Tobler’s Law, Urbanization, and Electoral Bias: Why Compact, Contiguous Districts are Bad for the Democrats

Jonathan Rodden and Jowei Chen sent me this article:

When one of the major parties in the United States wins a substantially larger share of the seats than its vote share would seem to warrant, the conventional explanation lies in manipulation of maps by the party that controls the redistricting process. Yet this paper uses a unique data set from Florida to demonstrate a common mechanism through which substantial partisan bias can emerge purely from residential patterns. When partisan preferences are spatially dependent and partisanship is highly correlated with population density, any districting scheme that generates relatively compact, contiguous districts will tend to produce bias against the urban party. In order to demonstrate this empirically, we apply automated districting algorithms driven solely by compactness and contiguity parameters, building winner-take-all districts out of the precinct-level results of the tied Florida presidential election of 2000. The simulation results demonstrate that with 50 percent of the votes statewide, the Republicans can expect to win around 59 percent of the seats without any “intentional” gerrymandering. This is because urban districts tend to be homogeneous and Democratic while suburban and rural districts tend to be moderately Republican. Thus in Florida and other states where Democrats are highly concentrated in cities, the seemingly apolitical practice of requiring compact, contiguous districts will produce systematic pro-Republican electoral bias.

My thoughts:

This is cool stuff. Lots of people (going back at least to Bob Erikson in 1972) have talked about the idea that the geographic distribution of voters in modern times favors the Republican Party. The idea is that Democrats are concentrated in high-density areas, and thus geographically-compact districting plans will tend to pack Democratic voters into districts where they have 80% of the vote or whatever, thus wasting their votes. But the present article goes further than previous speculation and even previous data analysis by working with the (nearly) exact location of the voters.

The analyses in the article are great, and it’s fun to see how they play around with the spatial data. A lot more can be done here, I’m sure.

But I’m confused by one thing they write: “we take a unique empirical approach to the analysis of electoral bias. Rather than using district-level information to simulate hypothetical tied elections, we use precinct-level data from an election that was almost an exact tie.” It seems to me they’re mixing two ideas here:
(1) Using precinct-level rather than district-level data.
(2) Using a tied election rather than taking an election that’s, say, 53-47 and shifting it by 3 percentage points.

For point (1), yes, of course precinct level data are better, and it’s great that they put in the effort to get such data. Presumably earlier researchers would’ve used precinct-level data too, had such data been readily available.

For point (2), sure, if you happen to have a tied election, fine. But if you want to extend inference to non-tied elections, then you gotta to what you gotta do. You can’t just keep going back to Florida in 2000 or Missouri in 2008 or whatever, over and over again.

Anyway, I’m not saying they’re doing something wrong here, it just seems funny how they’re presenting the strengths and limitations of their method. I didn’t read every word of the article, but I assume they could apply their ideas to non-tied elections just by shifting to 50/50. And, as Gary and I discussed in our 1994 articles, even if you don’t introduce any national swing at all, you still might want to include variability in your hypothetical replicated elections.

The punchline:

In contemporary Florida, partisans are arranged in geographic space in such a way that virtually any districting scheme favoring contiguity and compactness will generate substantial electoral bias in favor of the Republican Party. This result is driven largely by the partisan asymmetry in voters’ residential patterns: Since the realignment of the party system, Democrats have tended to live in dense, homogeneous neighborhoods that aggregate into landslide Democratic districts, while Republicans live in more sparsely populated neighborhoods that aggregate into geographically larger and more politically heterogeneous districts. This phenomenon appears to substantially explain the pro-Republican bias observed in Florida’s recent legislative elections.

More fundamentally, I guess this might be considered a pro-rural or pro-suburban bias, or an anti-urban bias which would fundamentally alter the representation of different parts of the state, no matter which parties happen to represent them.

One thing that surprised me is that Chen and Rodden did not suggest multimember districts as a way to balance the playing field. Is this a proposal that Democrats in Florida (or elsewhere) should be making?

One other question. If more Democrats tend to win in super-safe districts where they get 70% or 80% of the vote, does this imply that they will be more free in their voting patterns to indulge their personal preferences, compared to Republicans who (on average) might be under more electoral pressure and have to worry more about reelection?

Other things

The graphs are just beautiful. They clearly had fun working with these data.

A few minor comments:

– Table 1 is just silly. “[0.0141, 0.0145]”? Excuse me? “+0.219778”??? You gotta be kidding me here.

– Figures 1 and 2 are fine, but the kernel density in the corner is just tacky. A histogram is the way to go here: it’s better to just see the data directly.

– I have no problem with Figure 3, except that they shouldn’t use the red/blue color scheme–that’s highly confusing given that the colors meant something different in the other figures.

– Figure 4: I’m not really happy with a “local spatial autocorrelation index” that has numbers like 1000 and 2000. Perhaps you can give it a different name; we’re all trained to thing of “correlations” as going between +1 and -1. Also, with these colors, I think you’d get some improvement if you added purple for the close precincts. Otherwise you’re getting some noise from the essentially arbitrary colorings of the precincts that are near 50%.

– Figure 5: The y-axis goes below 0 and above 1. That’s a no-no when displaying proportions. Also, make the dots slightly smaller (I know you can do it; see Figure 1); the overlappage is a bit distracting.

– Figure 6: Cute.

– Figure 7. Something’s wrong with your histogram. On the label it says 1000 simulations, but the y-axis goes up to 600. If the highest histogram bar has 600 points, then the total histogram has many many thousands! Better, I think, to just remove the y-axis entirely.

– Figure 8. A bit confusing to have square graphs with axes on different scales. Just make x and y axes both go from 0 to 1.

– Figure 9: Hey, you used JudgeIt! Cool. Also, please label the lines directly on the graph, and give them different colors! Don’t use that ugly legend that forces the reader to go back and forth, back and forth, to read the damn graph. Also, can’t you go back earlier than 1992?

20 thoughts on “Tobler’s Law, Urbanization, and Electoral Bias: Why Compact, Contiguous Districts are Bad for the Democrats

  1. Pardon my ignorance, but what's wrong with a kernel density? Too opaque a connection with the data? I've had some unpleasant surprises using histograms lately, so I've been trying to get a feel for the alternatives…

    When people talk about this anti-gerrymandering stuff, are voting systems other than winner-takes-all considered? I know there's a theorem that there's no perfect system, but it seems like one could do much better than winner-takes-all.

  2. No doubt about it, the party is over.

    All over the print and electronic media this week, the poobahs and pundits are predicting major Republican gains in next year's elections. What is their basis for so bold a prediction? Historically, the party of a sitting president always loses in the midterm elections. It is as natural as autumn following summer. However, they fail to take into consideration one crucial factor: this is no ordinary time.

    Given their weird behavior in the last year or so – and given the fact that they will only continue to self destruct in coming twelve months – I cannot foresee them gaining any serious ground in either the House or the Senate on Election Day next. In fact I can only see their numbers diminishing even further. By this time next year, Sarah Palin will be yesterday's news – count on it.

    We can only hope that out of the carnage of the GOP's destruction will come a third party that is a tad more moderate and thoughtful – and I must emphasize the word "Hope". Than ain't never gonna happen, baby! It's easy to predict that the Democrats will be running things for a long time into the future. The problem with that little scenario is, as Machiavelli said, "power corrupts and absolute power corrupts absolutely" – and the Democrats already have more-than-their-share of corrupt political hacks. For every Russ Feingold there are about ten Max Baucuses. If the Democratic Party is going to be taken seriously in their self-proclaimed roll as the "the party of the people" (and that's getting harder to believe by the day) they need to be purged of their dead weight.


    Tom Degan
    Goshen, NY

  3. Given this finding:
    Democrats have tended to live in dense, homogeneous neighborhoods that aggregate into landslide Democratic districts, while Republicans live in more sparsely populated neighborhoods that aggregate into geographically larger and more politically heterogeneous districts.

    Why shouldn't we have expected that the Republican Party would be more open minding and accomodating of dissent and the Democratic Party would be monolithic and single-minded? My impression is that the reverse has happened. Has this topic been addressed directly somewhere?

  4. Just ask Obama-contributor James D. Watson about open-mindedness. Thank God all those Democrats stood up to support his right to free speech when the Republicans were out to get him in 2007.

  5. Interesting stuff.

    On a not very related note: how about DC get two Senators? That would offset some of the obvious bias towards "conservatives" (I use scare quotes on that term because I don't think it accurately reflects the pure stupidity of the Republican party of today) that comes from so many rural low population states getting the same two Senators as states like California & New York.

  6. Anne: I'll post my answer to your question in a separate blog entry; it's worth its own discussoin.

    Anonymous and Steve: It's an interesting question, how to measure tolerance of dissent. The Democratic Party is of course more ethnically diverse than the Republican Party and is also more ideologically diverse in the sense of including more of a mix of liberals, moderates, and conservatives. (I posted some graphs on the blog a month or so ago on this point.) Whether this translates into tolerance of diverse ideas or speech is another story.

    Marvin: Personally, I think California, New York, Texas, Florida, etc. deserve a lot more senators! I guess D.C. can get a couple too if they really want.

  7. The shift to multimember districts is not a free lunch. Either they're all the same size (like Chile's two-member districts or Mauritius's three-member districts) and you still have a gerrymandering problem, or they are different sizes (like in Portugal, Spain, Finland, Brazil, Argentina, …). If you have variable district magnitudes, then a large party that draws strength in rural areas can dominate low-magnitude districts with few competitors from both sides, while a large urban party must run in high-magnitude districts and get nipped at from both sides. Our analysis of this "variance effect" estimated it moved over 15% of the parliamentary seats in several Portugal elections, where variance is extreme (Monroe and Rose, AJPS 2002).

    [And you don't get far with PR in one big national district either, because then representation reflects regional turnout variations. The problem is most obvious in conflict-prone regions, like Sierra Leone 1996 or Iraq 2005, where turnout ranged from 89% down to 2% in Anbar and left a legislature with few Sunnis and a legitimacy problem.]

  8. Burt: I agree that multimember districts are no free lunch, and that gerrymandering is still an issue even with multimember districts, but doesn't it avoid the extreme "wasted votes" issue discussed by Chen and Rodden?

  9. The obvious multi-seat districts would be the states. That does put more people in competitive districts, but it doesn't really have with equalizing the value of votes, and it would further strengthen the extreme partisans who participate in not merely primaries but conventions.

    With only one seat, Wyoming obviously wouldn't be affected.

    Michigan is balanced enough that it would have one seat in play, or may three in wave years. Sort of like what we have now. We would all be in "the" swing district, but it would also mean that any vote in Michigan is worth only 1/15 of a vote in Wyoming, because there are 15 times as many people weighing in on that one swing seat.

    California is big enough that even 2% would flip a seat, so it would almost certainly have 2-3 seats in play. But that's an awful lot of people to have votes that effectively influence only 2-3 seats.

    And even the minority party would have very little incentive to put moderates in the first several slots.


  10. Who cares? The demogrpahic trends of the U.S. will soon make the U.S. a one party state. The number of House districts that are overwhelmingly Democratic is growing and the number of seats that the Republicans have any chance of winning is shrinking.

    In the future, the real election will be in the Democratic primary (just like is occurs in those very blue areas like Baltimore, Detroit, NYC, Chicago, LA, etc). That means that a relevant election will occur about once a generation when the incumbent retires.

    Instead of spending time thinking about arcane topics like gerrymandering or more Senators, why not spend the time thinking about how politics will work in the coming one party state and whether the current checks and balances will still function in the coming one party state.

  11. The logic of our paper can help explain the situation you describe. Because of the relative extremism of U.S. cities and the heterogeneity of suburban and rural areas, there is a left skew in the distribution of preferences across U.S. Congressional districts. This means that in order to win, the Democrats need to cover a much wider ideological range than the Republicans. This phenomenon is described in a separate paper:

  12. Thanks for the comments Andy.

    A couple of quick responses:

    Yes, we certainly intend to apply this technique to non-tied elections in other states by applying some variation on a uniform swing to the precinct-level data. Another option is not to transform the precinct-level data, but to contrast the simulation results with the seat share that would be expected with a normal distribution of vote shares across districts (Kendall and Stuart cube law).

    Maybe we weren't clear enough, but one big advantage to working with presidential or statewide votes aggregated in various ways is that Florida legislative elections are remarkably uncompetitive and most seats are uncontested, so legislative election results are not terribly informative.

    On another point, we hesitate to refer to this as pro-rural bias. That seems to imply that rural voters prefer some specific policies, and those policies will tend to be favored over the policies preferred by urban voters. Of course this is plausible, but it requires that we have information about the distribution of preferences across precincts and districts, which we do not (in this paper). We have only shown that on the binary partisanship variable, Democrats are more geographically concentrated.

    This does not imply policy bias. To make a case for policy bias, we would have to show that the median voter in the median district on some salient issue dimension is to the right of the statewide median voter. Nor do we have any story here about distributive politics in which urban voters get screwed.

    Both of those seem plausible, and we are working on it, but we wanted to be careful not to overclaim given our data.

    What should the Democrats do? As you suggest, presumably they should push for statewide PR. But of course, what is good for individual incumbents is not what's good for the party.

    As long as SMD will be retained (a pretty good bet), the Democrats need to draw pie-slice districts from the city center out into the exurban periphery. But urban incumbents are not keen on heading out to suburban shopping malls to fight for votes, and attempts by Democrats to draw more 'efficient' districts are often killed within the party.

    In any event, such districts would get the attention of the justice department.

    What I find baffling, though, is that some Democrats are joining the push for districting reforms that would require strict compactness criteria and respect for municipal boundaries. This would be self-defeating in most states.

    Finally, thanks for the kind words and advice about the graphs.

  13. "Steve Sailer | November 15, 2009 9:24 AM | Reply
    Just ask Obama-contributor James D. Watson about open-mindedness. Thank God all those Democrats stood up to support his right to free speech when the Republicans were out to get him in 2007."

    Interesting escalation of "working the refs" type social partisanry in what seemed to me to be a strongly technocratic, nonpartisan space.

    I also thought Prof. Gelman's response was interesting. It was more a concession to a unidirectional ideological push than a policing to maintain the technocratic nature of a space.

    Interesting from a social espistemological perspective.

  14. Superdestroyer, demographic shifts won't ever make the U.S. a one-party nation. If growth rates are higher among left-leaning subpopulations, the GOP will have to move leftward to stay competitive. And if Democrats got big majorities, they'd be emboldened to pursue farther-left policies as well.

  15. Some very good, absolutely fascinating analysis here. I feel that the pendulum — pushed by that growing 18 – 30-yr-old cohort — has started to inexorably swing, and that some of the assumptions and definitions will have to change (positively leftward) over the next generation, but…just FYI, we tried the multi-representational districts here previously in IL (for the state houses) and ended up abandoning it (as a waste of personnel and money)…Of course — a la Ryan, Blago, etc. — we MAY NOT be the perfect proving ground for such political theories or practices, but…I definitely agree that the topic SHOULD be considered and debated. The "fact" that the US is an alledgedly "center-right" country is the most fallacious assumption we regularly hear. It's about time for the philosophical REALITIES to completely emerge and be properly considered…And more fully representational – say, 53 – 47, rather than 70 – 30 – Congressional districts would be a MAJOR step in that direction…

  16. Bill,

    Places like Chicago, Maryland, NYC, Mass., demonstrate that you model does not work. Given the proper demographics or state hstiory, the Democrats have easily function as the one relevant party in a one party state. The idea that the Republicans can become Democratic-lite and still compete is laughable. Karl Rove's incompetence demonostrates that moving the Republicans to the left loses more votes than it gets.

    No matter how much the Republicans pander to Hispanics, the Democrats can always pander more.

    David Axelrod is laying the ground work for the coming one party state with his tax the rich (read upper middle class whites) and give the money to core Democratic Party groups strategy.

  17. Hopefully Anonymous: I am happy to have (informed) partisan discussion here. There's little point in studying politics if you don't care about the outcomes.

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