How to Win a Large Election
Forthcoming, Games and Economic Behavior
41 Pages Posted: 11 Jun 2009 Last revised: 29 Nov 2012
Date Written: October 2012
Abstract
We consider the optimization problem of a campaign trying to win an election when facing aggregate uncertainty, where agents' voting probabilities are uncertain. Even a small amount of uncertainty will in a large electorate eliminate many of counterintuitive results that arise when voting probabilities are known. In particular, a campaign that can affect the voting probabilities of a fraction of the electorate should maximize the expected difference between its candidate's and the opposing candidate's share of the fraction's potential vote. When a campaign can target only finitely many voters, maximization of the same objective function remains optimal if a convergence condition is satisfied. When voting probabilities are certain, this convergence condition obtains only at knife-edge combinations of parameters, but when voting probabilities are uncertain the condition is necessarily satisfied.
Keywords: elections, expected margin of victory, law of large numbers, local limit theorem
JEL Classification: D72, D81
Suggested Citation: Suggested Citation