The name is absent

(3.5) and (4.5) that rents are more likely to be higher under proportional elec-
tions, the higher is the standard deviation of reservation utility within economic
groups relative to the standard deviation of the popularity shock. As mentioned
above, the latter is negatively related to aggregate mobility across parties, while
the former is negatively related to within-group mobility. Summarizing, more
aggregate mobility and less within-group mobility make more likely higher rents
under proportional elections.

4.1.2. Single-party government

Equilibrium seat shares Let us compute equilibrium seat shares and policies
for a government supported by a single-party majority, say P =12.

As in the case of coalition government, the electoral formula makes a differ-
ence. The single-party incumbent wins the whole legislature if its vote share is
bigger than some threshold NVS that depends on the number of parties in the
opposition. Thus, the expected seat share in the next legislature for the single
party in government is:

E(NsP) = Prob(vP ≥ NVS) .

If the opposition is also made up by a single party, then we have IIVS = 1 ; if
instead the opposition is split in two parties, we have IIIVS = 1.

Using the distributional assumptions on the random popularity shock and
(3.1), we can rewrite the expected seat share of the single party in government as:

⁴

E (N sP ) = 2 + (2 -N Vs )^ψ + 4 X(V J — V ‘J ) .         (4.6)

2 2 φ4

J=1

Once more, the expression for the expected seat share is similar to that already
derived for the single-party government under proportional elections, equation
(3.6), and the term NVS enters as a constant, so the number of parties in the
opposition does not influence policy decisions.

The equilibrium expected seat share in the next legislature for the incumbent
does depend on the number of parties in the opposition, however. In a two-party
system, IIVS = 1, and the equilibrium expected seat share at the party formation
stage is the same for both parties: E(IIsP) = E(IIsP) = 1. In a three-party
system, with a single party in government and two parties in the opposition,
IIIVS = 1. Equation (4.6) then implies that the incumbent (large) party has an

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