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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

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             √                      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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