Hvg krause 47K. qxd

Politics, Policy, and Organizations

vote automatically against any majority party proposal. If enough ma-

jority party members vote against their party’s own proposal, their votes

when combined with the minority party votes could defeat this proposal.

With its monopoly agenda control, the majority party could avoid such

defeats by not proposing changes to any status quo policy that would risk

this kind of defection. The result can be a Majority Party Unicameral

Core that is substantially larger than the party median alone (or than

what is spanned by the party medians).

For example, in 

figure 3A the Conservative Party has a bare majority in

parliament (

five of the nine members) and its median member is C

3

. For

any SQ to the left of C

1

, there exists a policy at or to the right of C

1

that

would upset the SQ with the support of all 

five Conservative members;

hence the Core cannot include any points to the left of C

1

. However, for

any SQ lying between C

1

and C

3

a proposal to move policy rightward to-

ward C

3

would be rejected, at least by C

1

, because he or she would prefer

SQ; lacking the vote of C

1

, at most only four Conservative Party members

(C

3

, C

4

, C

5

, and perhaps C

2

) would support the proposal, and these three

or four members do not constitute a majority of parliament. Thus, the

proposal would fail (since the Labor Party members would all vote against

it as well). Hence, the Core must include the policies from C

1

to C

3

. Sim-

ilar arguments hold for policies lying on the right side of the Conservative

Party, and so the Core would also include the policies from C

3

to C

5

.

Overall, then, the Core here would be the set of policies from C

1

to

C

5

; that is, this Core spans the ideal points of all Conservative Party

members. Since the Core with perfect party discipline was just the pol-

icy at C

3

(see 

fig. 2A), the prospect of defection by majority party mem-

bers can thus increase the size of the Core.

4

For another example, consider 

figure  3B. The Conservative Party

here has seven members (two more than a bare majority of the nine-

member parliament), so policy change requires the votes of only 

five of

the seven Conservative Party members. In this case, the Majority Party

Unicameral Core need not include the ideal points of all the members

of the Conservative Party. For example, for any SQ to the left of C

3

there exists some policy at or to the right of C

3

that would gain both a

party and a parliamentary majority against SQ: 

five members—C

3

, C

4

,

C

5

, C

6

, and C

7

, who collectively comprise both a party and a parlia-

mentary majority—could agree on some policy at or to the right of C

3

that would upset this SQ. Hence, the Core cannot include any points

84

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to the left of C

3

. Similarly, for any SQ to the right of C

5

there exists

some policy at or to the left of C

5

that would gain both a party and a

parliamentary majority against SQ: seven members—C

1

, C

2

, C

3

, C

4

,

and C

5

, who collectively comprise both a party and a parliamentary ma-

jority, plus L

1

and L

2

—could agree on some policy at or to the left of

C

5

that would upset this SQ. Hence, the Core cannot include any

points to the right of C

5

.

However, for any SQ lying between C

3

and C

5

a proposal to move pol-

icy rightward would be rejected at least by C

1

, C

2

, and C

3

(and possibly

C

4

, depending on the location of SQ), leaving at most only four Conser-

vative members—C

1

, C

2

, C

3

, and possibly C

4

, depending on the location

of SQ—to vote for the move, and they are not a majority in parliament.

Similarly, for any SQ lying between C

3

and C

5

, a proposal to move policy

leftward would be rejected at least by C

5

, C

6

, and C

7

(and possibly C

4

as

Veto Points in Democratic Systems

85

Fig.  3. A two-party unicameral parliament without perfect majority party

discipline

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Politics, Policy, and Organizations

well, depending on the location of SQ), again leaving at most only four

Conservative members (C

1

, C

2

, C

3

, and possibly C

4

) to vote for the

move, and they are not a majority in parliament. (Again, recall that we

are assuming that the minority party automatically votes against any

majority party motion.) In sum, if the majority party members are not

perfectly disciplined, the core will span the policies from C

3

to C

5

.

5

For a third example, in 

figure 3C, if the majority party includes every

member of parliament the Core will include just the party median,

which is the chamber’s overall median as well.

When the majority party lacks perfect discipline (but retains monop-

oly proposal authority) and the members of the minority party auto-

matically vote against any majority party proposal, the size of the Core

is an inverse function of the size of the majority party. For example, as

the size of the majority party increases from a bare majority toward the

whole chamber in size (

figs. 3A through 3C ), the size of the Core will de-

crease toward the median of the entire parliament. If the majority party

has just a bare majority, the Core spans the ideal points of all the party’s

members, as from C

1

to C

5

in 

figure 3A. If the size of the majority party

increases to seven, as in 

figure 3B, the Core shrinks to the region spanned

by C

3

and C

5

. And if the majority party includes every member of par-

liament, as in 

figure 3C, the Core includes just the party median, which

is the chamber’s overall median as well. This pattern occurs because as

the majority party increases in size a decreasing proportion of its mem-

bership is necessary for a proposal to be approved by an overall parlia-

mentary majority; hence, the Core is smaller, and as the party grows in

size its own median converges on the median of the overall chamber.

Thus, when the majority party reaches its maximum size (i.e., when it

includes the entire chamber), the Core becomes the overall medium.

A Three-Party Unicameral Parliament with Perfect Coalition

Party Discipline

When a unicameral parliament has three or more parties, none of which

has a majority, a coalition government may have to be constructed. Con-

sider a case in which the nine members of parliament are partitioned into

the Labor, Green, and Conservative parties, each with three members,

and with the ideal points of the Green Party MPs lying between those of

the Labor and Conservative MPs. Assume that a coalition government

forms between the Labor and Green parties, that the parties in coalition

86

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