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
ρi = UiA - UiB - ωe .
(A.1)
All lobby members with a value of ρij less than ρi will prefer party A to party
B .Ifρij is uniformly distributed on the interval
fraction πiA of lobby members with a value of ρij less than ρi is
2φi, 2φi with length 1M, the
πiA
' = Φi (* + ⅛) = Φi (UA-UB-ω + ⅛)∙
(A.2)
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+ φi £UiA - UB - ω + αih (ZA - ZB)] . (A.3)
2
In a similar way, if the individual ideological preference of an outsider (ρov) follows
a uniform distribution on the interval
1 1
2φo , 2φo
the probability πoA that an
outsider will vote for party A can be shown to be
πA = + + φo £UoA - UB - ω + αih (ZA - ZB)] . (A.4)
2
Thus the expected fraction of total votes that will be cast in favour of party is
πA = αiπiA +(1- αi) πoA.
(A.5)
31
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