ECONOMY

keith krehbiel 231
No rolls
Minority party rolls
Majority party
gatekeeping
No rolls
−1
I
0
II III
IV V VI
1
q
2d − m
d m r
|d − m| |r − m|
2r − m
Fig. 12.4 Roll rate dependence on the distribution of the status quo
is defined as the proportion of final-passage roll calls on which these conditions are
met. A party with a low roll rate is presumed to have agenda power, while, conversely,
a party that is rolled often is said to be weak.
An immediate implication of the procedural cartel model is that a rational gatekeeper,
in this case the majority party, is never rolled. Consequently its roll rate
should be constant and zero. The minority party is expected to be rolled regularly
because it has no presumed gatekeeping rights. In contrast, the median voter model,
which Cox and McCubbins call the “floor agenda model,” implies that roll rates
for each party will be a function of the distance between that party’s median voter
and the legislature’s median voter. Cox and McCubbins then attempt to explain
variation in roll rates via regression analysis. Let r and d respectively denote the
majority and minority party medians, respectively. They estimate regressions of the
form:
Minority roll rate = · + ‚|d − m| + ε. (1)
Majority roll rate = · + „|r − m| + ε. (2)
The logic of the test is illustrated in Figure 12.4. Assume that at any given law-making
opportunity, legislators’ ideal points are spread out over a finite interval, say [−1, 1].
For ease of illustration, suppose the median of the minority party is d = −1/3, the
chamber median is m = 0, and the majority party median is r =1/3. Reflection
points 10 of the two parties therefore lie at −2/3 and2/3, and the policy space is
conveniently partitioned into six segments, I–VI.
Clearly, predicting roll rates under the cartel theory (or any given pivot model)
requires assumptions about the distribution of status quo points. In the simplest case,
suppose q is distributed uniformly over [−1, 1]. Then status quo points will arise in
segmentsIorVIwithprobability1/6+1/6 =1/3. None of these status quo points
elicit rolls, because majorities of both parties prefer the cartel-theoretic equilibrium
as possibly amended. Accordingly, such votes are regarded as more appropriate grounds for inference
than would be, say, procedural votes, frivolous amendments, etc.
¹⁰ A reflection point of, say, a party median p with respect to the chamber median m,denoted
R(p, m), is the point whose distance from p equals that between p and m butthatliesonthenon-m
side of p. With distance-based (Euclidean) preferences, R(p, m) =2p − m. By construction the pivotal
player with ideal point p is indifferent between m and its reflection point about p,i.e.R(p, m).