlock.
Compromise becomes unnecessary and irrelevant. I also know other people
who'd like to know how to solve this.
What I’d like is a way to draw election districts using a statistical
model that would maximize swing districts, where the unpredictable
voters hold the balance of power. I don’t actually know how to write a
map drawing rule for equal population districts to do that, but I assume
there are lots of ways, some more or less desirable for other reasons.
You’d have to experiment with it. Granted, almost anything would be
better than the present arrangement where politicians can treat voters
as property to be packaged for their own convenience.
On thing I’d like is if redistricting both maximized swing districts,
and also respected natural community boundaries. One way to do that
would be to let everyone ‘vote’ the boundaries of their own perceived
neighborhood. It could be done with crude or fancy tools, basically
letting people draw on a map what they think of as their neighborhood
and look at the overlay. Do it with sophisticated statistics, or just
view the composite in Photoshop and adjust the levels and contrast.
The rule I’d have in mind is that district boundaries not divide a
cohesive neighborhood more than once. I think local community
structures are something to value and make important again, and this is
one way to do it.
I’d also put some value on diversity in other variables, income and
cultural diversity, for example. If you put too high a value on
assuring diversity in every district, of course, it could have negative
effects. Then every debate would become bland and might turn on the
same homogenous inconclusiveness. One thing you want in good debates
is good interplay between the local debates. I’m sure we could make
headway with how to write the design rules if we understood now really
important it is to the health of our democracy and the welfare of the
Earth in the both the near and long term. We may be at a special
moment of crisis right now, but life is perennially at moments of
crisis, and our supposedly liberating form of government seems
perennially subject to the abuse of power or frozen in stasis partly
because of this minor design flaw. phil henshaw pfh[#]synapse9.com