The name is absent

Therefore, the expected seat share of P =1 is half that amount since it has
no chance of winning in the second half of the districts:

E(ιv sC ) =      ...⁺2(-⅛^[(1+β )2^{(V1 - v +    (A4)}

_ι '(V² - V²*) + ³(V³ - V³*) + ¹(V⁴ - V⁴*)]

2  22

E(_IVs²_C) is defined analogously.

Assuming a similar competition between P =2and 4, one easily derives the
equilibrium policies under a four party equilibrium:

_π,._gJ = ( ¾-¹[6(+β)] if J=^1,2                 _(A5)

IV ^gC [¾-¹[1 + β ], if J = 3,4

1            2      ⁴

IV ^rC = IV ^rC = —

C       C  _γψ

As one sees, spending on voters represented in the coalition increases with β
but spending on voters from the opposition decreases with β.

Merged opposition (three parties) We now look at the equilibrium policies
when the opposition merges and the coalition faces opposition party P = 34.We
proceed as above.

In districts d ∈ [0,1 ],the vote share for P = 1 remains the same and is given
by (8.1). On the other hand, the votes for P =34are given by

v³⁴ = +¹+^β (1 — F (V¹ - V¹* - δ)) +             (A6)

¹-^β(1 - F(V² - V²* - δ))                  (8.2)

1⁴

4 £(1 - F(VJ - VJ∙ - δ))}

J=3

This is exactly the double of v³ as given by (8.1). We can then derive the
expected seat share of P = 1.

1/ ιl ∖   ^{1 ψ}(⁴ 2 ) . ^ψ r∩ _{l z}3∖j∕τ∕1 τ∕1*∖       ( ʌ 7)

E(¹IIsC) = 4 ^- 2(6 + β)φ ⁺ 4(6+5)^{[(1+ β})⁴(^v " ^V )     (A7)

4

+(1 - β)2(V² - V²*) + 3 X(VJ - VJ*)]          (8.3)

J=3

48

<<   52   53   54   55   56   57   58   >>

More intriguing information