Targeted Campaign Competition, Loyal Voters, and Supermajorities

We consider a two-candidate campaign competition in majoritarian systems with many voters. Some voters are loyal, some can be influenced by campaign spending. Own loyalty with respect to a candidate is the voter's private information. Candidates simultaneously choose their campaign budgets and how to allocate them among the voters. We show that a candidate who has a group of loyal voters wins with a higher probability, but chooses the same expected budget size as the rival candidate. The equilibrium distributions of campaign spending target all voters equally in expectation, but target some voters more than others ex post.