“Flip-Flopping, Primary Visibility and the Selection of Candidates”

Assume that voters’ beliefs after observing liberal and moderate signals during the general election campaign are the same, that is, pCh 2 (μ) = p Ch 2 (λ) and W (p Ch 2 (μ)) −W (pCh 2 (λ)) = 0. In this case, both types of challengers would choose zero effort, which means that signals are perfectly informative and we must have pCh 2 (μ) = 1 and p Ch 2 (λ) = 0. Thus, p Ch 2 (μ) 6= pCh 2 (λ). Assume next that pCh 2 (μ) < p Ch 2 (λ) then using Claim 1 we obtain W (p Ch 2 (μ))−W (pCh 2 (λ)) < 0. In this case, liberal challenger will exert zero effort, in which case moderate signal would fully reveal a moderate challenger pCh 2 (μ) = 1. In that case, we obtain W (p Ch 2 (μ))−W (pCh 2 (λ)) > 0, which contradicts our assumption above.