of raising ∆ from 0 to any positive level (i.e. initiating targeted support) is increasing in the level of γ,
D
∆γ
(∆ = 0) = −
η
τ (k + 1)
·
k
X
m=1
[1 − (
m − 1
k
)] · ln[1 − (
m − 1
k
)] > 0
thus demonstrating that the more targeted support by party leaders impacts upon within-list vote
shares, the more party leaders can perturb upward the corruption equilibria by committing themselves
to favor compliant militants.
As in the case of CLPR, under OLPR with targeted support district magnitude also plays an
important role in determining the attractiveness of the offer L is able to make to militants. Figure 7
shows how the expected party vote threshold varies with ∆ for two different levels of district magnitude,
k
1
and k
2
, where k
2
> k
1
. Where district magnitude is large, an increase in targeted support leads to
a more rapid reduction in the EPVT than it does where it is small. Moreover, figure 7 shows that it is
possible for a militant in an OLPR system and large district magnitude to have a lower EPVT than he
would in a system with CLPR and small district magnitude. The horizontal lines show the party vote
threshold for a first ranked candidate in polities where district magnitude equals k
1
and k
2
. Note that
once ∆ exceeds the point ∆
0
, the expected party vote threshold for a polity with OLPR and k = k
2
is
lower than the party vote threshold for a polity with CLPR and k = k
1
. Thus, it is entirely consistent
with the model to expect more pervasive machine politics in a polity with OLPR and large district
28
Convention