1 Advances in Political Economy - Department of Political Science

EDITOR’S PROOF

230 G. Serra

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ifj’s performance showed low skill. I assume that a candidate’s performance in the

primary has a probabilityqof accurately forecasting the performance she would

have in the general election, withq∈(^12 , 1 ). In other words,sRIandsROhave prob-

abilityqof “being correct”. We can interpretsjas a noisy signal of candidatej’s

skill, and we can interpretqas the quality of this signal. More broadly,qis a mea-

sure of the effectiveness of primary elections as an information-revelation method.

In sum, the pre-candidates’ performances,sRI andsRO, are independently-

distributed random variables whose distribution depend onvRIandvROin the fol-

lowing way:

P

(

sj=high|vj= 1

)

=P

(

sj=low|vj= 0

)

=q

P

(

sj=high|vj= 0

)

=P

(

sj=low|vj= 1

)

= 1 −q

j=RI,RO

Once the party members observe the candidates’ performances, they can update

their prior beliefs aboutRI’s andRO’s skills using Bayes rule. This approach to

voting based on updated beliefs following a noisy signal has its roots in Condorcet

(1785), Austen-Smith and Banks (1996), and Feddersen and Pesendorfer ( 1998 ).

The candidates’ performances are public, and therefore the values ofsRIandsRO

are common knowledge. In particular, all the RAF members observe the samesRI

andsRO, and hence they update their beliefs based on the same information. Given

its interest in winning the general election, the RAF will vote for the candidate who

is believed to have the highest skill. When a party member is indifferent between

RIandRO, I assume she will vote for the one whose prior probability of being

high-skilled was largest. If both have the same prior, she will randomize equally.

5.2 Primary Voters Update Their Beliefs

These elements allow studying the behavior of primary voters. WhensRI=sRO,I

say that a member of partyR’s rank and file will “vote according to the signals”

if her strategy is to vote for the pre-candidate whose signal was highest, meaning,

whose performance was best in the primary campaign. On the other hand, if her

strategy does not depend on the signals sent during the primary, meaning that per-

formance in the primary is irrelevant, I say that a member of partyRwill “ignore

the signals”.

These concepts can be used to describe the RAF’s behavior during a primary.

As it turns out, their behavior will depend crucially on their prior belief about the

insider candidate’s valence,πRI. In all the results below, 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.

Lemma 1In a primary election,for each value ofπRI,the rank-and-file members

of partyRwill