The name is absent

Four party system Suppose that the legislature consists of four parties P =
1, 2, 3, 4 . Given the rules of government formation, only coalition governments are
possible in this case: coalitions of parties 1 and 2, and 3 and 4, are formed with
the equal probability, 2.

By (2.4), the expected utility for any of these parties, at the start of the
government formation stage, is thus:

IV W P = E(iv WcP ) = 1 £rP + E(iv sP )RP ] + 2 £E(iv sP)RP ] .      (3.9)

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With probability 1/2, party P is in a coalition government in the current period,
earning an expected utility given by the first square-bracketed term; with proba-
bility 1/2, the party is out of government in the current period, earning expected
utility given by the second term.

We established in the previous section that, in a four-party system, E(IV s^P_C )=
E(IV s^P_O) = 1/4. As seen from the government formation stage, the expected equi-
librium votes share is the same for the parties in government and opposition.
Using the expression in (2.5) for the expected value of seats in the next legisla-
ture, RP and the expression in (3.5) for equilibrium rents, rjCP, the right hand side
of (3.9) simplifies to:

IV W P = 1(1+ γ)rCP     .+   .                (3.10)

2             γφ

Two party system Instead suppose that the legislature consists of two parties,
P =12, 34. Only single party governments are possible, with equal probabilities,
1/2. By (2.4), the expected utility of a generic party P, at the start of the
government formation stage, is:

IIW P = E(ii WsP ) = ¹ £rP + E („ sP R ] + 2 £E („ s^pP )RP ] .       (3.11)

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The first term is the expected utility of party P when in government, in the current
period, and the second term is its expected utility when out of government.

We established in the previous section that E(IIsζ) = E(IIsP) = ɪ. Carrying
out the same kind of calculation as in the four-party system , the right hand side
of (3.11) simplifies to:

IIW P = 1[1 + γ ] rSP   2   +    ,                  (3.12)

2             γφ

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