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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?

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    Most election systems already criminalize this kind of conduct and there is little indication that this criminalization is ineffective. The secret ballot alone does a lot to undermine it and I don't see how the problem in general is specific to ranked choice voting.
    – ohwilleke
    Apr 21, 2022 at 19:45
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    A large scale operation to purchase votes based on unique ordering verified against the register would almost certainly be verifiable statically. It would be interesting to see if there is any data available from Australia, where ranked choice is already used. But while 8 items might have over 40,000 combinations to "sell" not all those combinations are likely and a large uptick of unlikely or illogical choices in a given election is probably detectable.
    – Jontia
    Apr 22, 2022 at 11:34
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    @ohwilleke Secret ballot is incompatible with publishing ballots for verification and ranked-choice voting, because the large number of possible ballots makes each one identifiable. You can pay someone to vote A and you can't tell if they did, not from the published ballot data. But you can pay someone to vote ABCDEFG and you can tell if they did, because probably nobody else voted that exact way. Apr 22, 2022 at 12:47
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    The Wikipedia article talks about the votes being published for a single specific election. Are the full vote lists in Ranked Choice elections generally published? I haven't been able to find that data for any Australian elections for example. If the full list is not published then it seems like the issue is solved.
    – Jontia
    Apr 22, 2022 at 14:38
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    @ohwilleke Enforcement is irrelevant because you cannot expect to catch people selling their ballots. It's not like shoplifting being illegal, it's more like gay sex being illegal. Apr 24, 2022 at 23:05

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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).

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    In systems like instant-runoff, voters should be expected to put their most unique votes first (e.g. Libertarians > Republicans), so truncating the end isn't too helpful. A selection after an extremely popular party might as well not be there because the runoff will not get to that point. Apr 22, 2022 at 12:48
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    Also worth noting that to been systemically important, vote selling and the like needs to make up a significant share of the total electorate. In a national, immediate sub-national, or large population local government, this requires a vast conspiracy of many thousands or millions of people with a common scheme of organization, and getting that many people to keep a secret is virtually impossible. A one off instance for four or five sold votes is hard to prevent but not much of a threat to the integrity of the system.
    – ohwilleke
    Apr 22, 2022 at 19:08

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