Sophisticated Attacks on Decoy Ballots: A Devil's Menu

Voting systems based on decoy ballots aim at preventing real ballots from being bought. Decoy ballots do not count in election outcomes, but are indistinguishable from real ballots. We introduce a “Devil’s Menu” consisting of several price offers and allocation rules, which can be used by a malevolent third party—called the adversary—to curb the protection offered by decoy ballots. In equilibrium, the adversary can buy the real ballots of any strict subset of voting districts at a price corresponding to the willingness to sell them. By contrast, the voters holding decoy ballots are trapped into selling them at a low or negligible price. Decoy ballots may thus be ineffective against vote-buying even if the adversary’s budget is limited.