ThreeBallot is a new voting method from Ron Rivest that is supposed to make elections more secure without compromising voter privacy. It got favorable reviews at first – Michael Shamos even endorsed it at a congressional hearing – but further analysis shows that it has some serious problems. The story of ThreeBallot and its difficulties is a good illustration of why voting security is hard, and also (I hope) an interesting story in its own right.
One reason secure voting is hard is that it must meet seemingly contradictory goals. On the one hand, votes must be counted as cast, meaning the vote totals reported at the end are the correct summation of the ballots actually cast by the voters. The obvious way to guarantee this is to build a careful audit trail connecting each voter to a ballot and each ballot to the final tally. But this is at odds with the secret ballot requirement, which says that there can be no way to connect a particular voter to a particular ballot. Importantly, this last requirement must hold even if the voter wants to reveal his ballot, because letting a voter prove how he voted opens the door to coercion and vote-buying.
If we were willing to abandon the secret ballot, we could help secure elections by giving each voter a receipt to take home, with a unique serial number and the list of votes cast, and publishing all of the ballots (with serial numbers) on the web after the election. A voter could then check his receipt against the online ballot-list, and complain if they didn’t match. But of course the receipt violates the secret-ballot requirement.
Rivest tries to work around this by having the voter fill out three ballots. To vote for a candidate, the voter marks that candidate on exactly two of the three ballots. To vote against a candidate, the voter marks that candidate on exactly one ballot. All three ballots are put in the ballot box, but the voter gets to take home a copy of one of them (he chooses which one). At the end of election day, all ballots are published, and the voter can compare the ballot-copy he kept against the published list. If anybody modifies a ballot after it is cast, there is a one-third chance that the voter will have a copy of that ballot and will therefore be able to detect the modification. (Or so the theory goes.)
Consider a two-candidate race between George Washington and Benedict Arnold. Alice wants to cast her vote for Washington, so she marks Washington on two ballots and Arnold on one. The key property is that Alice can choose to take home a copy of a Washington ballot or a copy of an Arnold ballot – so the mark on the ballot she takes doesn’t reveal her vote. Arnold’s crooked minions can offer to pay her, or threaten to harm her, if she doesn’t produce an Arnold ballot afterward, and she can satisfy them while still casting her vote for Washington.
ThreeBallot is a clever idea and a genuine contribution to the debate about voting methods. But we shouldn’t rush out and adopt it. Other researchers, including Charlie Strauss and Andrew Appel, have some pretty devastating criticisms of it. They’ll be the topic of my next post.