The name is absent

4.2. The equilibrium party system

We now turn to party formation and government formation under majoritarian
elections.

4.2.1. Government formation

We start by computing equilibrium expected payoffs at the start of the government
formation stage, for all possible party systems.

Four party system Suppose that we have four parties (N =4): P =1, 2, 3,
and 4. The government can either be a coalition of parties 1 and 2, or of parties
3 and 4, with equal probabilities. Moreover, as shown in section 4.1.2, E(IVs^P_C)=
E(_ivsP) = 4. The expected payoff for any party P, at the start of the government
formation stage follows from (2.4) and (2.5):

IV W P = 1[1 + γ] rCP   ²     ' ,                  (4.7)

2            γψ

where the right-most expression follows from (4.5).

Two party system In the case of two parties (N =2),P=12and 34,only
single-party governments are possible, both with equal probabilities, 1/2. Their
expected seat share in the next legislature are the same in government and opposi-
tion E(IIsS) = E(IIsO) = 2. By (2.4), (2.5) and (4.5), we compute their expected
payoff as:

IIW P = ₂[1 + γ ] rP   ².'.   .                   (4∙8)

As with proportional elections, this turns out to be exactly the same expression
as in the four-party case above (4.7). The intuitive explanation is also the same,
namely a higher expected vote share is balanced by lower expected rents.

Three party system Finally, suppose we have a legislature with three parties
(N =3),sayP =12, 3 and 4. Then, both single-party governments and coali-
tion governments are possible, with equal probabilities, 1/2. But the expected
equilibrium payoffs are no longer the same for all parties in the legislature.

Consider first the large party, P =12. Its expected payoff is still given by
(3.11). But, as shown in the previous subsection, the expected seat share of the

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