Chapter 10: Individual Roll Rates by 6a69CY

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									Individual Roll Rates

         Thus far, we have tested hypotheses derived from the cartel agenda model regarding the

aggregate roll rates of the majority and minority parties. In this chapter, we will derive and test

hypotheses regarding individual members’ roll rates--that is, how often each member of the

House votes against a bill that passes.

         We begin by presenting some simple averages of individual roll rates by party and

Congress, to see how majority status affects how often members suffer rolls. These analyses are

similar in some ways to our previous investigations of party roll rates, although as will be seen

the average roll rate within a party is not the same as the aggregate roll rate for that party.

         We then take a closer look at variations of members’ roll rates within each Congress. In

particular, we ask how roll rates vary with two factors: ideological location and majority status. 1

This level of analysis gives us better leverage than we enjoyed when examining aggregate party

roll rates, as we can explicitly control for members’ ideological locations when examining the

influence of majority status.

         To set the stage for our more detailed within-Congress analyses, we first derive

predictions from our cartel model regarding how a member’s probability of being rolled should

vary with that member’s ideological location; and then test those predictions against the

empirical record of 60 post-Reconstruction Congresses. Our examination shows that the

complete-information version of the cartel model does not fully fit the observed data.

Nonetheless, when we introduce an element of uncertainty to our idealized cartel agenda model



1
 . Our analysis resembles that of Lawrence, Maltzman and Smith (1999), who plot each member’s win rate (the
proportion of all votes on which a member is on the winning side) against his or her left-right scale position. We,
however, look not at all votes but rather only at final-passage votes; and we examine roll rates rather than win rates.
Roll rates are not simply the inverse of win rates, as they identify one particular class of defeat—voting against a bill
that nonetheless passes—and leave another sort of defeat—voting for a bill that fails—explicitly out of the picture.
(specifically, by incorporating stochastic voting along the lines laid out in the previous chapter)

the predictions of the cartel model are consistent with the evidence on individual roll rates.

       We conclude by conducting a multivariate analysis in which a member’s roll rate is

predicted as a function of (1) the member’s ideological location relative to the floor median and

(2) whether the member’s party is in the majority. We find that the probability of a member

suffering the passage of a bill against his or her wishes is significantly increased as that

member’s ideological location becomes more extreme, relative to the floor median; and also

when that member’s party is in the minority. That is, minority-party members are more likely to

be rolled than are equally extreme majority-party members.



Some preliminary comparisons

       To get an initial feel for how often members of the House are rolled, consider the

following summary statistics from the 83rd-105th Congresses. On average, Democrats were

rolled 11.4% of the time, when they held a majority, and 33.1% of the time, when they lacked a

majority. Similarly, Republicans were rolled 7.7% of the time, when they held a majority, and

29.0% of the time, when they lacked a majority.

       We present two graphs to show the data at a finer-grained, Congress-by-Congress, level.

Recall that the only Houses in this period with Republican majorities were the very first in the

series (the 83rd) and the last two (the 104th and 105th). With this in mind, look at Figure 11.1,

which displays average roll rates by Congress for the Democrats. As can be seen, the three

highest averages are achieved in the three Republican Houses. The drop from the 83rd

(Republican-controlled) to the 84th (Democrat-controlled) House is relatively modest (10

percentage points); but the surge from the 103rd (Democrat-controlled) to the 104th (Republican-
controlled) is more substantial (over 35 percentage points). In-between the initial and ending

peaks, the Democratic averages show relatively little variation, with perhaps a mild decline from

the 84th to 103rd Houses.



                               Figure 10.1 about here



       Turning to the Republican averages displayed in Figure 10.2, one finds a similar but more

nuanced picture. The three lowest average Republican roll rates occur in the three Houses that

they controlled. In-between, there is an initial peak in the 86th-88th Congresses, at slightly below

40%; followed by a valley reaching bottom in the 91st-92nd Congresses, at slightly below 15%;

followed by another peak near 40% in the 98th-103rd Congresses.



                                       Figure 10.2 about here



       These simple statistics seem consistent with the idealized cartel model, in that average

roll rates are lower in the majority party. In the next few sections, we specify in greater detail

what one should expect from the cartel model, when one looks in more detail at within-Congress

variation in roll rates. We then turn to various empirical analyses of the within-Congress data

that control for member preferences.



Individual rolls: Non-stochastic theory

       In this section, we consider what the idealized, complete-information cartel model

predicts about individual rolls. Recall that an individual member is rolled on a particular final
passage vote if and only if s/he votes against the bill in question, yet it passes. We consider

another sort of defeat--voting for a bill that fails--later in the book.



Basics

         In the idealized cartel model, an individual’s roll rate is a simple function of his or her

ideal point’s location, relative to the majority-party median (M) and floor median (F). To explain

this point, we shall henceforth focus on the case of a Democratic majority (for which M < F).

         The cartel model predicts that a member’s roll rate should be zero, if his or her ideal point

lies between the Democratic median (M) and the floor median (F). Such members could be

rolled if a bill, b, were voted against a status quo, q, such that the cutpoint c = (b+q)/2 lay

between M and F. But the idealized cartel model specifically denies that such (bill, status quo)

pairs are allowed on the floor, leading to the prediction that “moderate leftists” (those with ideal

points between M and F) are never rolled.

         Outside of this “no roll zone,” the cartel model predicts that a member’s roll rate will

increase monotonically, the further he or she is from this zone. That is, the idealized cartel model

predicts that the further left (or the further right) of the interval [M,F] is a member’s ideal point,

the higher that member’s roll rate will be.

         All told, the idealized cartel model’s predictions can be diagrammed as in Figure 10.3. As

shown in the bottom portion of the figure, the left-right spectrum can be divided into three

regions: the “far left” (to the left of M); the “moderate left” (between M and F); and the “right”

(to the right of F). We will derive predictions from the idealized cartel model for each of these

segments. 2


2
 . The size of the slope (and the extent to which the relationship is linear) both depend on the distribution of status
quo points.
                                 Figure 10.3 about here.



The far left

        Within this region, the idealized cartel model predicts that for members of either party,

the further left a member’s ideal point lies, the larger his or her roll rate will be. In terms of a

regression of an individual’s roll rate on his or her ideal point’s location, the theory predicts a

negative slope in this region.



The moderate left

        Members whose ideal points lie between M and F are protected from rolls in the idealized

cartel model because no bills that would roll them are ever scheduled. Since all members in this

region should have zero roll rates, there should be no relationship between ideal point location

and roll rate for a member whose ideal point is located in this region. In terms of a regression of

an individual’s roll rate on his or her ideal point’s location, the idealized cartel model predicts a

zero slope in this region.



The right

        Roll rates should increase monotonically with ideal points, for members whose ideal

points lie to the right of the floor median. In terms of a regression of an individual’s roll rate on

his or her ideal point’s location, the idealized cartel model predicts a positive slope in this region.



Individual rolls: Evidence
            In order to test the predictions just stated, we use our post-Reconstruction dataset that

covers every final passage vote on House bills occurring in the 45th-105th Congresses.3 For each

such vote, we code whether each voting member was rolled (that is, whether each voted against a

bill that passed). We then compute each member’s roll rate in each Congress (denoted Ri for

member i)--that is, the number of times the member was rolled, divided by the number of final

passage votes in which he or she participated.

            The main independent variable in the analysis is each member’s ideological location, xi.

Operationally, we use the first dimension of each member’s DW-Nominate score (Poole 1998) to

measure xi.

            In Figure 10.4, we plot each member’s roll rate (on the vertical axis) against each

member’s ideological location (on the horizontal axis), for three Republican Congresses (the

83rd, 104th and 105th) and three Democratic Congresses (the 86th, 92nd, and 96th). These

Congresses were selected to illustrate the range of results we have obtained. A complete set of

figures, for all 61 Congresses, is posted at www.mmccubbins.com/revisited.htm.



                                        Figure 10.4 about here



            Along with the raw data, each graph also displays a lowess regression line (a kind of

running average) and the location of the majority-party median (M) and the floor median (F).

The lowess lines in all Democratic Congresses (see Figures 10.4a-10.4c) look roughly like the

Nike swoosh: starting at the far left, the curve first declines briefly, then reverses direction and




3
    . In this analysis, we include final passage votes on bills in the H.R. series only.
proceeds upward.4 The members with the lowest roll rates are consistently slightly to the left of

the Democratic median. In stark contrast, the lowess lines in all Republican Congresses (Figures

10.4d-10.4f and those posted on the web) look roughly like mirror-image Nike swooshes:

starting at the far right, the curve first declines briefly, then reverses direction and proceeds

upward. The members with the lowest roll rates are consistently slightly to the right of the

Republican median.

         Interestingly, the floor median has a roll rate above 12% in the Congresses pictured, and

this is typical of all the Congresses studied. The members with the lowest roll rate are, as already

noted, slightly more extreme than the majority-party median. When it comes to avoiding the

passage of bills that propose unwanted policies, those near the floor median do not do the best;

rather, those near (and more extreme than) the majority-party median do the best.5

         In order to explore the relationship between ideological location and roll rate more

systematically, we run separate regressions of Ri on xi for each of the three regions noted above:

the far left, the moderate left, and the right. We include all Democratic Congresses in each

regression, allowing the constant term to shift (via the inclusion of dummy variables representing

each Congress, excluding the 84th) but pooling the slope coefficient on xi. The results are

presented in Table 10.1.



                                    Table 10.1 about here




4
  . The other figures from Democratic Congresses posted at www.mmccubbins.com/revisited.htm also look like Nike
swooshes, although the 84th is a bit flat on the left.
5
  . One can also run these analyses with common-space Nominate scores, in which case it is possible to locate the
filibuster pivots in the Senate and translate them into the House distribution of ideal points. When one does this, one
finds that the right pivot has a roll rate of 15-35% in the Democratic Congresses; while the left pivot has a roll rate
of 15-40% in the Republican Congresses. Similar findings arise if one defines the left and right pivots simply as the
40th and 60th percentiles of the House distribution.
        Our findings can be summarized as follows. In the far left and in the right, more extreme

members should be rolled more often, and that is what we find. In the moderate left, the idealized

cartel model predicts a nil slope but in fact the data show a significant positive slope.

        Because it fails in the moderate left region, we reject the complete-information version of

our model. In the remainder of the chapter, however, we use the more realistic incomplete-

information version of the cartel model, developed in Chapter 10, and show how it fits the data

displayed in Figure 10.4. In particular, we offer a partial explanation for why the lowest roll rate

is observed for members somewhat to the left of the Democratic median, with roll rates

increasing monotonically on either side of that minimum.



Individual roll rates

        In this section, we consider how the roll rates of individuals change as their ideal points

change, given that all members vote according to the stochastic model outlined in Chapter 10

(which itself is a version of the standard model proposed in Poole and Rosenthal 1997, among

others). We begin by considering roll probabilities on a single vote, then aggregate across all the

final passage votes held in a session.



Vote-specific roll probabilities

        In order to derive conclusions about the relationship between a legislator’s ideal point

and his/her roll rate, we assume for convenience that si = s for all i. If si = 0, then there are no

additional considerations and we have the complete-information model with which we began in

chapter 4. Here, however, we assume si > 0 throughout: members do not vote perfectly in accord

with their ideal points; there are some “errors” or “additional considerations.”
          Consider a particular policy dimension, j. Suppose that the status quo is qj and that a bill,

bj, is being voted against the status quo in a final passage vote. What is the probability that

member i will be rolled on this vote, denoted Rij(bj,qj) (sometimes shortened to Rij)?

          In the appendix weshow that, when the bill is to the left of the status quo (bj < qj), the

probability of a member being rolled on final passage increases as the member becomes more

conservative (as his or her ideal point shifts rightward). The basic reason is as follows. The

probability Rij(bj,qj) that a member i will be rolled on a particular final passage vote (pitting bj

against qj) is the probability that member i votes against the bill, times the conditional probability

that the bill passes, given that member i votes against it. This latter probability is unaffected by

changes in the location of the members’ ideal point, xi.6 Thus, whether increasing xi increases i’s

probability of being rolled depends on how increasing xi affects the probability that i will vote

against the bill. But more conservative members are more likely to vote against the (left-of-

status-quo) bill, hence they are more likely to be rolled.

          On the other hand, when the bill is to the right of the status quo (qj < bj), the probability

of a member being rolled on final passage decreases as the member becomes more conservative.

The more conservative members are less likely to vote against the (right-of-status-quo) bill,

hence they are less likely to be rolled.



Roll rates

Thus far we have imagined a single pair of alternatives (bj,qj) being voted on. In this section, we

consider how member i’s roll rate across the roll calls held in a given session, denoted Ri(xi),




6
    . Recall that members’ errors are independent.
changes with member i’s ideal point, xi. More formally, we consider the Ri(xi) curve’s slope,

Ri
    .
xi

        Our main point is that, in the stochastic version of the model, how Ri changes with xi

depends heavily on the proportion of bills that are to the left of their respective status quo points.

                                                                                                 Ri
If all (bj,qj) pairs were such that bj < qj, then we know, from the results stated above, that       >
                                                                                                 xi

0. In other words, if every voted-on bill proposes a leftward movement in policy, then roll rates

will increase monotonically with conservatism. Alternatively, if every voted-on bill proposes a

rightward movement in policy, then roll rates will decrease monotonically with conservatism.

                              Ri
        More generally,           depends on the proportion of bills that propose leftward moves,
                              xi

PLeft, as follows (see the appendix for a formal derivation):

        Ri
            = PLeft rbq  1  PLeft rqb .                                    (1)
        xi

Here, rbq represents how Ri changes with xi, on average, across the bills that are to the left of the

status quo; while rqb represents how Ri changes with xi, on average, across the bills that are to the

right of the status quo. Holding constant rbq and rqb, increasing PLeft increases the slope of the

Ri(xi) curve. That is, the larger the proportion of bills that propose leftward policy moves, the

more likely it is that roll rates will increase with conservatism.



Roll rates redux

        In this section, we return to the relationship between members’ roll rates and their

ideological locations, as displayed in Figure 10.4. Having developed the stochastic version of

our model, we can now partly explain why the lowess lines deviate in the way they do from the
predictions of the idealized complete-information cartel model. If members voted purely

according to the distance between the proposals facing them and their respective ideal points,

without the non-spatial errors or “additional considerations” introduced above, then the cartel

model would indeed make the prediction given in Figure 10.3.

       When members’ preferences are not purely stochastic, several things happen to

predictions of our idealized model. First, the members with ideal points between the majority-

party (M) and floor (F) medians are no longer expected to have zero roll rates: they have a

positive probability of being rolled on any final-passage vote, although that outcome is unlikely

when spatial errors are small. Second, as the proportion of final-passage bills that move policy

leftward increases, the minimum point of the R(x) curve shifts to the left (see the appendix).

Third, one expects the R(x) curve to increase monotonically on either side of its minimum.

       Thus, given (1) moderate variances in the errors or “additional considerations” (i.e.,

moderate values of (s1,…sT)); and (2) a heavy preponderance of moves toward the majority

party; one expects something similar to what all the lowess graphs in fact show. In particular, the

minimum of the R(x) curve is more extreme than the majority-party median (because of the

heavy preponderance of bills proposing to move policy toward the majority party) and the curve

bends upward on either side of its minimum. In particular, you see a positive slope for the R(x)

curve to the right of M, in between M and F. The addition of stochastic voting thus accounts for

the prediction errors in our idealized model.



A multivariate test

       In this section, we examine a somewhat different proposition—viz., that majority status

lowers members’ roll rates, holding constant ideological location. Under the cartel agenda
model, members of the majority party are protected from certain votes--those which would roll at

least half of them--ever taking place. Under the floor agenda model, once one controls for each

member’s ideological location, majority status should not matter.7

         To test this proposition, we regress each member’s roll rate on a constant, a variable

measuring the distance between the member’s ideal point and the floor median, and a variable

indicating that the member’s party is in the minority. As our data cover over a century of

congressional history, during which time there have been substantial changes in the majority

party’s advantage in setting the agenda, we allow the effect of our three variables to adjust when:

(1) Reed’s rules were adopted (1890); (2) the revolt against “czar rule” occurred (1910); (3) the

Rules Committee was packed (1961); and (4) the House was reformed (1974). If our previous

claims asserting the primacy of Reed’s rules are correct (see chapter 4), then the floor agenda

model may fit the pre-Reed data reasonably well—but it will not fit any of the post-Reed

periods.

         Our results, presented Table 10.2, can be characterized as follows.8 Members whose

ideal points are further from the floor median are more likely to be rolled in all periods of

congressional history we examine. Controlling for each member’s distance from the floor

median, however, there are (1) significant differences between majority-party and minority-party

members in every post-Reed period; and (2) significant changes in members’ roll rates

associated with each major watershed in House procedure.




7
  . From the appendix, the probability that member i votes for the left-of-cutpoint alternative is pij = (dj(cj-xi)/si).
Fixing each member’s ideal point (and standard error), the set of p ij’s for a given roll call, j, is a function solely of
the roll call parameters, dj and cj, or equivalently, bj (the bill location) and qj (the status quo location). Under the
floor agenda model, bj = Fj, the floor median on the jth dimension, while q j is drawn by Nature from a fixed
distribution. Thus, each member’s roll rate is purely a function of the distribution of status quo points. As this
distribution does not depend on which party is currently in the majority, majority status should be irrelevant.
8
  . As in previous chapters, we use an extended beta-binomial procedure to estimate the model.
                               Table 10.2 about here.



       Consider the difference between majority- and minority-party members first. Prior to the

adoption of Reed’s rules in 1890, there was no difference. Each member’s roll rate was a

function of how extreme that member was, relative to the floor median—but whether they were

in the majority or minority party did not matter. After passage of Reed’s rules, however, a large

difference opens up between the parties: specifically, a minority-party member is substantially

more likely to be rolled than a majority-party member equally distant from the floor median.

While this minority-party disadvantage shifts after the revolt against czar rule in 1910, again

after the packing of the Rules Committee in 1961, and yet again after the reform of the House in

1974, it remains large and statistically significant in all post-Reed periods.

       If minority-party members have higher roll rates on final-passage votes because of the

agenda power exercised by the majority party, as envisioned by the cartel model, then their

disadvantage should grow when congressional reforms bolster the power of the majority on the

margin. Three events since Reconstruction stand out as obvious points at which the majority’s

grip on the agenda may have strengthened: the adoption of Reed’s rules, the packing of the

Rules Committee, and the adoption of broader reforms in the 94th Congress. In addition, the

revolt against czar rule in 1910 is conventionally depicted as diminishing the power of the

majority party’s central leadership. Thus, an additional test of the cartel model is provided by

the interaction terms in Table 10.2, which allow the effect of minority status to shift after each of

the four events just noted. The cartel model predicts that the discrepancy in roll rates between

members of the minority and majority party should widen after the three majority-strengthening

rule changes but shrink after the majority-weakening change in 1910.
       This is indeed what we find (see Table 10.2). By far the largest increase in the minority-

party disadvantage occurs in 1890, with the adoption of Reed’s rules; smaller but still

statistically significant increases occur in 1961, with the packing of the Rules Committee, and

1974, with the adoption of a series of reforms. Between these majority-strengthening moves lies

the important revolt of 1910, sparking a substantial shrinkage of the minority-party disadvantage

(although the disadvantage remains large and positive).

       These results appear hard to explain from a perspective that takes majority-party agenda

power as nil, weak or tenuous. While one might seek to explain the finding that minority-party

members have higher roll rates in a given period by appealing to an unusual distribution of status

quo points in that Congress, there is no reason to believe that the distribution of status quo points

was unfavorable to the minority in every period, nor that the distribution would become less

favorable after each majority-strengthening reform and more favorable after the main majority-

weakening reform.



Conclusion

       In this chapter, we have investigated how individual members’ roll rates vary with their

ideological location. The basic empirical pattern that we find, in all Congresses, is the following.

First, the members with the lowest roll rates are slightly more extreme than the majority-party

median. That is, in Democratic Houses, members slightly to the left of the Democratic median

are the least often rolled; in Republican Houses, members slightly to the right of the Republican

median are the least often rolled. Second, to either side of this minimum point, members’ roll

rates increase monotonically.
       Theoretically, this pattern is inconsistent with a complete-information cartel model.

When one recalls that members’ ideological locations are only estimates, and that voting

behavior exhibits some variation around the central tendencies reflected in estimated ideal

points, the data become intelligible from a cartel viewpoint. As we show above, with stochastic

voting, members’ roll rates are highly sensitive to the proportion of bills that propose to move

policy leftward (or rightward). As we have already seen in Chapter 10, the proportion of leftward

moves is in turn a direct function of which party has the gavel. Putting these two observations

together, one can provide the following explanation for the empirical patterns in a typical

Democratic House. Most of the bills that reach final passage propose to move policy leftward

(typically about 80%). On these bills, more conservative members should have higher roll rates.

On the 20% of bills proposing to move policy rightward, in contrast, more liberal members

should have higher roll rates. Averaging across a large set of leftward moves and a small set of

rightward moves produces the patterns shown in Figure 10.4.
                                             Table 10.1:


                   The relationship between member ideology and roll rate
                   Post-Reconstruction roll call data set (45th to 105th Congress)




Region name       Cartel       Estimated slope          Std error

                  prediction

Far Left          Negative     -.212                    .008

Moderate Left     Zero         .225                     .017

Right             Positive     .550                     .005



Notes: The dependent variable is each member’s roll rate. Estimation by *. All coefficients

significantly differ from zero at the .001 level.
Table 10.2

              Pre-Reed       Interactions   Interactions   Interactions   Interactions
                             Post-Reed      Post-Revolt    Post-packing   Post-reform
Constant      -1.88          -0.35          -0.07 ns       -0.27          -0.33
Distance of   1.73           -0.73          0.48           -0.04 ns       0.95
member
from floor
median
Member is     -0.03 ns       1.73           -0.88          0.17           0.09
in minority
party


Notes: The dependent variable is each member’s roll rate in a given Congress. There were

25,142 observations.
                                        Figure 10.1
                 Average Democratic Roll Rate, 83rd through 105th Congresses




          .5

                                                                                                       R



                                                                                                           R




  Average
 Democratic
                R
  Roll Rate
                             D

                        D         D                                       D
                    D                           D            D   D
                                      D D   D        D                D        D
                                                         D
                                                                                    D        D
                                                                                        D        D D



           0
               83       85       87    89       91    93         95       97       99       101 103 105
                                                     Congress


Note: The symbol "R" indicates a Congress in which the Republicans held a majority of House
seats, while the symbol "D" indicates a Congress in which the Democrats held a majority.
                                      Figure 10.2
               Average Republican Roll Rate, 83rd through 105th Congresses




         .5


                                D                                             D   D         D
                            D        D
                                                                                                    D
                                                                                       D
                                                                                                D
                                          D
                                                                         D
                                                              D    D D
 Average
Republican
                       D
 Roll Rate                                    D          D
                   D

                                                   D D


               R
                                                                                                        R R



         0
              83       85       87       89       91     93       95     97       99       101 103 105
                                                       Congress


Note: The symbol "R" indicates a Congress in which the Republicans held a majority of House

seats, while the symbol "D" indicates a Congress in which the Democrats held a majority.
    Figure 10.3: Expected relationship between ideological location and roll rate under the

                                         cartel model




Predicted
  Roll
  Rate




                           M                            F
Figure 10.4.a. How members’ roll rates vary with their left-right ideological position. Congress
                                             86.
Figure 10.4.b. How members’ roll rates vary with their left-right ideological position. Congress
                                            92.
Figure 10.4.c. How members’ roll rates vary with their left-right ideological position. Congress
                                             96.
Figure 10.4.d. How members’ roll rates vary with their left-right

              ideological position. Congress 83.
Figure 10.4.e. How members’ roll rates vary with their left-right ideological position. Congress
                                            104.
Figure 10.4.f. How members’ roll rates vary with their left-right ideological position. Congress
                                            105.

								
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