The name is absent

The probability p_A that party A will win the election equals the probability that
π^A is at least one half. Using (A.3) through (A.5), this condition may be written
as

pA ≡ P_ωr π^A ≥ 1/2

= Pr '' (UA - UB) + 1 ^φo (U_o^a - UB) + αih (Za - Zb) ≥ ω
ωφ                     φ ^{o o}

where φ ≡ αiφ_i +(1- αi) φ_o is the average dispersion of ideological preferences

across the two groups of voters. As the general ideological preference ω is uni-

^α.       ■ ' ■ B ■ ¹ ι ■      ■ A ■ B ■ ∙ ■ Z ■       Z-                 ../

¹∕^ψ

¹ + ^ψ [α<≠, (UA - UB) + (1 - αi) φo (Ua^a - UB) + φαih (Za - Zb)]

2φ

(A.7)

Lobby officials choose their campaign efforts to maximise the objective function
(2.18), subject to the constraint that efforts cannot be negative. Since (A.7)
implies ∂pa∕∂Za = α_ihψ and ∂pa∕∂Z_b = -α_ihψ, the first-order conditions for
the solution to the lobby problem may be written as follows, where μ_A and μ_B are
the Kuhn-Tucker multipliers associated with the non-negativity constraints on ZA
and ZB, respectively:

α_ihψ ⁽U_i^A - U_i^B) - Z_A - μ_A =0,    -α_i hψ ⁽U_i^A - U_i^B) - Z_B - μ_B =0, (A.8a)

ZA ≥ 0,ZB ≥ 0,μA ≥ 0,μB ≥ 0, μAZA =0, μBZB =0.

(A.8b)

From (A.8) we get the results stated in (2.19) which in turn imply that

ZA- ZB = αihψ ⁽Ui^A - Ui^B) .                   (A.9)

Substituting (A.9) into (A.7), we find

PA = ¹ + ^ψ [α< (Φi + φαiψh²) (UA - UB) + (1 - “i) Φo (UA - UB)] . (A.10)
2φ

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