## Statistics and the filibuster

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Ezra Klein pointed out that Senate.gov provides a lot of historical data on the composition of the Senate and its procedures. One of the pieces of data it provides is the number of cloture motions filed in every congress since the 66th (1919-1920). I've plotted the data (in black dots) in the graph to the left. The red dots show the fit of a statistical model to the data in which the number of cloture motions is elated to the session in which they were filed, the proportion of Democrats in the Senate, and an indicator of whether the president is a Democrat or a Republican. As you can see, the model fits the data pretty well. (See the next page if you're interested in more details.)

As Klein points out, the number of cloture motions filed is an imperfect measure of how frequently the filibuster is used. For example, Senators often threaten filibusters and don't have to follow through. Still, the dramatic increase in the number of cloture motions filed over the last four decades must reflect a dramatic increase in the number of times bills have been filibustered in the Senate. There's a hint of an increase in the number of filibusters up to the 91st, but since then the number of filibusters has increased dramatically.

If you're thinking that's a Watergate effect, I'm afraid the timing isn't quite right. The dramatic increase in the number of cloture motions files occurs in the 92nd Congress (1971-1972) - pre-Watergate. I'm sure some political scientist has noticed this before and has a good explanation for why there was such a break with tradition in 1971-1972. It also can't be associated with the change in rules reducing the margin necessary to invoke cloture from 2/3 to 3/5. That rules change happened in 1975. If someone has a good explanation, I'd be delighted to hear it. In fact, the dramatic increase may not be so dramatic after all. Read on for an explanation.
The model I fit included a "change point" where the regression changed. But it turns out that if you fit a much simpler model without a change point, it also fits the data pretty well. A lot of what looks like a break around the 92nd Congress is really just exponential growth taking off. Not all of it, but a lot of it.

Here are a few details on the more complicated model I fit. First, you can see a plot of observed versus expected values in the plot at the left. Second, if you really want to see the details, you can grab the CSV spreadsheet with the data (clotureCounts.csv) and the R code (cloture.R) I used to drive a couple of JAGS scripts (cloture.txt and cloture-fixed-k.txt) and lake them for a testdrive yourself.

If you're not that interested, here's what you'll probably want to know:

• I assumed a Poisson response and used a log link in the regression.
• Although it looks as if there's a break in the relationship around the 92nd Congress, I decided to fit a changepoint model to let the data identify the point at which the slope of the regression changed. It identified the 92nd Congress as the change point with a high posterior probability (ca. 0.997).
• As you can see from the plot at the left, there doesn't seem to be an obvious pattern in the departures from expectation. While I'm sure better models are possible, it doesn't appear that there's any reason to include nonlinear terms involving these covariates.
• I ran 5 independent MCMC chains with a burnin of 5000 iterations, followed by a sample of 25,000 iterations, thinning by 5.
• The figures are produced from an analysis in which I fix the change point at the 92nd Congress.
• The Rhat statistics give strong evidence that the MCMC chains have converged.
If you're wondering why I haven't presented interpretations of the regression coefficients, it's because I haven't had a chance to make sense of them. I'm a biologist after all, not a political scientist. One thing that does occur to me is that the small difference in beta.cong between the two segments is consistent with most of the apparent break being the result of exponential growth taking off. If you're interested in staring at the coefficients and don't want to run the analysis yourself, here they are:

```Inference for Bugs model at "cloture-fixed-k.txt", fit using jags,
5 chains, each with 30000 iterations (first 5000 discarded), n.thin = 5
n.sims = 25000 iterations saved
mean    sd    2.5%     25%     50%     75%   97.5%  Rhat n.eff
alpha[1]        0.156 1.150  -2.116  -0.606   0.142   0.943   2.379 1.004  1100
alpha[2]        0.287 0.474  -0.636  -0.032   0.290   0.608   1.209 1.007   460
beta.cong[1]    0.064 0.022   0.022   0.049   0.063   0.078   0.107 1.002  4400
beta.cong[2]    0.083 0.006   0.072   0.079   0.083   0.087   0.094 1.004  1100
beta.pres[1]   -0.151 0.335  -0.809  -0.378  -0.150   0.074   0.509 1.002  2400
beta.pres[2]   -0.067 0.062  -0.187  -0.109  -0.067  -0.025   0.052 1.003  1700
beta.ratio[1]  -0.225 1.697  -3.622  -1.341  -0.177   0.924   3.021 1.004  1100
beta.ratio[2]   1.672 0.590   0.534   1.268   1.671   2.071   2.826 1.007   470
deviance      290.338 3.897 284.591 287.465 289.696 292.551 299.492 1.001  5100

For each parameter, n.eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor (at convergence, Rhat=1).

DIC info (using the rule, pD = var(deviance)/2)
pD = 7.6 and DIC = 297.9
DIC is an estimate of expected predictive error (lower deviance is better).```