Chapter 8 Vote Models

8.1 Hypotheses

  • Party
    • McConnell: top priority is making Obama a one-term president. Partisanship above all else.
    • Teamsmanship is paramount; party pressure overrules individual preferences (Lee)
  • Ideology
    • Individual policy preferences are paramount and almost always 1D (Poole and Rosenthal)
    • Single spatial dimension accounts for nearly all votes in polarized times
    • Ideological heterogeneity within parties is large (Shor and McCarty)
  • Opinion
    • Election motive might pressure legislators
    • But information about statehouse votes is very weak

8.2 Putting it all together: Vote Models

8.2.1 Outcome Variable

The outcome variable is a yea or nay vote in a roll call on a bill sponsored by a liberal (NPAT common space ideal point < 0). This was done to flip the votes in a common direction.

8.2.2 Key Predictors

The key predictors are legislator ideology (Shor and McCarty 2011) and district ideology (Tausanovitch and Warshaw 2013).8 Party is accounted for by subsetting the data into the two major parties. This allows allows the effect of ideology to be heterogeneous by party.

8.2.3 Model Choices

As before, I use a multilevel modelling setup to account for the obvious multilevel structure (and non-independence) of the data: specific roll call votes nested within individual states and years. The models include varying intercepts for states and roll calls (to account for baseline probabilities of voting yes), and varying slopes for each roll call (to account for heterogeneous bill characteristics that tap the key predictors differently). The results are essentially the average effect of these predictors.

The specific model I use here is a simple linear probability model. While a generalized linear model like logit is typically used for a binary dependent variable like vote, the more modern approach is to use a simpler linear model as the gains in interpretability typically more than make up for the losses inherent in allowing the predicted values outside of the 0-1 range. I ran the generalized models as well, and include them in the appendix. These are qualitatively identical to the linear

8.2.4 Legislator level results

I present two sets of results, one for each of my data sets. The NCSL subset I use as a proxy for salience, and another for the entire keyword-search dataset. Both data sets only include non-unanimous votes, since unanimous votes have no interesting variation to explain within roll calls. The search database is approximately five times larger than the NCSL data. In both cases, however, since I have hundreds of thousands of observations for each model, statistical significance is much easier to find, so substantive significance is going to be a more important benchmark.

Table 8.1 and 8.2 shows the results of our model for Republican and Democratic unified legislatures, and split.

Table 8.1: NCSL Vote Models
Democrat Republican
Intercept 0.457*** 0.399***
(0.000) (0.000)
District Conservatism 0.001 −0.004*
(0.713) (0.044)
Legislator Conservatism −0.035*** −0.034***
(0.000) (0.000)
Observations 159,333 180,398
AIC −234138.6 −130622.2
BIC −234028.8 −130511.1
Log.Lik. 117080.282 65322.102
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001
Table 8.2: Search Vote Models
Democrat Republican
Intercept 0.518*** 0.366***
(0.000) (0.000)
District Conservatism 0.000 −0.011***
(0.973) (0.000)
Legislator Conservatism −0.081*** −0.075***
(0.000) (0.000)
Observations 795,548 877,219
AIC −316398.3 215385.1
BIC −316270.8 215513.6
Log.Lik. 158210.152 −107681.549
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001

The intercept can be read as the average probability of voting yea, holding both legislator and district conservatism at zero (eg, moderate). Thus, in the search data, Democrats are about 16 percentage points more likely to vote for liberal health care bills than Republicans, while in the NCSL data, Democrats are 6 percentage points more likely to do so.

Legislator ideology is highly statistically and substantively significant. A one unit shift in ideology (eg, going from a moderate to a conservative Republican, or a moderate to liberal Democrat) results in roughly an 8 percentage point increase in the search data. The coefficients are also significant in the NCSL data, but only about half as large. Interestingly, there is not much difference in the effect of ideology on the voting behavior of members of both major parties.

We can plot the marginal effect of our key variable of interest. Figure ?? shows the effect of legislator ideology.

District ideology has no apparent effect on Democratic voting behavior, and a tiny one (in the expected direction) on Republican voting behavior.

References

Shor, Boris, and Nolan McCarty. 2011. “The Ideological Mapping of American Legislatures.” American Political Science Review 105 (3): 530–51.
Tausanovitch, Chris, and Christopher Warshaw. 2013. “Measuring Constituent Policy Preferences in Congress, State Legislatures, and Cities.” Journal of Politics 75 (2): 330–42.

  1. These are described as “conservatism” to account for the convention that higher scores indicate greater conservatism.↩︎