Answers to Questions about Rivest/Smith Antifraud techniques

By Warren D. Smith    Return to main range voting page

On 7 January 2008 the New York Times published an op-ed by William Poundstone about one (called "Twin") of the three Rivest/Smith antifraud voting protocols. New York Times readers then immediately sent in a vast number of questions/comments. Due to the severe word-count limitations of op-eds, Poundstone was of course unable to describe Rivest/Smith in full, and unfortunately did not provide a pointer to Rivest & Smith's paper nor the web subpages which do provide a full description. Most (in fact I think all) of the questions and answers were already known to us ("us" meaning Rivest & Smith) and discussed in our paper (pdf). The paper also is available in HTML format (but the pictures and formatting are not as nice); there also is an addendum discussing interesting stuff that was not in the paper, and a short press release, and a more detailed and clearer, but longer essay too. You can also read an analysis about cost-effectiveness vis-a-vis Kenya's apparently-rigged 2007 election, and a page about election fraud through history which debunks several widespread myths and tells you various things I bet you didn't know.


Adam Cherson (NY, NY): Basic elements for a fair and accurate voting:

  1. verification of the identity of each voter,
  2. secrecy of the ballot,
  3. a redundant paper record for future verification,
  4. an accurate counting system, and
  5. a way of independently verifying each of the prior 4 elements.

Response: Seems to be more of a statement than question, but Rivest/Smith incorporates all these elements. Nobody knows how you voted. There are redundant paper records that everybody can use to check things and to prove fraud (if there was fraud), which is maximum verifiability (and maximum independence of same). It is impossible for a fraud to have a good chance of escaping detection by those checks. Anybody in the world can download and count the all votes (ditto the lists of all voters who voted and all voters eligible to vote) which is maximum transparency and accuracy.

Cherson also continued by advocating use of biometric identification-verification techniques. Rivest/Smith take no position on that issue and it is a separate issue which either can be or can not-be used in combination with Rivest/Smith protocols.

Marty (Fishkill NY): "...have 95 percent assurance of...fraud" OK! THEN what will be done?

Response: First of all, the fuller quote was "95% assurance of detecting fraud." If the fraud is detected, then we will have 100% proof there was a fraud. If it escapes detection, then we'll have no proof there was fraud – but since it was unlikely to have escaped detection we will be pretty confident there was no fraud, and we will in fact know (pretty much) the exact numerical amount of confidence we have.

Second, assuming the fraud is detected – then what? Excellent question. As the paper discusses somewhat, we will be able to make estimates at that point of how big the fraud was and in what direction. We also will be able, by using "chain of custody" records for different ballot-ID-number ranges, to try to narrow down when and where the fraud occurred so that we can try to punish somebody and/or fix the problem.

Jimbo W. (Bonita Springs, FL): One question I have concerns initialization: how does voter number 1 get a random copy of someone else's ballot?

Response: The paper proposes that the first 10 voters on each machine get no copies of preceding voters's ballots. There have also been some other ideas.

S.Hunts (Cupertino, CA): I don't see what guarantees the integrity of a ballot from the time it is cast until it such time as a copy may be handed out as a receipt to another voter. Why couldn't poll workers siphon off and modify/replace ballots right after the ballots are cast?

Response: Another excellent question. Rivest/Smith depends on having certain simple kinds of voting machines which we must trust are doing what they are supposed to be doing. Well, to be more precise, we do not have to "trust" them since what they do is so simple and done in such a transparent (literally) way that everybody looking can see they are doing it.

Specifically, for the "Twin" scheme discussed in the op-ed, the machine needs to have a translucent glass ballot box in which ballots are being circulated around randomly; and it needs to, on command, spit out an official copy of a random ballot from inside the box. The voter should be able to see the validity of the copy. (In another variant, it also is possible to have the voters themselves make the copy using just an ordinary pen, looking thru glass at a randomly selected [by the machine, perhaps with some input from the human too] ballot. That can be done by taking advantage of the fact that "digital signatures" are unforgeable.) The machine has to be such that corrupt poll workers, etc cannot mess with the ballots in the box during the voting – that would defeat security. If the corruptors mess with the ballots and boxes after the voting day has ended, or alter the counts, etc, that does not bother Rivest/Smith – their fraud will then be detectable, with proof. So Rivest/Smith kind of boils down the security requirements to this: certain machines need to do what they are supposed to do during voting. If funny stuff goes on afterwards, that is ok. (Of course, we do not recommend therefore being totally lax about securing ballots after voting has ended. Naturally we want due diligence exerted to protect them even then. We are just saying, if that protection fails, our protocols assure that the public will know.)

Anak (Mountain View, CA): Assume I wanted to create confusion about a legitimate election result. What if I tampered with my photocopy of random voting record, to make it seem that this (forged) vote was never counted. How will officials now argue that this vote was never meant to be counted?

Response: Another excellent question. One answer is, the receipts have to be designed to be hard to tamper with. (E.g. counterfeiting money is hard.) When you come forward with your receipt saying "I have legal proof this election was fraudulent, right here, on this official, government-certified receipt" that has to mean something.

A second answer, discussed in the paper, is that the receipts could have "digital signatures" on them. This would completely prevent tampering and receipt-forging by anybody ignorant of the government's "secret key" number. (The government itself then could still forge receipts but the only reason for it to do that would be in order to prove itself fraudulent.) This then could be done even with low quality scrap paper, eraseable ink, (no need for fancy money-like paper etc); but you'd need to introduce "digital signatures" into the picture, which involves other issues (that's discussed in the paper).

joe m (brooklyn, ny): Brilliant! This proposal is simple, transparent and uses the internet the greater civic good. Further, while it addresses concerns with new voting methods, it will also highlight that old methods probably also had limitations.
(RoughAcres, New York): This is an elegant and simple solution – I LOVE it.
(MIke, Columbus): Very interesting idea. I would very much like to see this tried out somewhere.
Others: Similar.

Response: Thank you.

D. C. Greene (Kennett, MO): Politicians have been stealing votes and rigging elections ever since mankind began voting. There will never be a perfect system. Whether dropping pebbles in clay jar representing one's favorite to lead your village, or touching a computer screen to indicate your choice, someone will be working and perfecting ways to steal, nullify or switch your vote. I recall, years ago, as a community college student sitting in a class on government, taught by an elderly retired judge. In retrospect, the judge almost tearfully described how he helped steal local elections. It was easy, he said. Local political leaders would ask respected elderly citizens to act as poll watchers. The elderly folks would feel honored and would show up before the polls opened and stay until closing, perhaps late that night. Late that night, when many of the poll workers were pretty well exhausted and perhaps dozing off, the ballot boxes would be swapped with boxes stuffed with the right number of votes to assure the desired outcome. I am sure this practice was very common back in the days of paper ballots, which each voter marked and then dropped into the slot of a ballot box. And I suspect that vote rigging is even more common today in spite of all the bells & whistles and electronic gadgets used to record the vote. Vote fraud is further compounded by politicians and political parties that seek ways to make it easy to deliver bodies to vote their way. If you remember the story about "Landslide" Lyndon Johnson who was first elected to the U.S. Senate when the dead people in a rural Texas cemetery got up out of their graves and went to town an cast enough votes to swing the election in his favor. The "zombies?" even lined up and voted in the order that their graves were laid out back at the cemetery. Nowadays, politicians and their political parties seek ways to make it so easy to cast a ballot that not even the citizenship, legitimacy or identity of the people showing up to vote can be challenged. Voting machines are only a tiny part of the problem.

Response: D.C. Greene's thinking has been true throughout the past. However, with Rivest/Smith antifraud voting protocols, we can prove theorems that undetected fraud is impossible – subject to certain assumptions, which we can list. Then the only way to have fraud is to violate our assumptions – or risk detection with proof of fraud. I believe/hope our techniques can usher in a whole new level of security/reliability/transparency/confidence in elections, which humanity simply has never previously attained.

Now for example, if anybody switched or stuffed the ballot boxes at the end of the day, with Rivest/Smith, that would be detected by the voters, with proof of fraud, using the receipts. Won't work. If voters from cemeteries were recruited, then, to have a 5% fraud, you'd need 5% fake voters, and anybody checking the (published on a web site) list of voters-who-voted would detect 1 fake voter per 20 random voters checked. It thus would be within the reach of even a single person (e.g. newspaper reporter) to do the checking required to prove this nationwide fraud!

One more comment: it would be possible to make old-style paper-ballot voting secure if we have a never-sleeping, invincible incorruptible armed guard guarding all the ballots 24 hours day 7 days a week, etc. I don't consider that to be realistic, but we can at least conceive of it. Now here's my point. Even if we had all that perfect security, then there would be no way for the general public to know that. How could the general public be confident every guard was present 24 hours a day, etc, even if they actually were? So there would be no reason for public confidence in the election system's security even if it in fact were secure. That's a big advantage for Rivest/Smith – with our protocols we can provide such public confidence (not to mention, we do not need all those perfect-supermen armed guards).

Sam Lauber (unknown location in cyberspace): There's a serious flaw in the "Twin" proposal. It's vulnerable to this fraud (I'll call it the two-copy attack):

  1. A candidate ("Candidate A") bribes the poll-workers (with money delivered through a proxy).
  2. Poll-workers make two copies of every ballot.
  3. Before the polls open, a poll-worker goes inside a voting booth with the copies of the ballots, casts a few votes for A's opponent ("Candidate B"), and casts every other ballot for A.
  4. The poll-workers modify the bin so that the fraudulent ballots are the ones the voters get copies of, and the ballots actually cast by the voters get dropped into a shredder or otherwise destroyed...

Response: Rivest/Smith depends on the assumption that certain machines in the polling place actually do do what they are supposed to, and further that they are built in such a way that the voter (and, e.g, observers) can see with her own eyes they are doing it.

The tasks these machines perform are simple ones capable of being done by pre-computer technology.

So for example, in TWIN, the machine accepts your vote, drops it in the ballot box, and a random ballot previously in the box is copied and you get the take-home copy.

You can see because the ballot box is made of translucent glass, that your vote is really going in there and not being shredded. You can see that when, say, the ballot box is tumbled and shaken, a pretty-random ballot inside is being sampled. When it makes a copy, you can see with your own eyes that the copy is the same as the original (you see both thru glass).

I agree if the machines in the polling place are allowed during voting to do mysterious stuff not what the Rivest/Smith protocol says they are supposed to do, then RS is busted. However it is an underlying assumption of RS that that does not happen and everybody can see it does not happen. (Or if it does, everybody can see it does and the fraud is detected immediately.)

Now once the voting day has ended, of course, then, nobody can see the machines and they and the poll workers might commence nasty tricks. However, RS does not care in the sense that those manipulations then would be detected by the public, thanks to the RS protocols. (Also, if, say, halfway through the voting day they illegally closed the polls for 30 minutes and did some nasties, then re-opened the polls, RS would still seem immune to that.)

(Please, Anywhere): Ballot images are secret for good reason: It is easy to buy or coerce votes if ballots can be recognized by combinations of downballot contests, patterns of zig-zag oval filling, or "stray" marks. See for a real solution.

Response: Rivest/Smith do not propose to publicize the ballot images – for precisely this reason. All the vote-information on each ballot will be publicized on a government web site for easy lookup by checkers. But not the "image." (If the government tries to post fake information, that won't work; that would be detected with proof of fraud by the receipts.) Also, "zig-zag patterns downballot" won't work because Rivest & Smith in their paper insisted on ballot "debundling" for precisely that sort of reason.

"Scantegrity" is another antifraud voting protocol, mainly due to David Chaum, which also is interesting. Last time I checked I did not feel it had reached as completely-investigated a state as I would like, though. I have attempted to examine/explain scantegrity and compare with with Rivest/Smith, here. (There is a chart at the end listing relative advantages and disadvantages versus Rivest/Smith protocols.)

J N Harris (Greater Cleveland): Having been involved in raising flags about the dangers and weaknesses of electronic voting, I don't find this an "elegant and simple solution" at all. Instead, this proposal has all the makings of a logistic mess.

Consider the hackability of websites; the false assumption that millions of people – many without web access –will somehow all feel compelled through public zeal to go online (enough of this high-tech utopiana); that another bureaucratic layer will be added to an already strained process; that privacy issues will inevitably arise. In fact, there are so many holes in this piece of virtual Swiss cheese that I am amazed anyone can take this proposal seriously.

Here is a fairly simple and elegant solution that exists already: optical scanners with paper ballots that can actually be stored, referred to, and recounted. If we can get that system in place and working properly, we'll go a long way to eliminate public mistrust and help guarantee a more accurate vote count than presently exists.

Response: First of all, it does not matter if the government website, your computer, the entire internet, or whatever, is hacked. If so, that will be detected, with proof of fraud, by Rivest/Smith protocols.

Second, Harris is wrong that optical scanners etc work. Well... I do not want to disparage his idea – it would be nice. Indeed, I recommend precinct-based optical scanners, which preferably would be noncomputerized ones, as a comparatively simple, cheap, and durable presently-available technology with inherent paper trail. But I just want to say that that old-style idea is not fraudproof. For example, somebody alters or burns a box of ballots in Harris's storage warehouse. Result: game over, fraud is successful. (Also the manufacturer of the opscan machines could have put in secret "back doors" or radio controls to enable easy fraud anytime... you have to realize we are up against the likes of the NSA, Chinese equivalent, big corporations, etc all of whom have a lot of resources and motivation to fraud elections.) With Rivest/Smith, if a box of ballots is destroyed or altered, it does not matter in the sense that this fraud will be detected, with proof.

Third, Harris is correct that Rivest/Smith will be somewhat more complicated for voters and officials to deal with. ("Logistic mess.") We feel, however, that the extra complexity is manageable. For example, our schemes are simple enough to be explained to children, and thanks to the so-called "easy upgrade" property, we can allow "Luddite" voters, if they desire, to use old-style insecure voting, and their ballots get magically "contagiously protected" upon being mixed into the same box as the new-style secure ballots, a remarkable fact discussed in our paper.

The question is, are the advantages in having an unprecedented new level of election security/transparency/confidence worth the logistical hassle/cost? For one indication that they are worth it, at least in some places, please see this analysis of what just happened in Kenya.

C Goldman (Austin TX): Can this really work? I am not convinced, because the votes may still be counted by an optical scanner which we know can be easily hacked. IF you are only able to confirm someone else's vote, you still wouldn't know if yours was cast correctly, unless they also offer a paper receipt of your own vote.

Response: If an optical scanner is hacked, that will not matter in the sense that that fraud will be detected, with proof, via the receipts. The point is the hackers, the hacked computers, etc, all cannot know who has what receipts. It does not matter how smart, hacked, and evil they are. They still cannot know. So if they change enough votes to make the fraud large enough to be interesting, then they will be unable to avoid changing a lot of votes that have receipts in unknown hands. The fraud will then be spotted. "Hacking" is simply irrelevant to this truth.

But the fact that in "Twin" voters are checking somebody else's vote, and therefore are less motivated, does bother us. Rivest and Smith therefore invented two other protocols, called "VAV" and "ThreeBallot," which allow voters to check their own ballots, but still are both fraudproof and proof against vote-coercion and vote-selling.

Note also that you could turn in your receipt to some checker organization that you trust (such as, the League of Women Voters, international election protection groups like OSCE, or your favorite Political Party) and they could do the checking for you, as well as pursuing any legal battles that result if and when the check proves a fraud occurred. This option also goes a long way toward answering Harris's objection above that not everybody is internet-savvy.

David K. McClurkin (Beachwood, Ohio): It is vital that attention be given to how to involve voters who are not Internet-savvy or have no free access to the web site proposed. Would this proposal tend to exclude that demographic which tends to be the most persistent in showing up to vote?

severinagrammatica (Washington, DC): This plan discriminates against poor people and others without computers or those like my aged mother who uses the computer only for email. Lots of people eliminated. Are the MIT people, gulp, purposely trying to eliminate a substantial element of the already-oppressed masses who would vote Democratic?

Response: First: See last paragraph of above answer!

Second: There would undoubtably be some demographic biases in that some classes of voters would be less likely to check their receipts later, versus others. However, so long as nobody is 100% predictable, Rivest/Smith protocols would successfully cause any fraudsters to risk detection with proof of fraud. And even if a fraudster knew that Joe Schnozz was never going to check his receipt, indeed even if Joe helpfully handed the fraudster his receipt saying "Here! You have it now so you know I am not going to check this later!" then the fraudster still could not risk frauding the corresponding ballot because he could not know some other receipt was not floating around for it.

Alan T. Burrell (Avondale Estates, GA): How cumbersome this proposal is. Besides, a printout of a vote still does not assure me that it reflects a real vote, and not some fiction of the machine...

Response: Again (cf. answer above to Hunts), Rivest/Smith only works under the assumptions the machines in each polling place are doing what they are supposed to do – but that thing is so simple that voters ought to be able to see that (and could, e.g. videotape the machines not doing it then show the video on the Nightly News). In particular, as I said to Hunt, voter could verify she was getting a correct copy right then and there, and there is even a way to have the voter create her own copy with her own hands with her own pen, no photocopy machine needed.

Incidentally, in all the Rivest/Smith protocols (VAV, Twin, and ThreeBallot) the machines we need are sufficiently simple that they do not require a computer – what they need to do is doable purely mechanically.

Ray Padgett (Ponce de Leon, FL): Offers own "Vote By Mail Plan" [with detailed description that appears to have been truncated by the NY Times]

Paul Wertz (Eugene, Ore.): Observing this debate is like watching a city council meeting in Crazytown. Oregon dropped the voting booth system a few years ago and went to a vote-by-mail system that is as close to perfect and noncontroversial as it can get. We have 15 days from the day our ballots arrive at our homes to return them by mail – or drop them in postal-like white drop boxes. The system cut election costs. The results are verifiable. We often have huge voter turnouts. George Bush's friends at Diebold make not a penny. And there are no complaints. But, go ahead and keep dreaming up ways of tweaking the corrupt electronic systems if it makes you happy. Why solve the problem?

Response: The trouble with most vote-by-mail schemes is you can sell your vote. For example, you watch me voting by mail and sending it in. You then say "I know you just voted for X. Therefore I will pay you a bribe-reward, or mete out a punishment, depending on who X is." Padgett apparently wants to try to preserve anonymity by having a secret vote-ID number only that voter knows. So your vote is then published saying not "this is the vote of Joe D. Schnoz" but rather "this is the vote of voter #75875397."

That does not work, though:

  1. If Joe has no proof he is voter #75875397 then he cannot prove fraud in court later.
  2. If Joe does have proof he is voter #75875397, then he can sell his vote by saying "Hey vote-buyer! Here is proof I'm voter #75875397 and now checking the public list of votes, we see I voted for the candidate you wanted! So pay me now." (Similarly, Joe could be coerced by a vote-coercer.)
I won't say for sure that Padgett's scheme is unworkable because as I said, his description got truncated by the New York Times comment gizmo. But it looks likely to have one of the flaws I just described. The joy of the Rivest-Smith protocols is that they are immune to both fraud and vote-selling/buying/coercing.

Also, to Mr. Wertz: I have a lot of doubts Oregon made a good move by adopting vote-by-mail. It is trivial to "lose" ballots from a "wrong" zipcode containing too many of the wrong kind of voter. Or impose discriminatory enforcement of trivial rules just for zipcode A but not zipcode B to introduce biases. And vote-selling/buying/coercion now is made trivial by Oregon. Indeed, it seems to me, Oregon's system has all the same security holes ordinary Boss-Tweed-era paper-ballot voting had, plus lots more. One might even go so far as to say that Oregon is just asking for it. Dr. Charles Corry on mail-in-ballot problems. And check out Ruth Charles just below:

Ruth Charles (Winona, MN): I voted by mail and it was a disaster! My candidate pulled out of the race and my vote was no longer valid and I could not change it! MN has an excellent system for voting. We use optical scan ballots, that leave a paper trail. We have a mandatory audit of the voting machines one week after the election, which proved in 2006 to work! Check out for the full report. As an election judge who helped people vote that day, and as an observer of the audit, I was pleased that everyone who voted had their vote counted that day!

Response: Bingo.

Joe K (Berkeley, CA): [multipart question which I am splitting into numbered sub-questions]

  1. What happens if reviewers disagree about the validity of a vote?
  2. Doesn't the proposal assume that people won't behave strategically?
  3. Suppose in a closely contested election, Sam, a partisan of Party A, receives a photocopied ballot with a vote for the presidential candidate of Party B. If Sam promptly goes online and claims that the recorded ballot is incorrect and is really for the candidate of Party A, then either (a) there are no others commenting on the ballot, and Sam's lie would invalidate the vote, or (b) there will be others disputing what Sam says. Then what do you do?
  4. It seems that no matter what you do, there would be some probability of the vote being invalidated. Hence there is an incentive for strategic fraud.
  5. Who will verify the verifiers?

Response: Jeez Louise! – You are making me work for a living with this one...

  1. Q. What happens if reviewers disagree about the validity of a vote?
    A. Well first of all, the Rivest-Smith machine at the polling place is supposed to check your vote's validity and refuse to let you vote invalidly. If we don't have that, there are various ways you can imagine to try to make "Twin" degrade gracefully, which Rivest and Smith didn't discuss, such as, posting the vote on the public bulletin board along with a comment saying "invalid vote" or "reviewers disagree on this vote"... and these physical ballots would be saved for further argument/debate...
  2. Q. Doesn't the proposal assume that people won't behave strategically?
    A. Meaning what?
  3. Q. Suppose in a closely contested election, Sam, a partisan of Party A, receives a photocopied ballot with a vote for the presidential candidate of Party B. If Sam promptly goes online and claims that the recorded ballot is incorrect and is really for the candidate of Party A, then either (a) there are no others commenting on the ballot, and Sam's lie would invalidate the vote, or (b) there will be others disputing what Sam says. Then what do you do?
    A. Well, Sam can't just "go online" and invalidate a vote like nothing. He has to make a formal complaint (or have some helper group like the League of Women Voters, or Party A, make it for him) and that formal complaint is not going to be based on Sam's unsupported word, it is going to be based on him producing the receipt that proves it. And if Sam hasn't got such a receipt, since he made up a fantasy, that isn't going to fly. (To quote voting-expert Al Capone: "an unkind word and a receipt, will take you further than an unkind word alone.")
  4. Q. It seems that no matter what you do, there would be some probability of the vote being invalidated. Hence there is an incentive for strategic fraud.
    A. I'm not following you. And if receipts are unforgeable (and if you understand "digital signatures," you know how to accomplish that – counterfeiting money is merely difficult; forging something signed with a digital signature is literally beyond the capability of humanity) then Sam cannot forge a fake receipt to pull off his little prank.
  5. Q. Who will verify the verifiers?
    A. Not sure what exactly you meant by that. Rivest/Smith assumes there are machines at the polls which do certain specified tasks. These tasks are simple enough that computerized machines are not needed. If said machines do not do them, then that is immediately visible to the voters in the polls, who can take a videotape of the misbehavior to their local TV station if their complaints are ignored. Among these tasks are verifying the validity of ballots. Video a machine accepting an invalid ballot? Fine, you have proof of fraud.

Josh C (Livingston, NJ): The first thing that worries me about this system is not a technological problem, but a human one. If everyone gets a random vote that is not theirs, their willingness to share the information on that vote will increase dramatically. Of course, this is not a problem after the election, however, people would be much more willing to share the vote on their receipt during the election to some sort of online exit poll than if it were their own vote. Unlike mainstream news sources, these exit polls could be continuously updated throughout the day, causing problems not unlike the early calls of the vote in Florida in the 2000 Presidential election. Since the vote on anyone's receipt is random, the validity of that poll [could be excellent, perhaps good deal better than today's exit polls].

Response: This point has been raised before. My personal (Smith's) answer (which may disagree with Rivest's view and others's views) is, I'm dubious this is a "problem"; many might well consider it a "feature." (But a lot of people, especially Europeans, don't like it when I say that.)

To go into this a little, why do we care if early returns are announced (and they already are – voters in Hawaii know what happened in Maine already when they vote...)? Well, I think the reason is that voters with more knowledge have more power. For example, consider an A versus B versus C race. If I have the knowledge that C is well behind A and B, then I can choose to ignore C and just vote for A or B. If you do not have that knowledge, you might waste your vote on C, thus having less power than me. If I know A is well ahead of every rival, I can skip voting and have a fun time at a party, while unknowing you waste your time voting and have less happiness than I do. (Makes you jealous, right? You wish I too were unhappy?)

Now my point is, this is not a flaw in our security protocol. It is a flaw (if it is a flaw) in the voting system itself. (No matter what security protocol you had, somebody could still exit poll to get more knowledge=power. Even if you outlawed publishing exit poll results – which would probably be an unconstitutional repression of free speech – then the candidates could still privately poll and just tell their campaign organizations the results, keeping the power to themselves. That might make it even worse, actually.)

If the USA's current "plurality" voting system were replaced by a better one inherently more-immune to the "spoiler" pathology and more immune to "strategic" voting, then this problem would diminish. I strongly recommend that. There is a much superior voting system called "range voting" which also has a good simplified form called "approval voting." We recommend them. Rivest/Smith antifraud techniques also work happily with these improved voting systems, see answer to Diagoras below.

The question of which voting system to use (e.g. Approval versus Plurality) is an (almost) entirely independent question from the question of how to make that voting correct, secure, and fraudproof – and may be even more important.

Brad Friedman (CA): Please remind Poundstone that the legitimate fears are not of "voter fraud" as he misleadingly claims, but of election fraud.

Response: I (basically) agree: That would for sure have been preferable wording and probably was what Poundstone intended (i.e. this was accidental). But you'd have to ask him; I'm not his keeper...

Diagoras (New York): Potentially, rangevoting, as the developers call it, could solve the problem of confidence in the voting mechanism. Left unaddressed is the problem that single-choice ballots are a deeply flawed method of measuring voter sentiment. A nonpartisan vote-by-preference system, with so-called instant primaries, is vastly superior...

Response: Diagoras is confused about terminology but correct on the issues. The three antifraud voting protocols Rivest & Smith propose are called "VAV," "ThreeBallot," and (the one described in the op-ed) is "Twin." Not "rangevoting." They indeed would increase confidence in voting and decrease fraud.

But Diagoras is entirely correct that single-choice ballots (called "plurality voting", i.e, the voting method currently most-used in the USA) are a "deeply flawed method of measuring voter sentiment." A much better way of measuring voter sentiment, is range voting in which every voter scores every candidate on an 0-to-9 goodness scale (say), and the highest average score wins. I believe range voting also is superior to "preference-ranking" voting systems such as instant runoff and Borda in essentially all ways. There also is a system called approval voting, which is simpler than both plurality and range voting, as well as being greatly superior to plurality voting. With approval, the voter makes "yes/no" (approve/disapprove) decision on every candidate, as her vote. Most-approved wins.

Rivest/Smith security-enhancing protocols are usable with other voting systems, not just with plurality:

Voting system Allowed Rivest/Smith antifraud protocols
Plurality (name one candidate) voting VAV*, Twin
Approval (yes/no on each candidate) voting ThreeBallot, Twin
Range (score each candidate 0-9) voting ThreeBallot, Twin
Range with "no opinion" vote-scores also allowed VAV*, Twin
Borda, Instant Runoff, Condorcet (rank-order ballots)** VAV*, Twin

*: write-in votes not allowed.

**: "short ballot assumption" must be valid to prevent vote-selling – meaning that if there are too many candidates in the race, then Rivest/Smith techniques cannot prevent vote-selling.

By using both antifraud techniques and inherently superior forms of voting (like range or approval voting) at the same time, we could get the best of all worlds.

Please endorse range voting.

Erika A (New York, NY): How is this system any less hackable than paper ballots (which can be switched) and electronic machines (which can lie)? The results that appear on the... printout... could be changed in the moments between the votes are placed and actually printed out (the voting machines could be programmed to do this).

Response: The "voting machines" we have in mind are not computerized hence cannot be programmed. (Their and the polling-place protocols's sole functions are [1] make sure the ballot you give them is valid; [2] make sure you are an eligible voter and once you vote, your name is crossed off the list of eligible voters so you cannot vote again; [3] puts your vote into the ballot box while spitting out a copy of a random ballot already in that box to you as your take-home "receipt.") Also, the fact it is copying a random ballot from the box will be visually obvious to the voter receiving that ballot-copy (she can use her own eyes to verify the copy is correct and to see thru the semi-transparent glass ballot box that the selection did seem random).

The paper ballots cannot be "switched" without this fraud being detected, with proof, very soon, via all the take-home vote-receipts.

Erika A (New York, NY) continues: It is also unclear to me what you would do with suspicion of fraud (which also would show up on a hackable website, by the way) if all of the "evidence" has been dispersed into the general population and basically lost. How would we ever do a re-count?

Response: The evidence is dispersed but a substantial fraction can be re-gathered. To be concrete, suppose the Democrats feel they've been victimized by a fraud in race X. They can advertise "voters: please check your receipts for race X and/or send us those receipts and we'll check them for you. Especially send us ones that prove fraud." The Democratic party then owns, say, 1000 government-certified receipts proving fraud happened. They can use them in court. Also, any single individual or group who has 1 or more receipts proving fraud, can take it to the media and/or the courts. With proof of fraud – not just mere allegation but proof. (Also the internet could be used by the scrutineers as a communication device... for example The League of Women voters could make their own "mirror" of the government website, etc...)

Also, it does not matter if the website is "hacked." If it is, then the website will give out false information. Fine. If so, that information's falsity will be detected by the receipts. If the website gives out info that varies from recipient to recipient and time to time, that too can be spotted by comparisons (and the website will "digitially sign" its output, causing those comparisons to be unfakeable proof useable in a court of law under current US law about digital signatures; and the website will offer "full dataset download" option to whomever wants it; and then anybody in the world can count the votes, note – we in no way depend on government counters to add correctly).

Enthusiast: Great! Let's get Rivest/Smith up and running someplace and start using it!

Response: Unfortunately, it isn't so easy... To see why we aren't ready at present for prime time, check this.

In contrast, range voting and approval voting and shortest-splitline no-gerrymandering districting method are ready for prime time. You can endorse them. (Please!)

Brad Friedman (CA) again: [Twin] seems to offer a false sense of confidence that votes are being accurately recorded.

Response: The voter writes her vote on paper and verifies it is correct with own eyes before it gets put in the ballot box. When she receives the receipt (ballot copy) she also can verify with her own eyes it is an accurate copy. If votes are inaccurately transcribed from the paper ballots onto the government bulletin board (whether intentionally or inadvertently) then voters can, by using their receipt and comparing it with that bulletin board, prove this. They hold in their hands, a government certified proof, useable in a law court, that fraud or error occurred. For any large fraud, this spotting will be almost immediate, by massive numbers of people with massive numbers of proofs. Not only that, but we will know specifically which votes were inaccurately recorded and how they were inaccurately recorded (for a large random constant-fraction of them) with proof, valid in a law court, on every single one.

Let me continue: Mr. Friedman is a well known voting reform advocate who runs I challenge him to name any occasion, in all of US history, where that kind of level of immediacy, verifiability, and level of proof of fraud, and public-confidence in the claim of fraud or no-fraud, has ever been equalled, or even approached, by any "conventional" voting protocol such as the ones he generally talks about.

Fred Silverman (Bedford Hills, NY; F.S. is producer of the PBS special "who counts? Election Reform in America"; I am numbering his paragraphs for later reference): (1) [This is] yet one more way to rationalize the use of electronic voting machines. The issue is not to make a failed technology more palatable but to find a process that builds confidence in our electoral system.

(2) As long as private companies use proprietary software that the public is forbidden to examine, there will always be questions. Our election system must be transparent. Either we mandate an open architecture for our electronic voting or we go back to paper.

(3) A combination of vote by mail and paper ballots may be the most foolproof system. I certainly hope that the New York Board of Elections will allow our counties to choose this

Response: (1) Rivest/Smith does not require the use of "electronic voting machines." As we said right up front in our paper – indeed this was one of its big points – the Rivest/Smith protocols can be done entirely low-tech without computers and without electronic machines. (Admittedly the internet is used, but only as a communication medium, which in principle could be replaced by any other communication medium, electronic or not.) F.S. is thus entirely mistaken both about what we said and about our goals. He appears to be arguing with somebody else.

(2) I, at least (I can't speak for Rivest) think open-source software is a good idea, but that is not sufficient. Let me elaborate. LINUX is open-source software. Microsoft Windows is proprietary software. Both contain enormous numbers of bugs, are well beyond the capacity of any human or set of humans (even aided by the best verification software tools that exist) to verify. Both quite likely contain security "back doors" intentionally implanted by the likes of the NSA, Chinese Secret Service, etc. If the hardware or microcode of a machine contained secretly-implanted security holes, that could be even nastier. The idea of "going back to paper," including manual counting, is (a) compatible with Rivest/Smith [if desired], (b) is still used in many countries, e.g. Denmark, and (c) actually in many situations is actually cheaper than counting votes with machine aid. This last may seem surprising, but try the calculation yourself! (And see more discussion.)

(3) Re vote-by-mail, see our answer to Wertz above.

Cynthia J. Eiseman (Philadelphia): As the judge of elections at my polling place... I see two problems with Rivest/Smith's proposed method for averting election fraud: (1) Some voters will not like having ballots containing serial numbers; they will worry that their votes are not truly secret. (2) Where will election workers get randomly selected ballots to copy and give to the first few voters who come to the polling place on Election Day?

Response: (1) The voter comes to the polling place. She selects from a big pile of pre-numbered blank ballots, a random ballot. She fills it out with her vote and puts it in the machine/ballot box. Now. In what way, does the fact that this ballot said on it, "ballot #85776644," in any way render her vote non-secret?

(2) See above response to Jimbo W.

Jeff Schwarz (West Paterson, NJ): William Poundstone's suggestion is a good start. But it needs (1) a way to prevent someone from tampering with the cast vote before the photocopy is made. (2) It also needs a way to prevent people from adding votes, which would have no photocopy and so would never get checked on the Web site.

Response: We (in the paper) already do have these things.
(1) See above response to S.Hunts.
(2) The list of names+addesses-of-people-who-voted, extracted from polling-place sign-in sheets, is published on the web site too, along with the list of votes (but it does not say, and nobody ever knew, how each person voted). Extra votes cannot be added without making more votes than voters, which would be an instantly-detectable-by-all fraud. (And see also our answer to D.C.Greene.)

John David (Fairfield, Conn; I number his claims for reference): As a student of electronic voting, I read William Poundstone's proposal with some amusement and a lot of alarm. It is completely unworkable, given the workings of our electoral system and its laws.

(1) The proposal itself has some merit. But it cannot* be adapted to actually work in the context of the election laws of some states, which do not have strictly interpreted recount laws, which prohibit the examination of ballots except under official recount circumstances.

(2) Using serialized ballots to randomly verify the results of an election is not a new idea, and it is entirely obvious. (3) But rather than having the public get involved, this would have to be carried out correctly at the state Department Of Elections level. (4) What this really brings up is the entire lack of a government-sponsored official advisory committee to give scientific guidance and recommendations to the states on how to make our elections safe and secure in this new electronic age.

*Actually the published letter in the NY Times of 9 January said "can," but I think "cannot" was intended by David.

Response: (1) It probably is true that State and/or Federal election laws would need to change to implement Rivest/Smith antifraud voting protocols. For example, there could be a law saying "implement Rivest/Smith antifraud voting protocols"!

(2) I'm not sure that Rivest/Smith was so "obvious." It actually kept striking me, when I was working on this paper, how incredibly simple the final voting methods were, but how incredibly hard it nevertheless was, to think of them. (Perhaps David is just a lot smarter than us, or perhaps he is not fully understanding our proposals, I cannot say which. Anyway, I'm glad he thinks it is obvious.)

(3) I don't see why it is more "correct" for the state dept of elections to carry this out than the public. Indeed, I think the opposite. Plus, the whole point is that maybe the public does not trust the dept. of elections. With Rivest/Smith protocols, they do not need to trust them.

(4) The good news is that actually there is such a committee, and Rivest is a member of it. It is called the EAC (Election Assistance Commission). It was created by HAVA (Help America Vote Act). The bad news, in my (Smith's) opinion, is this is a toothless body which has been constructed to be dominated by voting machine industry flacks who can be counted upon to deter any prospect of real reform. I am not necessarily speaking for Rivest in that opinion, though.

Robert T. Carlson (Port Richmond, Calif.): This is a welcome and novel idea.. inspired by the open source software movement... [but] the random ballot receipt system... could be rigged by voting machine manufacturers that programmed their machines to spew bogus random receipts. Thus a more secure system would be doublechecked by another layer of exit polls not subject to manufacturer manipulation. [There are great exit polls in Germany.]

Response: First, Rivest/Smith specifically wanted the machines to be noncomputerized hence not "programmable." Second, they want the machines to be such that the voter can see, with her very own eyes, that the copy is a genuine copy of a random ballot that previously was present in the ballot box. These means she can see both the original and copy thru glass, and she can see the random selection mechanism thru glass, and it really does seem random.

We certainly have no objection to more layers of defense, including exit polls. (But: warning: I speculate Germany contains a more-homogeneous population than most countries which causes its exit polls to perform anomalously well.)

Incidentally, while we are in no way opposed to "open source," we wish to emphasize that it in no way prevents cheating, a point made very strongly by Ken Thompson in his Turing Award Lecture "Reflections on Trusting Trust," [Communications of the ACM 27, 8 (August 1984) 761-763]

Rob Harmon (Vashon, Wash.): William Poundstone offers some intriguing ideas for reducing the possibility of voter fraud. It should be noted however, that unless the software that randomizes the ballots is open source, there will be no way to ensure that the ballots are indeed random. Therefore, regardless of how well the system works, the public will continue to distrust it.

Response: There is no "software for randomizing the ballots." Therefore there is no worry that it is not open source, or closed source, or whatever. With Rivest/Smith's proposal, the randomization is done by hardware at the polling place. (E.g, most simply, this "hardware" might just be a big translucent glass box full of ballots which you shake, then pick one to make a copy of as your take-home receipt.) The public, since it can see with its very own eyes how the randomization is working, and the machine/box is constructed in such a way as to make it obvious what is happening, can trust it.

Jean Camp (Bloomington, IN): ...This system embeds an inappropriate degree of blind individual trust in technical expertise. Your average voter could no more do the math than your average cryptographer could do brain surgery...

Response: Actually you have the right idea in mind, but have it exactly wrong about Rivest/Smith. The whole point of Rivest/Smith is that you do not have to trust the experts!

For example, right now, you have to believe the voting machines are counting correctly, the election officials are not cheating, etc. etc. That's blind trust. With Rivest/Smith, if those things/people are cheating, you will catch them. Get it? No trust involved. Verification involved. By you. Personally. In a way simple enough to explain to children.

It doesn't matter if the government's bulletin board, the internet, the election workers, etc etc all are corrupt. It doesn't matter if the fraudsters have got huge supercomputers and armies of hackers helping them. If the Rivest/Smith assumptions are met, i.e. the machines in the polling places do what they are supposed to and the protocols are followed in each polling place, then all the corruption, hacking, and supercomputers in the world aren't going to allow the evil government to tell who has a receipt for what. So they can't fake it without the fraud being detected, with proof, by the voters themselves via the receipts.

And you don't need to trust any expert. You can see it all by yourself.

(65 comments so far as of 8 January... I've tried to answer all the best questions...) – Warren D. Smith.

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