Equilibrium policies Consider first targeted government spending. When set-
ting these policy instruments, each coalition member P maximizes its expected
seat share, E(NsPC), as given by (4.2), taking as given the equilibrium policies set
by its partner. As we have seen, the weights of the different voters in (4.2) are the
same as under proportional elections — cf. (3.2). This means that the allocation
of equilibrium targeted spending coincides with that under proportional elections.
In equilibrium, a coalition government under majoritarian elections thus sets gCJ
according to (3.3) in Section 3.1.1. In other words, when electoral districts are
homogenous, coalition governments make the same spending decisions, indepen-
dently of the electoral rule.17
Next, consider the choice of political rents. Here, the electoral rule has a
direct effect on equilibrium policy. Following the same approach as in Section
3.1.1, the first order conditions for equilibrium rents are still given by (3.4). But
the trade-off between rents and expected seats is somewhat different. Imposing
the condition that future equilibrium rents and current equilibrium rents are the
same, and using (3.4) and (4.2), we obtain equilibrium rents captured by each
party in a coalition government under majoritarian elections18 :
,*P _ 4
(4∙5)
C = . ∙
C γψ
Comparing this expression and the corresponding one under proportional elec-
tions, equilibrium rents in the two systems depend on the relative magnitude of φ
and ψ. Without additional assumptions on these parameters, we cannot tell how
the electoral rule shapes political rents∙ We can think of each of these density pa-
rameters as measuring the inverse of the variability in the distribution expressed
in units of reservation utility∙ Because a uniformly distributed variable with den-
sity θ has variance proportional to -12 , we know that ψ = |td^) ∙ It follows from
17To be precise: when party P chooses gI , I being a group in the opposition, the effect
on his vote share and on that of his coalition partner are the same∙ Hence, to maximize his
expected vote share, he maximizes the right hand side of (4∙2)∙ But when choosing gJ, party
P = J maximizes the right hand side of (4∙2) multiplied by 2, since the effect on his vote share
can differ from that on his coalition partner’s vote share - cf∙ footnote 15∙ This change in
the ob jective function does not affect the first order conditions that define the optimal policy,
however, and thus has no behavioral implications∙
18 Recall that, by the government budget constraint, higher rents grabbed by party P imply
exactly the same loss of votes for both coalition partners∙ Hence, the remark in footnotes 15
and 17 do not apply, and it is correct to evaluate the effect of higher rents on expected seats on
the basis of (4∙2), as we have done∙
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