1 Advances in Political Economy - Department of Political Science

EDITOR’S PROOF

When Will Incumbents Avoid a Primary Challenge? 237

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Fig. 5 The

candidate-selection method as

a function of the ideal point

of the median primary voter,

XRM

B&W IN PRINT

intuitive but is seldom mentioned in the existing literature. The same intuition can

be obtained from Fig.5. For low values ofXRM(which I label “moderate primary

voters”) the party will endorse an insider candidate. For intermediate values ofXRM

(which I label “partisan primary voters”) the party will hold a competitive primary

election. For high values ofXRM(which I label “extremist primary voters”) the party

will endorse an insider candidate. Consequently, the CSM has a non-monotonic re-

lationship with the ideal point of the median primary voter.

From the results above it is clear that the thresholdTdetermines how likely pri-

mary elections are. The interval(XRE−T,XRE+T)corresponds to the values that

XRMshould take for the nomination to be delegated to party members. Such inter-

val can therefore be interpreted as thelikelihood thatRwill adopt a primary.Fora

largerTit is more “likely” that the internal divergence betweenR’s establishment

and RAF will be lead to a primary. Then a way of phrasing the previous theorem

is thatthe likelihood of opening the CSM decreases with the internal divergence

between the party’s leadership and the primary voters.

7.1 Comparative Statics

We would like to gain insight on what makes the adoption of primary elections more

likely. According to the previous theorem, the likelihood of adopting a primary is

given byT. Hence, I study howT changes with the parameters in the model. As

it turns out, the results will crucially depend on the value ofπRI. To be specific,

I need to divide two cases. The first case isπRI∈( 0 ,π)corresponding to low and

intermediate priors, and the second case isπRI∈[π, 1 )corresponding to high priors.

Recall thatπandπrefer to two constants whose values areπ≡ (^1 −q)

2

1 − 2 q+ 2 q^2 and

π≡ q

2

1 − 2 q+ 2 q^2.

I start with low and intermediate prior beliefs about the skill of the insider candi-

date, which corresponds to the situation where primaries are most attractive.

Theorem 4Suppose the initial expectation that RI is high-skilled,πRI,is such that

πRI∈( 0 ,π).Then the thresholdT,which determines the likelihood of primaries,

is:

1.Strictly positive

2.Strictly increasing withS