Clearly the equilibrium expected seat shares for P =1, 2 will be lower when
the opposition is united. Equilibrium policies will however also be different:
J
IIIgC
1
IIIrC
H-1[8⅞+β) ] if J = 1, 2
¾^1[1 + β ],
if J =3, 4
(A8)
24
III rC = —
C γψ
One sees that compared to (8.2), J =3, 4 receive more public goods and
J =1, 2 receive less even though there is still overspending for the former and
underspending for the latter. The reason is that a united opposition is a more
serious contender because it receives more votes than a single party in a divided
opposition. On the other hand, reward and punishment votes from voters not
represented in government are split between the coalition parties. This gives an
incentive to the incumbents to please more the groups from the opposition and to
spend less on its constituencies.
One sees here that in a coalition government, the equilibrium policy does
change with the number of parties in the opposition. This is thus different from
what we have under homogeneity where equilibrium policy depends only on the
government structure and not on the number of parties.
As above, an increase in β leads to an increase in spending on voters from the
coalition parties and to an decrease in spending on voters from the opposition.
8.1.2. Single party government
We now analyze the case where J =1 and 2 merge to form a single party P =12.
Analyzing first the case with a split opposition, the vote share of that party
in the first half of the districts will be
12
1++β F (V1 - V1* - δ) +
1--β F (v2 — V2* — δ) +
14
(A9)
4 \F (v J - v J • - δ)
J=3
49