To recap: As we discussed in earlier posts, alpha-NOMINATE is a new form of NOMINATE that is fully Bayesian and is meant to replace W-NOMINATE which is now getting close to being 34 years old (the multidimensional version, written by Nolan McCarty and Keith Poole, is over 25 years old). NOMINATE was designed by Keith Poole and Howard Rosenthal during 1982-1983. It used a random utility model with a Gaussian deterministic utility function (see pages 14 – 15 of the linked 1983 paper) and logistic error (random draws from the log of the inverse exponential). The Gaussian deterministic utility function is able to capture non-voting due to indifference and alienation.

Alpha-NOMINATE is a mixture model in which legislators’ utility functions are allowed to be a mixture of the two most commonly assumed utility functions: the quadratic function and the Gaussian function assumed by NOMINATE. The “Alpha” is a parameter estimated by Alpha-NOMINATE that varies from 0 (Quadratic Utility) to 1 (Gaussian Utility). Hence, in one dimension with Alpha = 0, Alpha-NOMINATE is identical to the popular IRT model. Thus Alpha-NOMINATE can actually test whether or not legislators’ utility functions are Quadratic or Gaussian.

Below we apply Alpha-NOMINATE to the the 114^th House through mid-March 2016. There have been 834 total votes of which 718 are scalable (at least 2.5% in the minority; that is, votes that are 97-3 to 50-50). We used the R version of Alpha-NOMINATE to perform the analysis. We used 4000 samples from a slice sampler in one dimension with a burn-in of 1000. The first graph shows the Trace and Density plots for alpha.

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The mean of alpha is 0.99986 with a standard deviation of 0.00014 strongly indicating that the Representatives’ utility functions were Gaussian.

Below is a smoothed histogram of the 3000 configurations after burn-in. The divide between Democrats and Republicans is a very deep one.

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Of more interest, however, are the clear divisions in the Republican Party shown in the smoothed histogram. The gap between Speaker Ryan and the head of the Freedom Caucus Jim Jordan (R-OH) is very wide. Given the turmoil in the Republican Presidential Nominating process, it is growing harder and harder for Speaker Ryan to restore “regular order” and pass a budget. With Hillary Clinton leading both Donald Trump and Ted Cruz in the polls and the competition between Trump and Cruz to gain the 1237 delegates they need for the nomination likely to drag out until at least May and perhaps even to the convention in July, this is likely to paralyze the House Republican Party for some time. This potential paralysis has motivated one of the members of the Freedom Caucus, Paul Gosar (R-AZ), to lead an effort to stop any post-Presidential Election or “Lame Duck” session of Congress for fear that spending “deals” would be struck by the leaders of both Political Parties. Depending on the state of the Presidential race in September this issue could get entangled with Presidential campaign politics. (The House is scheduled to go into recess on September 30th.) All in all, it will not be a boring year!

The next five plots show the estimated ideal points for the 435 Members who served during the 114th through mid-March along with their 95% Credible Intervals. Furthest left is Grijalva (D-AZ) at -2.38 followed by Lee (D-CA) at -2.16. On the far right are Massie (R-KY) at 4.16, Amash (R-MI) at 4.52, and Jones (R-NC) at 5.73.

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(Clarifications made 0020UCT 9 January 2016)

To recap: As we discussed in earlier posts, alpha-NOMINATE is a new form of NOMINATE that is fully Bayesian and is meant to replace W-NOMINATE which is now about 33 years old (the multidimensional version, written by Nolan McCarty and Keith Poole, is almost 25 years old). NOMINATE was designed by Keith Poole and Howard Rosenthal during 1982-1983. It used a random utility model with a Gaussian deterministic utility function (see pages 14 – 15 of the linked 1983 paper) and logistic error (random draws from the log of the inverse exponential). The Gaussian deterministic utility function is able to capture non-voting due to indifference and alienation.

Alpha-NOMINATE is a mixture model in which legislators’ utility functions are allowed to be a mixture of the two most commonly assumed utility functions: the quadratic function and the Gaussian function assumed by NOMINATE. The “Alpha” is a parameter estimated by Alpha-NOMINATE that varies from 0 (Quadratic Utility) to 1 (Gaussian Utility). Hence, in one dimension with Alpha = 0, Alpha-NOMINATE is identical to the popular IRT model. Thus Alpha-NOMINATE can actually test whether or not legislators’ utility functions are Quadratic or Gaussian.

Below we apply Alpha-NOMINATE to the first Session of the 114^th House. There were 705 total votes in the during the first Session of which 614 are scalable (at least 2.5% in the minority; that is, votes that are 97-3 to 50-50). We used the R version of Alpha-NOMINATE to perform the analysis. We used 4000 samples from a slice sampler in one dimension with a burn-in of 1000. The first graph shows the Trace and Density plots for alpha.

Click image to enlarge

The mean of alpha is 0.99986 with a standard deviation of 0.000014 strongly indicating that the Representatives’ utility functions were Gaussian.

Below is a smoothed histogram of the 3000 configurations after burn-in. The divide between Democrats and Republicans is a very deep one.

Click image to enlarge

Of more interest, however, are the clear divisions in the Republican Party shown in the smoothed histogram. Ryan Lizza in a recent article in the New Yorker, 14 December 2015, discusses these divisions in a particularly lucid fashion. He quotes Charlie Dent (R-PA, CS DWNOM Score of 0.243 on the first dimension) that there are 70-100 Republicans like himself that will vote with the Democrats to pass the Omnibus bills to keep the government running, 70-80 “hope yes, vote no’ Republicans, who voted against those bills but secretly hoped they would pass; and the the 40-60 members of the rejectionist wing, dominated by the Freedom Caucus, who voted against everything and considered government shutdowns a routine part of negotiating with Obama” (p. 37). The Rejectionist wing’s de facto leader is Ted Cruz (R-TX, CS DWNOM Score of 0.975).

Fueled by talk radio the Rejectionists would shut the government down until their demands are met no matter what the cost. Essentially, the House Republicans are being held hostage by these extreme True Believers. Cruz is running a sophisticated campaign for the Republican nomination and it is conceivable that he could win. Cruz suffers from the same delusion as Barry Goldwater in 1964. Out “there” are millions of dissatisfied voters who suddenly will flock to the polls when a “true” conservative is nominated (see, Converse, Clausen and Miller, 1965. “Electoral Myth and Reality: The 1964 Election.” American Political Science Review, Vol. 59, No. 2 (Jun., 1965), pp. 321-336). The first page of that 1965 article is eerie because it could easily be read as a description of the current debate within the Republican Party.

The reality is that there are not millions of Republicans who will flock to the polls to vote for either Ted Cruz (the most despised Man in the Senate) or Donald Trump. As Bret Stephens advises Wall Street Journal readers in his Global View column on 22 December 2015 “Let’s Elect Hillary Now,” he sees the Republican Party losing on the scale of 1972. If so, there will be a decisive turn towards European style Social Democracy (i.e., a vast increase in social programs and greatly increased taxation) under Hillary Clinton (CS DWNOM Score of -0.373 as Senator from New York). However, to make things even more complicated, Bernie Sanders (I-VT, CS DWNOM Score of -0.513) may very well upset Clinton in Iowa and win New Hampshire. Clinton is the overwhelming favorite but is widely distrusted by the public (for example, Bill Clinton’s escapades are beginning to resurface — a particularly toxic one is the Juanita Broaddrick rape allegation). Nevertheless, the smart money is on Clinton and a crackup of the Republican Party.