The name is absent

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 .

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

'  = Φi (* + ⅛) = Φi (UA-UB-ω + ⅛)∙

1∕^φi         ∖    ^2φ√      ∖                ^2φi∕

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^{+ φ}i £UiA ^- UB ^{- ω + α}ih (ZA ^- ZB)] .           (A.3)

2

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

outsider will vote for party A can be shown to be

^πA = + ^{+ φ}o £Uo^{A -} UB ^{- ω + α}ih (ZA ^- ZB)] .           (A.4)

2

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

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