Negative Vote Buying and the Secret Ballot

We o¤er a model of negative vote buying paying voters to abstain. While negative vote buying is feasible under the open ballot, it is never opti-mal. In contrast, a combination of positive and negative vote buying is optimal under the secret ballot: Lukewarm supporters are paid to show up at the polls, while lukewarm opponents are paid to stay home. Surprisingly, the imposition of the secret ballot increases the amount of vote buying a greater fraction of the electorate votes insincerely than under the open ballot. Moreover, the secret ballot may reduce the costs of buying an election