The name is absent

8. Appendix: Heterogeneity and majoritarian elections

In districts d ∈ [0, 2 ], J = 1 constitutes a share ¹⁺+^β of the electorate while J = 2
constitutes only a share ^1-β of voters while in districts d ∈ (2, 1], it is the opposite.
Groups J =3, 4 each form a quarter of the electorate in each district.

8.1. Equilibrium policy choices

As in sections 3 and 4, we derive first the equilibrium policy under coalition and
single-party government and then analyze equilibrium party formation.

8.1.1. Coalition government.

We first look at the case where parties P =3, 4 remain split.

Split opposition (4 parties) In districts d ∈ [0,1 ],the competition will be
between P =1 and P =3or 4. The latter are expected to have an equal number
of votes so let us focus on the competition between P =1 and P =3.Thevote
share for P =1 is given by

v¹ =     4 ' F (V¹ - V¹* - δ) +

1⁴

8 £ F (V J - V J ∙ - δ)
J=3

Similarly, the vote share of P =3is given by

4(1 - F (V³ - V³* - δ))

Note that P =3gets only half of the votes of the disgruntled voters from
J = 1 since P =4gets the other half. We can then calculate

Pr ob⁽v¹ ≥        2 ⁺ 2 φ 4 ■       .+ ^{[(1 + β})2(V^{1 -} V ¹∙>    ^(A3)

- ^β(V² - V²*) + 3(V³ - V³*) + 1(V⁴ - V⁴*)]

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