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Appendices

Appendix 1. The probabilistic voting model with a public sector lobby

In this appendix we derive equation (2.19) giving the optimal lobby campaign
efforts and equation (2.20) determining the probability that political party A will
win the election.

According to (2.16) the lobby swing voter who is indifferent between the two
parties has the ideological bias

ρ_i = U_i^A - U_i^B - ωe .

(A.1)

All lobby members with a value of ρ_i^j less than ρ_i will prefer party A to party

B .Ifρ_i^j is uniformly distributed on the interval
fraction π_i^A of lobby members with a value of ρ_i^j less than ρ_i is

2φi^, ₂φi with length 1M^, the

πi^A

' = Φi (* + ⅛) = Φi (UA-UB-ω + ⅛)∙

(A.2)

1∕^φi ∖ ^2φ√ ∖ ²^φi∕

Using (2.17) to eliminate ωe from (A.2), we may thus write the probability that a
lobby member will vote for party A as

^πA =q⁺^φi £UiA ^- UB ^-^ω⁺^αih (ZA ^- ZB)] . (A.3)

In a similar way, if the individual ideological preference of an outsider (ρ_o^v) follows

a uniform distribution on the interval

1 1

2φo ^, 2φo

the probability π_o^A that an

outsider will vote for party A can be shown to be

^πA = + ⁺^φo £Uo^A^- UB ^-^ω⁺^αih (ZA ^- ZB)] . (A.4)

Thus the expected fraction of total votes that will be cast in favour of party is

π^A = αiπ_i^A +(1- αi) π_o^A.

(A.5)

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