Yesterday I wrote about Ron Rivest’s ThreeBallot voting system. Today I want to start a discussion of problems with the system. (To reiterate: the purpose of this kind of criticism is not to dump on the designer but to advance our collective understanding of voting system design.) Charlie Strauss and Andrew Appel have more thorough criticisms, which I’ll get to in future posts. Today I want to explain what I think is the simplest problem with ThreeBallot: it has no natural way to handle write-in votes.
(For background on how ThreeBallot works, see the previous post.)
The basic principle of ThreeBallot voting is that each voter fills out three ballots. Every candidate’s name must be marked on either one or two of the three ballots – to vote for a candidate you mark that candidate on exactly two of the three ballots; all other candidates get marked on exactly one of the three ballots. The correctness of ThreeBallot depends on what I’ll call the Constraint: each voter creates at least one mark, and no more than two marks, for each candidate.
But how can we maintain the Constraint for write-in candidates? The no-more-than-two part is easy, but the at-least-one part seems impossible. If some joker writes in Homer Simpson on two of his ballots, does that force me and every other voter to write in Homer on one of my three ballots? And how could I, voting in the morning, know whether somebody will write in Homer later in the day?
We could give up on the Constraint for write-in candidates. But the desirable features of ThreeBallot – the combination of auditability and secrecy – depend on the Constraint.
In particular, it’s the at-least-one part of the Constraint that allows you to take home a copy of one of your ballots as a receipt. Because you have to mark at least one ballot for every candidate, a receipt showing that you marked one ballot for a particular candidate (a) doesn’t force you to help that candidate, and (b) doesn’t prove anything about how you really voted – and that’s why it’s safe to let you take a receipt. If we throw out the at-least-one rule for write-ins, then a receipt showing a write-in is proof that you really voted for that write-in candidate. And that kind of proof opens the door to coercion and vote-buying.
Alternatively, we can declare that people who cast write-in votes don’t get to take receipts. But then the mere existence of your receipt is proof that you didn’t vote for any write-in candidates. I don’t see any way out of this problem. Do you?
There’s an interesting lesson here about election security, and security in general. Systems that work well in the normal case often get in trouble when they try to handle exceptional or unusual cases. The more complicated the system is, the more likely such problems seem to be.
In the next post I’ll talk about some other instructive problems with ThreeBallot.