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A theory has occurred to me recently. Like most ideas, the first step is figuring out whether someone else has already had it.

Suppose we want to maintain the secret ballot. One downside to the secret ballot is that we cannot, by definition, confirm afterwards that our individual ballots were counted properly. But suppose the voter was allowed to cast a second, special ballot. This one would be clearly marked as uncountable, but it would be traceable after the fact. Assuming all ballots to be treated the same except for contributing to the final total, this would allow for the accuracy of the overall system to be quantified, without revealing any individual ballots.

Did I invent something new here? Or is this a known thing? I have a problem of not knowing what to Google. I've been calling these "calibration ballots" in my head, but that's probably not the best name.

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    Sounds like a recipe for confusion.
    – James K
    Dec 22 '17 at 14:14
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    If the vote is listed on the traceable ballot, you no longer have private votes. If it's not, you have no way of knowing that your vote has been counted the way you marked it.
    – janh
    Dec 22 '17 at 14:33
  • @janh I think the idea is that the second ballet wouldn't actually have a vote on it, but the election officials would record receiving it, so the person who cast it could have some indication whether their real ballot (which was part of the same batch) was actually counted. Dec 22 '17 at 15:23
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    @IllusiveBrian "has been counted" isn't really important, though, if it has been counted for something other than what you voted for ;)
    – janh
    Dec 22 '17 at 15:47
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    @IllusiveBrian exactly, which is why you'd need to be able to verify that it has been counted and counted the correct way, which still making it impossible for a third party to verify either, even with your cooperation.
    – janh
    Dec 22 '17 at 16:23
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It's less political theory, and more cryptography that you probably want to look at in order to answer your question. The idea of trying to maintain ballot secrecy, while allowing the anonymous voter to confirm that their ballot was counted how they intended is not new. This wikipedia article references proposals going all the way back to 2004.

https://en.wikipedia.org/wiki/End-to-end_auditable_voting_systems

I'm not nearly familiar enough with cryptography to really determine if any of the various proposed systems are viable, but it seems to be at least possible to combine both ballot secrecy, and still allow an individual to confirm their vote was counted correctly.

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Any system that allows one to establish that the vote was counted properly cannot coexist with full secrecy of the ballot. We can make a promise that the vote is counted. We can even verify that a particular ballot was marked as counted. But we can't prove that the ballot was counted as written and still maintain secrecy.

The reason should be obvious. If I can verify that I voted for, e.g., Gary Johnson on my ballot, then someone else can use the same verification method to see that I voted for Gary Johnson.

Some of the academic literature is confusing on this point, as they will define either verification or secrecy more loosely. For example, they may provide a decryption key. Without that, no one can check my vote. But with that, anyone can check my vote. The system relies on my control of the decryption key. So a criminal steals my decryption key and knows how I vote. That's an example with secrecy defined loosely.

An example with verification defined loosely would be where I get a receipt that says that ballot #35 was counted. It doesn't say for whom. Great. What does that tell me? Absolutely nothing. I'm still relying entirely on the system to have counted my vote correctly.

A more specific example from Wikipedia:

After the voter selects their candidates, a DRE machine prints out a specially formatted version of the ballot on two transparencies. When the layers are stacked, they show the human-readable vote. However, each transparency is encrypted with a form of visual cryptography so that it alone does not reveal any information unless it is decrypted. The voter selects one layer to destroy at the poll. The DRE retains an electronic copy of the other layer and gives the physical copy as a receipt to allow the voter to confirm that the electronic ballot was not later changed. The system guards against changes to the voter's ballot and uses a mix-net decryption procedure to ensure that each vote is accurately counted.

Note that I can't actually verify that my vote was counted correctly. I can only verify that the system reports that it counted it correctly and that the stored copy hasn't changed from when I cast the vote. If I trust the voting system, then I'm happy. But that's the problem. This doesn't establish trust in the voting system; it requires it.

In a regular voting system, I am also stuck relying on the system.

Alternately, it is apparently possible to decrypt the ballot so as to count it. But this takes us back to the secrecy problem. If the system can decrypt the ballot, then someone else could. This is why passwords are stored as one way hashes rather than encrypted. Encryption is insufficient security.

Even a one-way hash won't work here. It allows exactly what we want to avoid but doesn't allow for counting. If we reenter the ballot, we can verify that its hashed value matches. But we can't count the ballot with it. Because you can't turn a hash into a value, only a value into a hash.

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