Hvg krause 47K. qxd

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 4B, 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

---

Fig. 4. A party coalition unicameral parliament with perfect coalition party discipline

---

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 4E.

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

---