The name is absent

In the other half of districts, the expression will be similar with V ² replacing
V¹.

On the other hand, the vote share for P =3is given by (8.1).

The expected seat share of P =12 is then

E(s¹2) = ₂ + ψ + ₄(XX(VJ - VJ')
φ

Note that the expression between square brackets has the same "weights " for
the groups represented in government and for those in the opposition. The equi-
librium policy is thus the same as in proportional and majoritarian homogeneous
elections! Heterogeneity thus does not affect the equilibrium policy when there
is a single-party government. The reason is that the single party is represented
equally in all districts. We are back to a case with symmetry. We do not expect
this result to hold under alternative representations of heterogeneity.

One verifies easily that the case with merged opposition will deliver similar
results. In essence, it becomes a 2-party contest like the one analyzed in the
homogeneous case.

8.2. Equilibrium party formation

Let us now look at possible equilibria. We first inspect the conditions for a two
party equilibrium.

Let us first look at the incentives for P =12to merge or to split given that
P =34has merged. In a two party equilibrium, the expected seat share of P =12
will be 2 whether it is in the opposition or not. The expected payoff of a merger
for party 1 is then 2 II WP² = ¹+-ψ^γ. In a three party equilibrium where P = 1 and 2
remain split, party P = 1 or 2 gets IIIWP = 2 [1 + E(IIIsP)γ2] ɪ +¹E(IIIsP) ɪγ2.
From (8.3) we know that E(IIIsC) = 1 — -2((¹1 ._β²)φ). Assuming that P = 34 are in
power, one can then derive that E(IIIs^p) = 1 — ɪ. One can then derive the
condition for P =12 to merge:

1 + γ φ _ 1 + γ Std(δ)   2 — β   1

γ ψ γ Std(ω)   6 + β   3

The right hand side unambiguously declines with β making the condition more
difficult to fulfill as β increases.

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