11
Stated in layman’s terms, this assumption means that high values of r
i
are at least as common as
low values.
12
The two pathological cases are as follows. Firstly, if E[
l
k+1
] = E, a slight increase in the value of
D will change the number of equilibria from two to three. If for some reason militants had coordinated
around the higher of the two equilibria when E[
l
k+1
] = E and they coordinate around one of the two
lower equilibria when the Pr(seat) curve shifts upwards, then the shift will not have resulted in a higher
equilibrium level of p but a lower one. Secondly, if E[
l
k+1
] = E, a slight decrease in the value of D will
also change the number of equilibria from two to three. If for some reason militants had coordinated
around the lower of the two equilibria when E[
l
k+1
] = E and they coordinate around one of the two
higher equilibria when the Pr(seat) curve shifts downwards, then the shift will not have resulted in a
lower equilibrium level of p but a higher one. As these cases are the result of knife-edge equilibria, their
substantive importance is limited.
13
The reader can verify this by setting l =
b
l and σ =
b
σ + ε where ε is some small constant. The
inequality will be satisfied if and only if k ≥
b
k ≡
b
l
1
2
+
b
σ+ε−
τ
η
(
1
2
−p)
− 1.
14
For a discussion of the potential of equilibria to emerge in the latter case, all of which result in
equal vote shares, see Cox (1990).
15
The Kumaraswamy distribution is a continuous and double-bounded distribution like the Beta, but
it has a pdf and cdf which are much easier to work with and thus it recommends itself for modelling
exercises like the current one. See Kumaraswamy (1980) for details.
16
The emphasis here on how electoral institutions determine the types of political corruption is similar
to a point made by Rose-Ackerman (2001), who argued that party-centered presidential democracies
were more prone to "legislative corruption" and candidate-centered presidential democracies more prone
to "presidential corruption."
38
Convention