1 Advances in Political Economy - Department of Political Science

EDITOR’S PROOF

232 G. Serra

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I will focus on the key properties that will buttress the rest of the paper. I start by

rephrasing the previous considerations in terms ofπR, which is the variable that

partyRis seeking to maximize.

Theorem 2The probability thatR’s nominee will be high-skilled,πR,givenR’s

nomination process,mR,is given by

πR≡P(vR=V|mR)=

{

πRI ifmR=elite

πRI+S ifmR=primary

whereSis called the primary skill bonus and is given byS≡P(vR=V|primary)−

P(vR=V|elite).

This demonstrates how the information revealed in primary campaigns is trans-

lated into a better nominee in terms of valence. Holding an internal contest will

increase the probability of nominating a high-skilled candidate in the amountS.Is

that a small or a large benefit? I answer that question in the next subsection.

5.3 What Makes Primaries More Appealing?

I begin by establishing whether primaries have a benefit to party leaders.^6

Lemma 2The primary skill bonusSis strictly positive forπRI∈( 0 ,π)and zero

forπRI∈[π, 1 ).

Primaries therefore do bring a benefit for small enough priors about the insider’s

skill. When the insider candidate is weak, meaning thatπRIis below a certain thresh-

old, forcing her to compete with an outsider candidate increases the excepted skill

of the nominee by a strictly positive amount. The reason is that forπRI∈( 0 ,π)

party members will take a serious look at the outsider candidate’s performance in

the primary to decide whether she is more convincing than the party insider. This

result was expected as it conforms with previous findings in Serra (2011).

The surprising result comes from high priors about the insider’s skill: in such case

a primary election might not bring any benefit whatsoever. When the insider candi-

date is strong, meaning thatπRIis above a certain threshold, forcing her to compete

with an outsider candidate does not increase the expected skill of the nominee at

all. The reason is that forπRI∈[π, 1 )party members find the insider candidate so

compelling that they will vote for her regardless of the outsider candidate’s perfor-

mance in the primary. This result is new with respect to the papers about primaries

that I am aware of.

(^6) As mentioned before, the symbolsπandπrefer to two constants whose values areπ≡ (^1 −q)^2
1 − 2 q+ 2 q^2
andπ≡ q
2
1 − 2 q+ 2 q^2.