The name is absent

1                               1⁴

IV ' = sP = 4[F (V P — V ‘P - δ) + 2 £ F (V J — V ‘J - δ)]     (3.1)

J=3

Among the terms between square brackets, the first reflects the share of voters in
group P whose reservation utility is satisfied, and the second the share of satisfied
voters from other groups (J =3, 4). As the latter split their vote equally between
the two parties in the governing coalition, the second term is multiplied by 1/2.
Finally, since each economic group constitutes one quarter of the population, the
whole expression is pre-multiplied by this number.

As ωⁱ has the same uniform distribution in each group, F(ω) = 2 + φω. Recall
also that the expected value of the popularity shock δ is zero, at the time policy
is set. After some simplifications, the expected seat share in the next legislature
for party P reduces to:

E (ιv sP ) = ₄ + 4 V P — V‘P ) + ¹XX (V J - V ‘J )] .

44       2

J=3

Thus, the expected seat share in the next legislature depends linearly on the
weighted indirect utilities of the voters from J = P and from the opposition
parties. As mentioned above, the density φ of the idiosyncratic reservation utilities
measures within-group mobility and hence the response of the expected seat shares
to economic policy. Note that the groups represented by a party in government
receive twice the weight of the groups in the opposition. Finally, whatever the
equilibrium policies at the policy formation stage, V^J = V^‘J , by definition of
V ^‘J . Equation (3.2) thus immediately implies that the expected equilibrium seat
share in the next legislature for a coalition partner, at the party formation stage
is 4. Thus, in the expected equilibrium continuation payoff _ivWPP, given by (2.4)
above, we will be able to set E(_ivsP) = 1. By the symmetry of the model, the
expected seat share at the party formation stage for a small party in opposition
is exactly the same; i.e., in _ivWP we set E(_ivsP) = 1.

What would happen if the opposition instead consisted of a single party? It
is easy to verify that the expressions for the expected vote shares for government
coalition parties at the party formation stage are exactly the same: i.e., we have
E(_ivsP) = E(iiisP) = 4 for P = 1, 2. A single opposition party can expect to
capture the remaining votes E(_iiisP) = 2.

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