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In the 2020 United States Presidential Election in Dixville Notch, New Hampshire, Joe Biden received 5 votes and Donald Trump received 0 votes. Biden received 100% of votes cast.

In the 2016 United States Presidential Election in Kalawao, Hawaii, Hillary Clinton received 14 votes, Jill Stein 5, and Donald Trump 1 vote. Trump almost received 0% of votes cast.

There are probably rural places where the result is reversed and the Republican candidate may get 100% of the vote.

Apparently, Gir Forest in India had exactly one voter.

In the 2013 Falkland Islands sovereignty referendum, only 3 people voted No.

When at least two or three votes are cast for an alternative there is still somehow a secret ballot, but when 100% votes for a single alternative, the principle of the secret ballot is violated. The secret ballot is guaranteed by the Universal Declaration of Human Rights, Article 21.3 (emphasis mine):

The will of the people shall be the basis of the authority of government; this will shall be expressed in periodic and genuine elections which shall be by universal and equal suffrage and shall be held by secret vote or by equivalent free voting procedures.

(since this declaration is universal, it applies worldwide, including in the United States; moreover, the United States voted in favour of this declaration in the United Nations and was leading in drafting the text in the first place, so arguably it should apply in the United States; however, I don't know if it's actually a law)

Are there any systems or proposals for systems to mitigate this problem? I could imagine either a rule that voting precincts must have a minimum size (in the extreme case of a precinct with one voter, their vote could never be secret), or where any precincts with 100% for any candidate must be grouped after the election with others such that the result is less than 100% (effectively merging precincts after the election; voters could still verify the combined result but not the individual result per precinct, but secrecy were maintained).

(the counterpart, preventing any results where a candidate receives 0%, is probably not feasible, due to obscure candidates who may receive less than 0.01% of the vote nationwide, and thus 0 votes in many precincts; but with larger precincts, the nationally winning candidate getting 0% of the vote should be unlikely)

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  • Comments are not for extended discussion; this conversation has been moved to chat.
    – JJJ
    Nov 6 '20 at 0:19
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By your reasoning, polling stations would have to be big enough to make a "mixed" outcome highly likely. That goes against the principle that polling stations should be local if possible, near enough that people can vote in person without undue travel.

No size is perfect, and the possibility of a secret vote becomes more important where one votes for the unpopular candidate, not the popular candidate. In the Kalawao example, one voter bucked the neighbourhood trend and went for Trump, and it is impossible to tell which of the 20 really did it.

Publishing only aggregated numbers goes against the principle that citizens should be able to do the math themselves. Poll watchers are legal in many places, and a grassroots group could try to add their own tallies, that gets harder if they cannot compare with the official numbers step by step.

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    I guess the question is which is more important. The secret ballot or poll watching. Also in the Kalawao example the one Trump voter knows everyone else didn't vote for Trump so the secrecy is lost in that way. Nov 4 '20 at 16:27
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    Publishing only aggregated numbers goes against the principle that citizens should be able to do the math themselves — do you mean that they should be able to reproduce the count? If the published result is "station A + B: Trump 18, Biden 2", voters can recount A+B to verify this (what they can't do is trace individual ballots back to A or B, but is that strictly needed?).
    – gerrit
    Nov 4 '20 at 16:41
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    (BTW, I've been that person; the only one to vote for a particular candidate in my polling station, I was satisfied to see the official results for that candidate as having 1 vote rather than 0 votes)
    – gerrit
    Nov 4 '20 at 16:45
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    @gerrit, what I mean is citizens can feel confident if they can, in principle, become pollwatchers at the local polling station, and then follow the numbers getting reported up every step of the way. Even if they never bother to do that, the fact that they could keeps the process honest.
    – o.m.
    Nov 4 '20 at 17:35
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    Even if there are no "pollwatchers", publishing precinct level results is an important check against manipulation. The local poll workers will typically tabulate the results for their precinct and report them in. They can later verify that the published results match their own records. Local poll workers and the decentralized organization of elections makes it very hard to execute large scale election fraud, and publishing fine-grained election results is the way to preserve that security all the way to the top-line numbers.
    – jkej
    Nov 4 '20 at 19:25
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The secret ballot is a design principle with various procedures and rules that flow from that principle. But, it is not a rule of independent legal force itself, so it can't be violated when quirky circumstances cause someone's voting choice to be disclosed.

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    This sounds like the real answer to me. All the rest are mostly non-answers, where as this explains that the intent of the Declaration of Human Rights is to shape the voting system, rather than prevent all quirky disclosures
    – Numeri
    Nov 5 '20 at 9:27
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    The Declaration of Human rights is also not enforceable law. It is not self-executing. en.wikipedia.org/wiki/…
    – ohwilleke
    Nov 6 '20 at 23:36
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Ballots are secret to prevent powerful people from applying economic and social pressure on a large scale: e.g., so that someone like (say) Jeff Bezos or Elon Musk cannot threaten to fire any of the thousands of their employees who might vote for the 'wrong' party. That threat to livelihood is far more effective at quelling the vote that any more direct threat from the opposing party. People will willingly confront an opponent, but balk at the loss of career or social status.

In the kind of polling stations this question asks about — comparatively remote communities of a small number of people — these considerations don't really apply. There aren't many secrets in such communities to begin with, nor is there the kind of power base that makes social and economic pressure a problem. Most everyone knows most everyone else, they all have a good idea how each person is going to vote, and any surprises or misjudgments are more likely to result in arguments in the local grocery store or bar than in any economic or social penalties. If the grocery owner fires his stock-boy because he thinks the stock-boy voted the wrong way, that is not much of a threat to the stock-boy or the community as a whole.

Ballot privacy is far more important in large communities that have broad diversity and complex, abstract social interconnections. Small towns are small towns; things are 'personal' there, and that 'personal' interaction offsets any purely political differences.

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    My intuition would be the opposite. Urban people aren't as personally engaged in their neighbor's lives.
    – ohwilleke
    Nov 4 '20 at 22:50
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    @ohwilleke: ...which makes them far more likely to treat their neighbors instrumentally, rather than personally. It's hard to disregard the rights of someone one has a personal relationship with; it's easy to disregard the rights of faceless groups. This is basic social psychology; it's worth reading up on it. Nov 5 '20 at 4:41
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    I have the impression that many people in small villages care a lot about what neighbours think of them, so it seems there would be a lot of pressure if votes were not secret.
    – Mark
    Nov 5 '20 at 8:33
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    Plus the declaration of human rights doesn't mention exceptions to ballot secrecy for small villages.
    – Mark
    Nov 5 '20 at 8:34
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    This sounds incredibly patronising. How exactly is dismissal of employee not a threat to livelihood, career or social status in a small village? On the contrary, in a small village, there are far less opportunities for employment, and therefore each position is much more important than in eg. Jeff Bezo's Amazon, which has offices in major towns where another job is quite a possibility.
    – Gnudiff
    Nov 5 '20 at 9:27
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This problem is well known and doesn't have a simple solution that makes everyone happy.

One commonly applied solution (apparently not in the USA, though) is to not publish results from small communities or even from individual voting stations at all, but to publish aggregate regional results. For the local area that includes three villages, or for the district of the city that includes several voting stations.

There is no perfect secrecy on these things in all cases, however, especially for remote places that count locally. If your community has 10 people with voting rights, there's a pretty good chance that 2 or 3 of the same people will be doing the counting.

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    Even in a small community, only the register of who is eligible to vote is more or less public. The records of the election commitee, e.g. recording who has already voted, are not public and are accessible only to the commitee itself. Only, if a district has 100% turn-out and 100% for candidate A, I can say - as an outsider - who voted for whom.
    – Dohn Joe
    Nov 5 '20 at 15:07
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    Yeah, but if it's really 5 people as in the example, that's not much of a secret, either. People in such communities know who went to vote and who not, simply because it's so easy to keep track of it that you don't even have to try.
    – Tom
    Nov 5 '20 at 16:23
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    @DohnJoe - it may be true that the names of voters who have voted is not public during the course of the election. However, I'll tell you that the identity (including addresses, age, etc) each person voting in each of the elections in past 5 years is able to be purchased, and in some cases at no charge in many jurisdictions. If you desire proof, I'll be glad to send you the spreadsheet.
    – BobE
    Nov 5 '20 at 19:34
  • @DohnJoe In California, each precinct has three public lists of everyone eligible to vote at that precinct. The poll workers have one of the lists at their table, and every time someone comes in, their name is crossed off the list. Throughout the day, the poll workers post their current list, and get a new list. So if you come into a polling station at the end of the day, you'll be able to see the names of everyone who voted before the poll workers started on the last list. Nov 6 '20 at 1:48
  • I guess there are two different situations being discussed right now: secrecy of the ballot to the general public (the 100% turn-out and 100% candidate A result); and secrecy of the ballot using some kind of inside-information (lists of people who actually voted). The former case is quite clear, the latter case differs between states and countries. In my country, I am not aware that the lists of people who actually voted are publicly accessible. Information leakage on the part of election officials is a different game. A poll worker might be able to infer facts, which the public is not.
    – Dohn Joe
    Nov 6 '20 at 8:15
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You could print 10000 fake votes for each candidate, shuffle them and deliver them to all the polling stations.

At the end, you just subtract 10000 from the state result of each candidate.

If this is worth the effort is a different question.

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    Interesting, I thought about adding noise but couldn't think of a way, but it seems pretty simple in the end. Just looks a little similar to fraud if the government is casting 20.000 votes. What stops them from casting 30.000 (then again what stops them now)...
    – Mark
    Nov 5 '20 at 20:54
  • @Mark What stops them now — I don't know how it works in the US, but in The Netherlands, each voter has one voting card which they hand in upon voting. If the number of ballots is very different from the number of collected voting cards, something is very wrong (small differences can happen due to errors or people being given a ballot but not using it).
    – gerrit
    Nov 5 '20 at 21:56
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    @gerrit We don't do it that way and voter ID is an open political issue in the US right now that varies by state. Some states require an ID, some states don't require anything, the rest are in between.
    – gormadoc
    Nov 5 '20 at 23:36
  • Still, this only works if the fake` vote assigned to the voting station where 100% voted for A, was different than A.
    – Ángel
    Nov 6 '20 at 1:45
  • @Ángel Ultimately, no system can ensure democratic procedures. Plenty of totalitarian states had and have theoretically democratic procedures but are in practice dictatorships, in particular those where a nominally communist party claimed or claims to rule in the name of the people.
    – gerrit
    Nov 6 '20 at 7:27
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I doubt it's literally illegal, but I do agree this effectively makes votes not anonymous. Its hard to argue otherwise since we know each person's vote.

And this is a problem, because if voting isn't anonymous, it is more likely that people are pressured into changing their vote, especially in small villages where people tend to watch eachother closely.

This is a problem with privacy in general. You couldn't identify me by city + age, but if I were 117 years old, or lived in Buford Wyoming, then city + age is suddenly excessive information. It's generally a hard problem to solve for all edge cases.

Some things that may help against this:

  • Make sure there are more (expected) votes per voting location, by eliminating some rural voting locations.
  • Try to predict voting outcomes and if a very homogeneous result is expected, move/merge voting locations to have more votes or more diverse votes.
  • Instead of actually merging voting locations, merge the votes with other locations before counting starts.
  • After counting, if the result is nearly homogeneous, merge counts with another location before reporting. People who were present for counting will still know. And everyone will still know the result was nearly homogeneous because the merge happened.
  • Do not release actual counts, just a winner. Probably increases the chance of fraud by a lot.
  • Somehow hide who has voted where. But I don't see a practical way to do that.
  • Add noise, in a way that does not affect the outcome, like @JFabianMeier's answer.

Some practical problems with solving this:

  • Voting should be accessible, so there should be a lot of voting locations, also in sparsely populated areas.
  • Fraud should be hard, so it helps if people can observe the counting process, and regional results are known (so counters can check them).
  • Anything you do based on expected votes could go wrong (maybe 200 eligible voters live nearby but only 3 actually voted).
  • Anything you do based on actual votes (like merging results) is too late to hide results from those present when counting.
  • Just because the result is not unanimous does not mean it is anonymous. If only 2 people voted differently, then I only need to know two people's votes to know everyone's (e.g. me and my wife might be those two).
  • On a purely theoretical level, you cannot 100% guarantee anonimity while releasing vote counts, because there is a theoretical possibility that everyone everywhere votes the same way. Not a practical concern in the USA at all.

In the end, the organisers have to balance different principles. Probably making voting accessible to remote areas and preventing fraud won out against edge-case-anonimity.

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    hide who has voted where is the situation in The Netherlands. Each voter is sent a voting card, which they can use along with their ID to vote in any voting station within the area to which the election applies, so for municipal elections they can go to any place in the municipality, for national elections to any place in the nation (when voting by mail they mail it in). The voting cards are kept by the polling station, and the match between the number of voting cards and the number of votes cast offers some protection against vote stuffing. It isn't hard to do in practice.
    – gerrit
    Nov 5 '20 at 15:38
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    As a side-effect, when national elections happen in tourist season, some tourist areas may see turnouts of 120% or above ☺
    – gerrit
    Nov 5 '20 at 15:40
  • While this seems applicable in general, I cannot see how this solves the problem of a polling station at the end of civilization. If one guy is taking a 5h drive to the next village to vote there, it is even more clear who is voting differently
    – Manziel
    Nov 5 '20 at 17:03

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