EDITOR’S PROOF
When Will Incumbents Avoid a Primary Challenge? 223277
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322Fig. 1 The effect of a
valence advantage forR
overLB&W IN PRINT3.3 The General Electorate
The electorate cares about the policy implemented after the election. To simplify
the analysis, I will assume that there is a median voter, which I callM, whose
preferences are decisive in the election. I normalize her ideal point to zero.
In addition to the policy implementedx, the electorate also cares about the skill
vof the winning candidate. The utility function ofMis given byUM(x, v)=−|x|+vMwill vote for the party whose candidate maximizes her utility. I make the
following indifference assumptions. IfMis indifferent between the two parties, she
will vote for the one whose candidate has the highest skill. If both candidates have
the same skill, she will randomize equally between the two.
It is worth looking more closely at how the median voter makes her decision in
this kind of model. As elaborated in Serra (2010),M’s appreciation for a candidate
decreases with the distance between her ideal point and that candidate’s platform,
and increases with the candidate’s valence. In essence, the valence parameterv
“shifts up” the utility function ofM. An example of howMevaluatesRandL
is illustrated in Fig.1, where it is assumed thatvL<vRand|xL|<|xR|. In the case
depicted in this figure, candidateRis strictly preferred to candidateLin spite of
having a more extremist platform. CandidateRis able to win the election because
her higher score in the valence dimension more than compensates her extremism in
the policy dimension.3.4 Timing and Solution Concept
The timing of this election is the following:
1.Assessment of the candidates’ skills: Parties announce their candidates who
start campaigning. The candidates’ campaigning skillsvLandvRare observed.