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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
(3.2)
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, VJ = 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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