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Theoretical work on legislative districting

Stephen Coate (Dept. of Economics, Cornell) and Brian Knight (Dept. of Economics, Brown) wrote a paper, “Socially Optimal Redistricting,” with a theoretical derivation of seats-votes curves. The paper cites some of my work with Gary King on empirically estimating seats-votes curves. Coate and Knight sent the paper to Gary, who forwarded it to me. It’s an interesting paper but has a slight misrepresentation of what Gary and I did in studying seats-votes curves and redistricting.

Coate and Knight’s paper centers on a derivation of optimal curves under a theoretical model of voters. I don’t have much to say on their model and theory (see below for a couple of comments); the main reason I’m writing this is to update their characterization of empirical work on seats-votes curves (on pages 3-4 of their paper). They cite some of the work of Gary and myself but incorrectly state that we work with the so-called “bilogit” curve, which is a model that Gary created in the 1980s and then abandoned for our more flexible approach. We don’t actually assume any functional form for the curve–it is not restricted to be linear, or cubic, or bilogit, or any parameteric family of curves. We fit the model using JudgeIt.

To put it another way, we model district-level votes. We don’t model the seats-votes curve directly. The seats-votes curve is a consequence of the votes, not something that is specified on its own. As a result, the seats-votes curve is not restricted to any particular form. (See this our 1994 AJPS paper for details of our model and fitting procedure, and our 1990 JASA paper for an earlier version of the model.)

What are seats-votes curves?

On page 4 of their paper, Coate and Knight write that “the underlying foundations of the [empirical] analysis are opaque. While the seat-vote curve is an undeniably elegant construct, the relationship between seat-vote curves and districting is not clear.” I think our 1994 AJPS paper should clarify this for them. Basically, the fundamental concept is the vector of vote proportions for each of the parties in each district. This vector has a probability distribution (representing what could happen for a future election, or what could have happened for a historical election), and the seats-votes curve (as we define it) is the function of expected seats, given votes. This relates to districting because districting affects the vector of vote proportions (mostly by moving votes from one district to another, also by affecting the decisions of candidates to run, campaign strategies, etc.).

A couple of minor comments

I question some of the assumptions of the model (in particular, the claim that “every citizen votes sincerely for the representative whose ideology is closest to its own”–this would seem to be contradicted by the fact of a large and consistent incumbency advantage) but I certainly respect the idea that theoretical work must begin with a highly stylized model.

I also think it’s funny that they refer to lower-case “democrats” and “republicans.” A political scientist would never do that! It would be like a minister referring to “jesus” and “god.”

In summary

I’m not trying to knock the Coate and Knight paper. As they point out, empirical and theoretical projects are judged by different standards. An empirical model is supposed to be realistic and fit the data; a theoretical model is supposed to be conceptually compelling and have as few “exogenous” factors as possible. Two different ways of understanding social phenomena. I just wanted to clarify that the existing empirical methods for estimating seats-votes curves are pretty sophisticated and go far beyond fitting two- or three-parameter models. So, developing theoretical models is great, but they won’t have the descriptive power of our empirical models. (Or, to look at it the other way, the empirical models will never have the simplicity of the theoretical models they’re developing.)