How to win a large election

► We model the optimization problem of a campaign trying to win an election when agentsʼ voting probabilities are uncertain. ► With a small amount of uncertainty and a large electorate, many counterintuitive results that accompany certain voting probabilities disappear. ► For fractions of voters, a campaign should maximize the difference between its share and its opponentʼs share of the vote. ► When a campaign can target only finitely many voters, maximization of the expected share of the vote remains optimal. ► For finite policies, a required convergence condition that normally does not obtain is necessarily satisfied when voting probabilities are uncertain.