ECONOMY

keith krehbiel 227
Outcomes
p
I II III
IV
V
v
m
No policy change
f
Gridlock Interval
f
m
v
p
Status quo q
Fig. 12.2 Equilibrium in the pivotal politics theory
It is merely an analytic convenience that the proposer is the median voter. Any
right-of-median voter would make the same proposal because he or she faces the
same optimization problem: to make the filibuster pivot indifferent between the
optimal proposal p ∗ and the status quo q. Any proposal less than 45 is not optimal
for such proposers because it fails to extract all available rents. Any proposal more
than 45 is not optimal for such proposers because it triggers a successful filibuster
and leaves the undesirable status quo point in effect. Only with x =45isthereno
alternative proposal that can both beat a filibuster and gain a majority. Therefore, the
equilibrium proposal in such cases is, in general, 2 f − q.
From the opposite end of the spectrum—that is, a status quo point that lies on the
upper end of the spectrum—the president and the veto pivot (the 66th legislator in
this scenario) are the constraints against which bill proponents optimize. Dispensing
with an example, suffice it to say the equilibrium proposal is 2v − q. 6
With only a couple of qualifications, these two examples of pivotal voters serve
effectively as building blocks for the complete statement of equilibrium in the pivotal
politics game. Figure 12.2 graphs all possible equilibrium outcomes (vertical axis) as
a function of variable status quo points and fixed ideal points (horizontal axis). As
many as five types of behavior occur in the model, defined in terms of the extremity
of the status quo relative to pivotal legislators’ ideal points. For status quo points
in the most extreme intervals, I and V, the super-majoritarian constraint does not
bind proposal-making, and the median voter outcome results. Therefore, the graph is
⁶ This example assumes that the president’s ideal point p is greater than 66. Substitute p for v
otherwise. Formally, the game is multistage, finite, and complete information in structure. As an analytic
convenience, it suffices to focus on the behavior of at most four players: the median voter, a president, a
2/3 veto pivotal voter on the president’s side of the median, and a 3/5 filibuster pivot on the side of the
median opposite the president (see Krehbiel 1996)