Is there a ranked voting variant that prevents vote selling and identification?

Question

As acknowledged also on Wikipedia, one of the drawbacks of ranked choice voting is that "it is likely that many preference voting patterns will be unique to individual voters, which could allow voters to identify themselves in a context of corruption or intimidation, undermining the secrecy of ballots".

For instance, candidate A, could offer 20$ to voter X to vote for candidates ABCDEFG in this exact order, 20$ to voter Y to vote for ABCDEGF, and 20$ to voter Z to vote for ABCDGFE; then, since these orderings are unique and unlikely to happen by chance, they can verify that each one of the bribed people voted as instructed.

Since the number of orderings is large and choices past the first few don't matter, this allows for large-scale vote buying, by giving a different unique ordering to each bribed voter. The problem can be mitigated by limiting choices on the ballot to a small number, for instance 3, but with a large number of candidates even this does not help much.

Is there a ranked voting variant that could prevent this, without introducing other more serious drawbacks? Maybe something is possible using cryptography? Or is this an open problem in the context of ranked voting?

Answer 1

Yes, I see the problem and I think it is special for ranked voting because only then the number of possible unique ways to vote can be much, much larger than the number of voters and so make a particular vote identifiable and this particular bribing scheme attractive.

However, it relies on the whole ballot statistics to be made public. Not the whole ballot will be needed to determine the result. Some of these ranked choices will be inconsequential. Maybe one could truncate votes successively by parts that are not necessary to determine the winners before publishing. In your example, maybe it's enough to simply publish that three voters voted for ABCD??? and hide the endings that are not needed for finding the decision.

I imagine one could iteratively first only count the first part of the vote and then only further parts if they are needed until all available positions are assigned and then stop counting and maybe even destroying the remaining part (literally cutting off ballot papers) and aggregate the starting parts (if ABC didn't make it, then ABC and ACB and CBA ... neither so it could all be filed under ABC).

Drawback is that frequently election results have to be recounted, so destroying or aggregating part of votes could be seen as very risky. They might be needed later even if that seems very unlikely now.

A practical approach against this is limiting observation of ballot results to the public to small random samples. So everyone can inspect the results, but only a tiny random fraction of them. Not sure if this increases trust in the method though.

Or truncate ballot results before publishing so that in every published category are at least two votes. This may make the results not fully comprehensible to the public, but would reduce the risk of giving away identifiable information. Again, a trade-off.

Or one could limit the length of the ranking so something reasonably small (see not more than 4 choices long), and then do further election rounds should that not be enough to uniquely determine the winners of the election. But that may lead to different outcomes, may be regarded as unfair.

I'm actually not as confident as commenters that one could prove the bribing from outside. Those doing the bribing may be able to choose orderings that are likely to be unique but still sufficiently random for most statistical tests. It probably depends on how many of the votes one wants to buy.

Summary: I see the risk and all I can think of is some kind of limitation (cutting off) of the number of choices (while counting, while publishing or while voting).