have joint monopoly control of the agenda (i.e.,
the Conservative Party
cannot make a proposal), and that a coalition proposal must be adopted
by a majority vote of each party in the coalition before the coalition’s
proposal can be presented in a
floor motion. Assume further that the par-
ties in the coalition have perfect discipline, so that all the members of
each party vote for any policy proposal made on the
floor by the coali-
tion. And assume,
finally, that the opposition party automatically votes
against any motion made by the governing coalition. What is the set of
equilibrium policies in this system?
For example, in
figure 4A any policy to the left of L
2
could be upset
by some coalition proposal at or to the right of L
2
: L
2
and L
3
(who com-
prise a majority of the Labor Party) would vote for such a proposal, as
would G
1
, G
2
, and G
3
(all the members of the Green Party), and these
five members collectively comprise a parliamentary majority. Similarly,
any policy lying to the right of G
2
would be upset by some coalition pro-
posal lying at or to the left of G
2
: G
2
and G
1
would vote for such a pro-
posal, as would L
1
, L
2
, and L
3
, and these
five members comprise a par-
liamentary majority. But no policy in the region spanned by L
2
and G
2
could be upset. For instance, an SQ at L
2
could not be upset by any pro-
posal to its right because L
1
and L
2
would vote against it (i.e., a majority
of the Labor Party would oppose the move), and an SQ at G
2
could not
be upset by any proposal to its left because G
2
and G
3
would vote against
it (i.e., a majority of the Green Party would not support the move).
Hence, the set of equilibrium policies is de
fined by the region spanned
by the ideal points of the median members of the two parties—by L
2
and
G
2
—in the governing coalition; these policies comprise the Party Coali-
tion Unicameral Core.
An alternative coalition would be for the Green Party to unite with
the Conservative Party (see
fig. 4B). In this case, the Core would shift
rightward and would span the ideal points of G
2
and C
2
.
To determine the Core, we need only determine the median member
of each of the outermost parties in the governing coalition. In
figure 4A,
for example, these median members are L
2
and G
2
; the Core here is thus
the set of points spanning the ideal points of L
2
and G
2
. In
figure 4
B, the
outermost median members are G
2
and C
2
and the Core here is the set
of points spanning the ideal points of G
2
and C
2
. In each case, the ideal
points of no other members need be depicted.
As long as neither party of the coalition has a parliamentary majority,
Veto Points in Democratic Systems
87
the Core will span the ideal points of the median members of the outer-
most parties in the coalition. Thus, the size of this Core will be a func-
tion of the distance between the median members of these two outer-
most parties in the coalition. For example, if L
2
and G
2
are close together,
as in
figure 4C, the Core will be small; indeed, if L
2
and G
2
have the same
ideal point the Core will be a single policy, as in
figure 4D. But if L
2
and
G
2
are far apart, the resulting Core will be large, as in
figure 4
E.
A Three-Party Unicameral Parliament without Perfect Coalition
Party Discipline
If the coalition parties’ discipline is imperfect, some party members may
vote against their coalition’s own proposal to replace SQ; if enough
members of the coalition parties defect in this manner, the coalition’s
motion could be defeated. We continue to assume that the majority
coalition has monopoly agenda control authority and that the opposi-
tion party members automatically vote against the coalition parties’ pro-
posal. To avoid defeat, the coalition’s leaders would propose no amend-
ments to SQ that would risk this kind of defection. What impact would
this lack of party discipline have on the size of the Party Coalition Uni-
cameral Core?
For an answer, consider
figure 5A, in which the Labor Party has three
members and the Green Party has only two; their coalition now has only
five members, which is a bare majority in the parliament. Since defection
is possible by members of the parties in the coalition, defection of any of
either party’s members would result in the defeat of any coalition pro-
posal. For any SQ to the left of L
1
, there exists some proposal at or to the
right of L
1
that would defeat this SQ with the support of all
five coali-
tion members. Similarly, for any SQ to the right of G
2
there exists some
proposal at or to the left of G
2
that would defeat it with the support of
all
five coalition members. But for any SQ lying at or to the right of L
1
and at or to the left of G
2
there exists no proposal that could defeat it
with the support of all
five coalition members. Whereas the Core with-
out perfect party discipline would span just the ideal points of L
2
and G
2
(the coalition parties’ median members), the possibility of defection in-
creases the size of the Core to span the ideal points of L
1
and G
2
.
However, the possibility of defection does not necessarily increase the
size of the Core. Consider
figure 5B, in which the Labor-Green coalition
has six members. Even allowing for the possible defection of members of
Veto Points in Democratic Systems
89