Abstract
Krehbiel’s (Pivotal politics, 1998) seminal work on pivotal politics in the US Congress emphasizes the importance of supermajoritarian rules and veto players in determining what bills can pass. We illustrate empirically that the volatility of the pivot points has increased markedly since the mid 1970s, and we link changes in pivot volatility to the degree of party polarization. In general, median and supermajority pivots shift considerably more than the overall mean and, when politics is polarized, the congressional median and supermajority pivots can change dramatically when a shift in control occurs. The relative volatility of median and supermajoritarian pivots varies with the degree of polarization and the extent to which there is continuity in party control. We develop a theoretical model to explain the nature of these relationships.
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Notes
The standard assumption is that the preferences of those who are pivotal either decide outcomes or act to constrain the scope of feasible outcomes; thus, voters expected to be pivotal are more likely to be offered or to extract resources in the form of side payments from others who wish to influence their votes. Groseclose and Snyder (1996) provide a powerful antidote to this common wisdom by showing that sequential vote buying models in which two competitors seek to influence outcomes can lead to offers to those with locations beyond that of the pivotal (median) voter. Such supraminimal coalitions may minimize the potential for extracting resources from the vote buyer. In such cases, the pivotal voter may not be the voter who is expected to receive the largest payoff. Here, our focus is simply on identifying the location of pivotal voters rather than modeling their expected payoff.
Any model in which voters are arrayed along some given dimension allows us to label voters according to where they are located on that dimension. Consider for example, the redistribution models of Meltzer and Richard (1978, 1981, 1983), or social insurance and special interest group models of welfare spending (Husted and Kenny 1997), where voters may be located according to income.
Legislative polarization is defined here simply as the difference between the ideological location of the mean Democrat and the mean Republican.
In fact, even for a normal distribution, the sample median is a less robust estimator than the sample mean (Mood et al. 1974, p. 257).
A quantile is to a fraction as a percentile is to a percent. For example the 2/3rd quantile of the DW NOMINATE scores in the House is that value for which 2/3rds of the House members have lower (more liberal) values (i.e., the 2/3rd quantile is approximately the 67th percentile). The 3/5th quantile is the 60th percentile.
DW NOMINATE scores were obtained from the Voteview website http://voteview.com/dw-nominate_textfile.htm (see Carroll et al. 2009). In House districts listing two occupants in a particular Congress (typically owing to the resignation or death of the first), only one occupant (the first one listed) is included in our dataset to avoid distorting the median and other quantiles. Similarly, when three or more Senators are listed for one state in a Congress, low roll call tallies are used to indicate incomplete terms, with the second listed low-tally Senator omitted. In questionable cases, biographical information was consulted.
In the House, the average absolute change from Congress to Congress for the quantiles Q(1/3), median, and Q(2/3) is 0.029, 0.094, and 0.043, respectively; the corresponding value for the mean is 0.034. Using the root mean square of a quadratic regression of quantile on year as the measure of volatility yields similar results. We prefer to use absolute change in a quantile as it is conceptually simpler.
In the Senate, the average absolute change in the five quantiles, Q(1/3), Q(2/5), median, Q(3/5), and Q(2/3) is 0.031, 0.032, 0.061, 0.055 and 0.035, respectively; the corresponding value for the mean is 0.028.
The mean absolute change statistics for the override pivot, cloture pivot, and the median, respectively, are 0.130, 0.074 and 0.061.
Filibuster-proof, unified governments were achieved in those elected in 1940, 1962, 1964 and 1976. Had only a 3/5 majority been required for cloture before 1975, three more governments would have been filibuster-proof (1942, 1960 and 1966).
See plots in Fig. 8 in the Appendix. The Shapiro–Wilk test of goodness of fit for the three Congresses plotted in Fig. 8 does not reject the normal distribution for the 103rd and 109th Congresses, provided that the extreme outlying score for one member, Ron Paul, is omitted for the 109th. However, normality is rejected for each of the party delegations for the 87th Congress, because each party delegation has a long tail to the right.
In each scenario, for simplicity, π D and π R are each initially set at 0.5.
Of course, successive Congresses or legislatures are not independent, in particular because many incumbents are retained. So we do not expect the legislatures to vary as much as independent random samples. However, over a period of time, variation can be expected. Furthermore, the relative amount of variation as parameters (such as divergence between parties, intraparty variance, and so on) are varied is still meaningful.
See Mood et al. (1974, p. 257). For this theoretical section, we use standard deviation as a measure of volatility of quantiles because it is analytically more tractable than mean absolute change, which we have used for the empirical analysis. Because of the non-linear, secular trends in some of the empirical quantiles, standard deviation would be misleading there, whereas root mean square error from a quadratic regression would be more meaningful (see note 7 above).
Note that, although the sample median—when considered with regard to sensitivity to extreme outliers—is a more robust estimator of the population median than the sample mean is as an estimator of the population mean, for many distributions the sample median is a less precise estimator of its population counterpart, i.e., is likely to be more variable over time due to statistical variation. This is particularly relevant to the analysis of scores such as DW NOMINATE scores that are bounded in principle and hence tend not to have extreme outliers.
In general, for a normal distribution with standard deviation σ, the standard error for the qth quantile is \(\sigma_{q} = \sqrt {q\;\times \;(1 - q)} \;*\;\sigma /\phi [\Upphi^{ - 1} (q)]/\sqrt n ,\) where ϕ and Φ are the standard normal density and cumulative distribution functions, respectively.
For the mixed normal distribution, the standard deviation (standard error) of the mean is \(0.5\sqrt {[4\sigma_{D}^{2} + (\mu_{R} - \mu_{D} )^{2} ]/n},\) where σ D (=σ R ) is the common intraparty standard deviation and μ R and μ D are the respective means of the partisan delegations. Thus, the standard error of the mean increases with both divergence and intraparty variance. The standard deviation (standard error) of the median can be calculated from formulas for the distribution of the sample median, such as in Hogg and Tanis (2001, p. 276). (Note that the mean is the same as the median for each party distribution because each party distribution is assumed to be normal).
Note that in the regression model with interaction term, the effect of changing control of the chamber on change in the chamber median cannot be determined from the sign of the coefficient of change in control alone; that conclusion must involve the coefficient of the interaction term as well. (If the model is run without interaction term, the coefficients for change in control and change in seat share are both positive and significant, but polarization is not significant and the R-squared is only 0.66.) The full estimated regression equation for the House is given by M = b 0 + b 1 ChControl + b 2 ChSeatShare + b 3Polarization + b 4Polarization × ChControl, so that if ChControl = −1, M = (b 0 − b 1) + b 2 ChSeatShare + (b 3 − b 4)Polarization = 0.356 + 1.043ChSeatShare − 0.774Polarization. If, instead, ChControl = +1, M = (b 0 + b 1) + b 2 ChSeatShare + (b 3 + b 4)Polarization = −0.394 + 1.043ChSeatShare + 0.834Polarization. Similar equations hold for the Senate.
The standard deviations of the partisan delegations are not statistically significant when added to the model.
Patterns are similar if the mean absolute change is replaced by the standard deviation.
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Acknowledgments
Grofman’s work on this Project was supported by the Jack W. Peltason Chair, Center for the Study of Democracy, University of California, Irvine.
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Appendix
Appendix
See Fig. 8.
Histograms for selected Congresses, by party delegation, with normal fits. Democrats in House, 87th Congress (1961–1963) (N = 263), Republicans in House, 87th Congress (1961–1963) (N = 174), Democrats in House, 103th Congress (1993–1995) (N = 258), Republicans in House, 103th Congress (1993–1995) (N = 178), Democrats in House, 109th Congress (2005–2007) (N = 202), and Republicans in House, 109th Congress (2005–2007) (N = 235)
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Brunell, T.L., Grofman, B. & Merrill, S. The volatility of median and supermajoritarian pivots in the U.S. Congress and the effects of party polarization. Public Choice 166, 183–204 (2016). https://doi.org/10.1007/s11127-016-0320-0
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DOI: https://doi.org/10.1007/s11127-016-0320-0