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Just How Doomed Is the GOP?

By Jay Cost

The consensus right now among pundits is that the Republicans have simply lost the House of Representatives. The Democrats get 25 seats now - easy. Democrats are hiring committee staff. Nancy Pelosi is measuring for drapes. Even the general of the Republican campaign - Tom Reynolds - is going down. It's Over-with-a-capital-O.

Simply stated, the Republicans are doomed.

But are they?

One of the problems with making estimates like this is that, even when we have strong reasons to expect that the Democrats will pick up 25 seats, there is still a good chance that they will pick up less than 15 seats. The reason is that our estimate - regardless of the solid reasons that inform it - is only a central tendency. We must therefore expect some random variation around it. If we run the same type of election again and again and again - we would find, if we are right, that the average result will indeed be 25 seats. Sometimes, however, more seats will switch; sometimes less seats will switch, including less than 15.

This is the case whether we are conscious of probability theory or not, whether we use numbers or words to gauge how vulnerable the Republican majority is.

Another problem: is anybody really predicting that the Democrats will pick up 25 seats? Oh sure - people are saying 25 seats, but is that based upon anything more than a "spitball" assignment of probabilities to individual races? It is one thing to draw up a list of races "on the table," it is quite another to determine how many seats on it the Democrats will pick up. There are right ways to do the latter task, and there are wrong ways. Are we using a right way?

These issues interested me over the weekend, and induced me to do a little number crunching.

My task was two-fold. First, draw up a consensus estimate of how many seats will switch. When we apply probability theory to the big House race rankings out there (Cook Political Report, Rothenberg Political Report and Congressional Quarterly), how many seats do we come up with? My working hypothesis is that, while the consensus opinion uses Cook, Rothenberg and CQ to estimate big Democratic gains, it is not using them properly. Specifically, it is not making use of probability theory to predict. Accordingly, the true consensus estimate has yet to be specified. Think of it as the Greek distinction between opinion and true opinion. There is a consensus opinion, but it suffers from some logical mistakes along the way, so it is not true opinion.

Second, make a rough estimate of the probability, based upon these rankings, that the GOP will hold the House. This is based upon the working hypothesis that these rankings show a switch of less than 25 seats, and therefore we should maintain that the GOP, even in this current "climate" (or, perhaps more specifically, assuming that these rankers have evaluated the climate properly), has a sizeable, albeit less than 50%, chance of retaining the House.

Before we get into this - note that this should not be taken as an endorsement of any of these rankings. The idea here is that I am correcting the conventional wisdom based upon the data it most frequently uses. I am not making any comments about whether that data is valid. My final "conclusions" are not my conclusions, strictly speaking. What follows is meant to correct the media's flawed deductive process, which means that the premises are being assumed true for the sake of discussion.

Also note that, as these rankings change, so also will these estimates change.

Caveats and curlicues now aside, let's get to it. Cook, Rothenberg and CQ assign each House race to one of several categories.

1. CQ's categories are: Safe Democratic, Democratic Favored, Leans Democratic, No Clear Favorite, Leans Republican, Republican Favored, Safe Republican.

2. Cook's categories are only nominally different. He also has 7 overall: Solid Democratic, Likely Democratic, Lean Democratic, Toss-Up, Lean Republican, Likely Republican, Solid Republican.

3. Rothenberg adds 2 extra categories for a total of 9: Solid Democrat, Democrat Favored, Lean Democratic, Toss-Up/Tilt Democratic, Pure Toss-Up, Toss-Up/Tilt Republican, Lean Republican, Republican Favored, Solid Republican.

As of this writing, each ranker assigns seats in the following way.

 
Solid
Dem
Likely
Dem
Lean
Dem
Toss Up
Lean
GOP
Likely
GOP
Solid
GOP
Cook
184
10
13
25
14
17
184
 
Safe
Dem
Dem
Favored
Lean
Dem
No Clear
Favorite
Lean
GOP
GOP
Favored
Safe
GOP
CQ
183
12
13
18
17
25
167
 
Solid
Dem
Dem
Favored
Lean
Dem
Toss- Up
/Tilt Dem
Pure
Toss Up
Toss- Up
/Tilt GOP
Lean
GOP
GOP
Favored
Solid
GOP
Rothenberg
198
2
4
9
13
7
8
13
181

(Note: CQ Politics lists 26 seats as "GOP Favored" and 166 as "Safe GOP." However, a hand count of the races in each category yields the numbers in the above chart.)

The first problem that confronts us is: what probability should we assign to each category? None of the authors assign any for us. "Lean Democratic" is never operationalized. Our choices could have a major effect - different values could mean big changes in the final estimate. Obviously, "Toss-Up" is easy. That is 50%. So also are the "Safe" and "Solid" categories. They are all 0% (or 100%, depending upon your perspective). But, in between, there are gray areas.

As every good social scientist will tell you - when you are faced with a difficult "definitional" question like this, the best move is to punt: I have chosen to use multiple standards, and I am just going to leave the decision about which one is best up to you. There is no need to get bogged down in a philosophical question about what precisely it means to be a "Likely Democratic Seat." There probably is no right answer, anyway.

Accordingly, the use of multiple standards is prudent. So, I have 4 different "models." Each model assigns specific probabilities to specific categories differently. Note that these are not the only reasonable ways to operationalize these categories, though I think each of these is indeed reasonable.

Here are the different probability assignments for CQ Politics (and Cook, whose categories are only nominally different). Each cell gives the probability of a Democratic pickup for any given seat in the category.

 
Solid
Dem
Likely
Dem
Lean
Dem
Toss Up
Lean
GOP
Likely
GOP
Solid
GOP
Model 1
100%
83.33%
66.67%
50%
33.33%
16.67%
0%
Model 2
100%
95%
66.67%
50%
33.33%
5%
0%
Model 3
100%
100%
75%
50%
25%
0%
0%
Model 4
100%
95%
75%
50%
25%
5%
0%

A major difference between each model is how the "Favored" categories are treated. Ultimately, I think Cook, Rothenberg and CQ have some ambiguity built into their "Favored" categories. What does it mean to be "Favored?" Does it mean that, as of right now, the opposite party stands some chance in these races, proportional with the other categories (e.g. Model 1)? Does it mean that, as it stands, they have no chance; and, while these are the races that might become competitive, there is no reason to expect that they will - and therefore no reason to assign a non-zero probability (e.g. Model #3)? Does it mean that, as it stands, they stand no chance, but we should expect at least a few of them to become competitive, and therefore there is a reason to assign a non-zero probability (e.g. Models 2 and 4)? Obviously, on this issue, Model 1 is quite different from Models 2, 3 and 4 - while the latter are all fairly similar.

The other big difference between them is the "lean" category. How much is the favored party actually favored in this category? Again - there is no precise answer. I used two different definitions, both of which I think are reasonable.

Nevertheless, I will say that, for CQ Politics and Cook, Model 1 seems to be the furthest from what they imply. Cook and CQ both imply that their "Favored" categories are merely an on deck circle, but that we currently have no reason to expect any of them to come to the plate. Both Cook and CQ seem to suspect only latent vulnerabilities there. If those vulnerabilities are activated, those races would be upgraded - and therefore, right now, the chance of a switch in any given race is roughly 0%.

As Cook and CQ's categories are only nominally different, let's move on to Rothenberg's. Again, each cell represents each model's take on the probability of a Democratic capture of each individual seat in that category.

 
Solid
Dem
Dem
Favored
Lean
Dem
Toss- Up
/Tilt Dem
Pure
Toss Up
Toss- Up
/Tilt GOP
Lean
GOP
GOP
Favored
Solid
GOP
Model 1
100%
87.5%
75%
62.5%
50%
37.5%
25%
12.5%
0%
Model 2
100%
95%
75%
62.5%
50%
37.5%
25%
5%
0%
Model 3
100%
100%
83.33%
66.67%
50%
33.33%
16.67%
0%
0%
Model 4
100%
95%
83.33%
66.67%
50%
33.33%
16.67%
0%
0%

The differences between each model are the same here as they were for Cook and CQ. It all gets down to what "Favored" and "Lean" mean. While I thought Model 1 was a poor operationalization of Cook and CQ, it seems to be a decent operationalization of Rothenberg. His "Favored" category seems to me to be different than Cook's and CQ's. He has fewer races in them - and I think that the implication is that there is some level of competition right now, as it stands.

From these probability tables, it is now quite easy to derive an estimate of seat switches for each ranker and model. It is just a matter of "plugging and chugging" - as my 9th grade geometry teacher used to say. Each ranking category satisfies the assumptions of the binomial distribution. Accordingly we can derive the expected number of Democratic or Republican seats in each one by taking the number of seats in each category and multiplying that number by the probability we have assigned. We can then get a gross of how many seats the Republicans get and a gross of how many seats the Democrats will get. A simple matter of subtraction and we get the following estimates of net Democratic pickups:

 
Cook Political Report
Rothenberg Political Report
CQ Politics
Model 1
18.00
18.10
17.50
Model 2
17.20
17.30
16.00
Model 3
16.75
16.50
15.00
Model 4
17.10
17.00
15.65

As we can see, the results are somewhat contrary to the conventional wisdom. The range here is between 15 and 18 seats switching - which is more consistent with the House still being a toss-up, with a slight lean toward the Democrats. This does not smack of a blow-out.

We can also see that CQ's ranking is most sensitive to changes in models, while Cook's is the least sensitive. This is reducible, I think, to the fact that CQ has many seats in the outlying categories, while Cook has relatively few. This should serve as a good warning about betting on any estimate: specific predictions will ultimately come down to how you assign probabilities to the outlying races, which are the least susceptible to confident probability assignment!

So much for the first task. The second task follows pretty quickly - once we bear in mind that these estimates are central tendencies, and that we should expect variation around them. Our question now: what is the chance that the variation will be such that the GOP holds the House? Unfortunately, the answer is much rougher because the calculations are quite complicated. Depending upon the ranker and the model, the probability of a GOP retention ranges between a little better than 33% and a little worse than 50%. This would mean that - following Rothenberg's categories - the House itself falls somewhere between "Toss-Up" and "Toss-Up/Tilt Democratic."

And note that these estimates are predicated upon the currently bleak environment for the Republicans staying constant. As things stand right now, the odds of a GOP retention, according to these arguments of these rankers, are somewhere between 1/2 and 1/1. If Cook, Rothenberg and CQ are your guide - you should not take the GOP at even money, but anything less than that is a bet worth taking.

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