Good Math, Bad Math

After last week’s New Hampshire primaries, I’ve gotten a lot of email requesting my take on the uproar surrounding recounts and voting machines.

For those who haven’t heard, there’s been some chatter
about cheating in the election.
In polls leading up to the election, Barack Obama was
leading by a large margin. But he ended up losing the election to Hillary Clinton by a couple
of percentage points. The argument about fraud centers on the fact that there are two voting
methods used in NH: electronic optical scan machines, and hand-counted paper ballots. In the
districts that used paper ballots, the vote results tended to look more like the poll results -
significant lead for Obama. In districts that used optical scan, the results were strongly in
favor of Clinton. This discrepancy, combined with the pre-election polls, have led some people
to suspect that the Clinton campaign somehow cheated.

So, my take? It doesn’t look like there’s anything wrong with the results, but we should do an audited recount anyway.

Looking at the results, there is a discrepancy, but it’s not a particularly dramatic one.
Different districts in states tend to vary. Rural districts vote differently that urban ones;
richer districts vote differently from poorer districts. And the way that districts count their
votes are not independent from those factors. Large urban districts are much more
likely to have optical scan machines; small rural districts are much more likely to hand-count.
When you look at the votes, and at polls, you find things like Clinton tended to do better in
urban districts – the places that were most likely to have optical scan. The differences
between voting patterns in districts with different kinds of voting machines is consistent with
the expected (and measured) difference between the populations of those districts. The vote totals make good sense, and from a mathematical perspective, there is absolutely no reasonable ground for suspecting fraud of any kind.

So why recount?

Because every election should have an audit recount. What I mean by an audit recount is randomly select 5% of the polling places throughout the state, and recount them by hand. If there are any significant discrepancies between the reported count and the result of the hand recount, then recount all of the votes.

Every election should have a recount, because elections are easy to steal. Whether you use a touch-screen electronic machine, an optical scan machine, a mechanical lever-pull machine, or a simple wooden box where people put ballots, it’s easy to cheat and steal an election. That’s why recounts are so important: you need to check, to make sure the results make sense. It’s ludicrous to create a legal requirement that every vote has a voter-verified
paper trail if you never check that paper trail. NH requires the paper trail, but then basically throws it away without ever looking at it. That’s just ridiculous. The paper trail itself does nothing unless someone looks at it. And the integrity of an election is so important that we absolutely should check it, even if there’s no reason to suspect fraud.

In fact, it’s arguably more important to check it when there’s no reason to
suspect fraud. Lousy cheaters are relatively easy to catch, if anyone cares enough to look
out for them. Ballot stuffing is, in generally, pretty easy to catch. What’s hard is when you’ve got a clever cheater.

To give a totally trivial example, back when I was in high school, I auditioned for the all-state band. A rival, who had a very dishonest private teacher, really didn’t want to see me get in – he wanted to be able to show that he was better than me. So his teacher went in to the scoring room, took the scores, and changed them. How do we know that? Because the system judged each person in three categories, and each judge in each category gave a score out of 100 for each audition. So an audition score ranged from 9 to 900. The dishonest teacher took the
scores, and changed all 9 of them to “3/100″, giving me a total audition score of 27/900. The next lowest audition score out of 500 people auditioning was in the 400s. It was obvious that there was cheating going on, because the guy changing the scores was
cheating. If he’d just knocked my scores down by 10%, I would have been kept out just as effectively – but we would never have known that he anyone cheated.

In general, elections are a lot like that. Most of the time, cheaters do stupid stuff. If you shift 50,000 votes in a 100,000 person voting district, no one is going to believe the results. If you find 10,000 votes counted in a district with 5,000 people, you know something is wrong. If the bottom-of-the-ballot bozos get no votes at all, you know something is wrong. But under those conditions, someone will always call for a recount, because something is obivously wrong. On the other hand, if someone consistently switches 2% of the votes in every voting district, it can have a huge impact on the outcome, and it won’t be obvious
that there’s anything wrong. But an audit check will catch it.

Some folks that I respect greatly have made the argument that the closed-source
nature of the voting machines software is relevant to the discussion of recounts. I disagree, strongly. Even if the voting machines used open-source software, and the hardware was carefully verified with published schematics, I’d still say we need to recount. Technology, no matter how good, is no guarantee of anything. No matter how open and secure the code is, no matter how good the hardware, a clever human can intervene in the process and cheat. We can’t let our confidence in an openly developed voting system blind us to the fact that there are always dishonest people who try to cheat. Never forget the recount riots in Florida,
to try to prevent anyone from figuring out if the count was wrong: people who want to cheat will find a way, and will use any argument to try to prevent people from detecting their
cheating. The only way to even have a chance of defeating cheating in elections is to
check the count, every time.

Comments

  1. #1 Susan B.
    January 14, 2008

    Perhaps I’m missing something, but wouldn’t the recounts be subject to just the same dangers of cheating that the original counts are? Especially if a recount was done every time, a smart cheater would know to expect this and find a way to rig the recounts just like the original results.

  2. #2 Krisztián Pintér
    January 14, 2008

    not that i want to interfere how you vote, but as a foreigner, i’m simply frightened about your election system. election is the very basis of democracy. it not just have to be cool, it have to LOOK cool, and not even the shadow of doubt can exist.

    here, in hungary, we use only paper ballots, hand counted. not because we never heard about that recent invention called computers, but because people don’t trust electronic voting system. if people don’t trust it, it is not good. period.

    if anytime a party accuses the current leadership with stealing the election, they can reply: your own delegates were there, in the counting comittees, thousands of them. they were all … what? bribed? if a large portion of your own people can be bribed to forge result against you, you are a dumb idiot, and better loose.

    in case of real doubt, every single ballot is saved for monthes. and they automatically recount votes in every district where the results are close (few percent diff).

    to be more ontopic in a math blog, here is an interesting article how to do electronic voting that you can trust. not cheap, though. http://eprint.iacr.org/2007/162

  3. #3 Mark C. Chu-Carroll
    January 14, 2008

    Susan:

    You’re correct that you can cheat in a recount, too.

    The idea, though, is to have a *separate* mechanism with *different* people for the recount.

    It’s very hard (not impossible, but very hard) to create a
    way of cheating that can get past two separate counts by two different groups of people, and produce the same results.

    So while recounting can’t prevent all cheating – nothing can – it dramatically raises the bar, and makes it much harder to get away with cheating without getting caught.

  4. #4 Matthew L.
    January 14, 2008

    The recounts aren’t necessarily more vulnerable, because if you’re only recounting 5% of the state’s votes automatically, you can use a slower, more expensive method to count the votes, one which is harder to rig.

    Instead of machines which, once compromised, silently record the wrong votes, we could use a large selection of volunteers to count the votes by hand. If there’s one thing people are bad at, it’s keeping secrets, so it seems unlikely that anyone could pay off or intimidate all the counters without anyone complaining, leaking to the press, etc. Preferably, we would have a system for taking any interested volunteers (at random) to help with the recount, making it harder to stack the panel with your supporters.

  5. #5 Eric Lund
    January 14, 2008

    As a New Hampshire resident, I agree with your take. It’s particularly easy to implement here because we only have about 300 precincts in the entire state (in cities, one per ward; elsewhere, one per town). About half of those precincts count by hand; the rest use optical scanners (in terms of population it ends up being about 20-80, since as you point out the cities and larger towns are the ones that use machines). So the secretary of state need only pick 15 precincts (fewer if you trust the hand counts) at random the morning after the election to give you the 5% check rate.

    I’ve heard that Kucinich was interested in having a recount done. Good for him if true and he follows up. But you are right that an audit should be automatic.

  6. #6 Coin
    January 14, 2008

    Large urban districts are much more likely to have optical scan machines; small rural districts are much more likely to hand-count. When you look at the votes, and at polls, you find things like Clinton tended to do better in urban districts – the places that were most likely to have optical scan.

    Something I would be interested to see is a sort of “red vs blue” map of NH showing which areas use optical scan and which areas use handcounts. It seems like looking at things laid out that way would make the demographic differences leading to the optical-vs-hand discrepancies stand out very clearly. (Incidentally, does anyone know where to obtain that information, which districts use which vote-count method? It doesn’t seem to be anywhere obvious on the NH secretary of state website.)

    This said I’m glad the recount is happening, even though I’m sure it won’t change anything. Recounts, when allowed to go forward, can only increase people’s trust in the democratic process. Good for Kucinich for stepping up on this.

    What I like is the reasoning of the guy who’s paying to have this recount done on the Republican side:

    [Albert] Howard, 41, who works as a chauffeur in Ann Arbor, received 44 votes Tuesday night. At one point during that evening, however, Howard said he had as many as 187 votes and wanted to know what happened to them.

    Makes sense enough to me.

  7. #7 Gerald
    January 14, 2008

    How about the claims that votes for Clinton and Obama have been switched? The stats they cite look very convincing:
    http://www.eurotrib.com.nyud.net/story/2008/1/12/191247/981

  8. #8 Peter J. Nicol
    January 14, 2008

    We Australians find the American system very strange.

    Could not have this debate in Australia. The entire vote is hand counted, with representative from all parties ‘scrutineering’ it at every stage, as the ballots come out of the boxes and are counted, in full view of everyone.

    We have a national, independent body that conducts all federal and state elections, and is responsible for drawing the boundaries.

    You point about elections being easy to steal does not apply in Australia.

    In addition, we have compulsory voting (or compulsory attendance at the polling booth, as some pedants would have it), and a preferential system.

    Debates about stolen elections simply do not happen.

  9. #9 Jim
    January 14, 2008

    Yes, an audit of every vote is an excellent idea. In most cases there isn’t fraud (I believe), however, it would help up people’s confidence in the system. It would also help to cut down on fraud. The mere knowledge that there is going to be an audit or check would discourage some people from cheating. I think most cheating is done with people who can’t vote. (eg they are dead, but some how vote every year)

    So an audit and a way to guarantee (or at least raise the confidence level) that those voting are eligible to vote and get to vote only once per election. Yes, you have to balance that with not disenfranchising people who have a legal right to vote.

  10. #10 Mark C. Chu-Carroll
    January 14, 2008

    Jim:

    I actually worry about the “guarantee that those voting are eligible” thing.

    In the US, there’s a long history of biased authorities denying the right to vote to people based on race, or ethnicity, or poverty, or expected voting preference.

    So far, every attempt to supposedly guarantee that only legal voters are voting has actually been slanted to make it difficult for people liable to vote for the “wrong” candidates to actually cast their votes.

    For example, Georgia tried to create a program that required people to show a state issued ID like a drivers license. That might seem like an OK idea – but it turns out that for many non-wealthy urban dwellers, having a drivers license is quite rare – if you’ve never had a car, why would you have a license? And they made getting a non-drivers license state ID difficult – a small number of ID issuing centers in incovenient locations with a relatively high fee to get the ID. So the proposed rule made it hard for a large number of likely democratic voters to get the ID necessary to vote. And it was quite clear that that was the real motivation behind the rule: to turn Georgia into a reliable conservative voting state by excluding a large pool of voters.

    As a result, any attempt to create a system for catching illegal voters at the polls is going to *decrease* confidence, not increase it. Especially since there’s never
    been a shred of evidence that there’s a lot of illegal voters.

    There is a reasonable system in wide use that doesn’t exclude voters. Where I live, and in many (most? all?) other states, you do need to show some kind of ID – not necessarily state issued, but *something*, the first time you vote. After that, you’ve got a signature in a records book, and you need to sign that book before you can vote. If your signature doesn’t match what’s in the book, then you can be asked to either show ID, or file a provisional ballot.

    That same system has been used in the three states in which I’ve voted: NY, NJ, and Delaware. I know from family that it’s also used in Ohio and Florida.

    If there was *nothing*; if you could walk into a voting center with no ID, no registration, no signature, nothing; and then vote, then I’d agree that we need to do something to prevent illegal voting. But that’s not reality. We require prior registration, and witnessed signatures on voting day.

    What kind of evidence is there that there’s a lot of illegal voters getting past that system? If there’s already something reasonable in place, and there’s no evidence of fraud getting past it, and every attempt to create stricter systems seems to be put forward with questionable motivations, then why should we trust any attempt to create a stricter verification system?

  11. #11 Jeremy Clark
    January 15, 2008

    For what its worth, there are more mathematically sound ways to verify the results of an election than a manual recount, but they require slight to major modifications to the voting system.

    Tallying votes requires two steps: (1) collect the cast ballots together and (2) count the collection of ballots to see if it matches the electronic tally. (1) seems trivial but its not verifiable through a manual recount–ballots could be added or removed to/from the collection and they could also be modified.

    The only way to unconditionally verify (1) is if the voters have some sort of privacy-preserving receipt they can use to see that their ballot made it to the count (but doesn’t show how they voted). This is the basis of a number of new mathematical voting systems: Punchscan (disclosure: I work on this system), Scantegrity, ThreeBallot, Pret a Voter, etc.

    However until one of these are adopted, randomized manual recounts can significantly increase the probability of detecting voter fraud.

  12. #12 Dave Briggs
    January 15, 2008

    So, my take? It doesn’t look like there’s anything wrong with the results, but we should do an audited recount anyway.

    I agree! Never hurts to recheck. I certainly hopes someone pulls out ahead and makes it a landslide so we don’t end up with fervent recounts about hanging chads or the like ever again!
    Dave Briggs :~)

  13. #13 jim
    January 15, 2008

    Mark,
    That is why I qualified it with “Yes, you have to balance that with not disenfranchising people who have a legal right to vote.” In the Georgia case the authorities did offer to provide the ID for free and go to the person’s residence to take the picture etc. It is interesting how people can claim they are being disenfranchised by that – the inconvenience of getting an id at any DMV office – but somehow can make it to a polling place on a particular day.

    There is evidence of vote fraud all the time. In the last election in Washington state a close race was thrown in favor of one candidate despite there being more votes in that area than people registered.

    In Oregon we have mail in ballets. You receive your ballet about a month before the election and you have until 8:00 PM on election day to turn in your ballot. You can mail it in in advance (must arrive by 8:00 PM on election day) or turn it in at a polling place or the post office up until 8:00 PM. It is nice to be able to sit down and go through all the issues etc. and take your time. Also I don’t have to rush to a polling place on election day. I think it does increase the percentage of eligible voters voting. I do see several things wrong with it.

    1. Less chance of the vote being secret and without influence. Husband could bully a wife into voting the way he wants. (or visa versa) In the polling place the other party can say they voted x and vote y and no one would know.
    2. Yes, you sign the back of the envelope the ballot goes into – across the seal, but that doesn’t validate you voted, just someone did. Less secure than having to go to a polling place.(that envelope goes inside another envelope to mail) There isn’t much of a check other than they mailed you the ballot.
    3. Lost in the mail or tampered with in route. You do have the option of turning it in at the polling place. This is a low probability.

  14. #14 Mark C. Chu-Carroll
    January 15, 2008

    Jim:

    WRT the Georgia fiasco: Polling places tend to be very localized. I don’t even live in the city, and yet I’ve never lived more than two miles from my polling place. In any urban area, I’ve never seen a polling place that wasn’t in walking distance of the homes of people voting there.

    On the other hand, in NJ, when I first got my license, I lived a solid 45 minute drive from the nearest DMV office. Where I now live in NY, DMV is 20 miles from my home. Friends who live upstate are at least 2 hours from the nearest DMV.

    Can you see the difference between those two? The polling place two blocks away, and the DMV two hours away?
    That’s a damned big difference.

    The “we’ll go to their homes and take their pictures” was also a crock. The staff of the agency that was supposed to do that was capable of going to the homes of a couple of *hundred* people per month; whereas there were *at least* several hundred *thousand* people who would have needed IDs. Even jumping the staffing by a factor of ten wouldn’t have made it possible for them to get IDs for everyone who needed them to vote. That claim, that they’d be able to get IDs for people without transportation to the DVM was a fraud, clear and simple.

    WRT voter fraud:

    If you’ve got more votes in a district than registered voters, then you’ve clearly either got someone at the polling place cheating (in which case adding more protection to catch fraudulent voters won’t help), or the people at the polling place are *not* checking the voter register before letting people vote (and again, if the poll workers aren’t checking peoples registrations, what makes you think that they’ll check their IDs?)

    I’m not opposed in principle to programs designed to ensure that only legal, registered voters get to cast ballots. But I’m very skeptical of demands for more complex schemes to validate voters when there’s no reason to believe that the *current* scheme is insufficient. Every story I’ve been told about voter fraud involves either ballot stuffing (which requires a compromised poll-worker), or non-enforcement of the current voter registration checking mechanism. Every proposal that I’ve heard for validating voters doesn’t seem to offer much, if any, actual additional protection to the integrity of the election process, but creates a discriminatory voter on one segment of the population.

  15. #15 Polymath
    January 15, 2008

    Remember what Stalin (supposedly) said:

    Voters don’t determine elections. Vote counters determine elections.

  16. #16 Zach Cox
    January 15, 2008

    Spot On!

    The idea of the “audit recount” is right on. And to do it you need access to one of the immutable bits of THE VOTE. Those immutable bits include:

    The Ballot Itself (must be something that the voter created and hand carried to the ballot box)

    The Ballot Box (must be a secure repository for the ballot to be placed in. And could have an optical scanner attached to help with the ‘preliminary count’ that would be accepted if the ‘audit recount’ passes).

    The Polling Place (must be a physical location near the voter’s home that he visits on Election Day. This could be modified by early voting polling places that would of course require photo id and would record who participated so the rolls for that election could be marked to prevent multiple voting).

  17. #17 Martin Valiente
    January 15, 2008

    In Venezuela there are recounted 55% of voting boxes in public acts. Even so, there are people who are unable to accept an adverse result.

  18. #18 Brian Utterback
    January 15, 2008

    But NH is a split delegate state, and Obama and Clinton ended up with the same number of delegates. so it was effectively a tie. Nothing I have read has suggested that the count was sufficiently perturbed from the polls that it would actually change the outcome. I am all for accuracy, but sometimes it just isn’t worth the bother.

  19. #19 David
    January 16, 2008

    I agree that a 5% mandatory check on ballots should be performed to insure that the election is not being rigged.

    However, I have to agree with Jim on providing valid ID. I grew up very poor and lived in a trailer park as a kid. I can tell you that the vast majority of poor people have cars. Crappy cars but cars nonetheless. Even those who don’t own cars still learn how to drive and get a license. This might be different in New York city where people don’t routinely drive, but even then I just don’t buy that getting a valid ID is an onerous burden. Quite frankly, if someone can’t figure out how to get an ID then I’d rather they didn’t vote.

  20. #20 Andrew Briscoe
    January 16, 2008

    The Clinton vs. Obama thing probably was correct, but the worse thing was that 0 votes were counted for Ron Paul, even though many people came out saying they voted for him. Only after they had been called out did they “find” 31 votes that had been lost due to “human error.”

  21. #21 Andrew Briscoe
    January 16, 2008

    Also making voting non-anonymous would make cheating near impossible.

  22. #22 Coin
    January 16, 2008

    Andrew Briscoe, anonymous voting is necessary to prevent an entire range of election abuses that don’t have to do with “cheating” in the sense of miscounting.

    Also:

    the worse thing was that 0 votes were counted for Ron Paul, even though many people came out saying they voted for him. Only after they had been called out did they “find” 31 votes that had been lost due to “human error.”

    According to MSNBC, Ron Paul received 18,303 votes in New Hampshire. What exactly are you talking about?

  23. #23 Cain
    January 16, 2008

    Mark, care to comment on your fellow scienceblogger’s analysis of the situation?

  24. #24 CHCH
    January 17, 2008

    Mark! You are not even commenting on my statistics, much less doing them yourself. At this point in the debate, if you are not doing one of those two things, you are adding to the noise that confuses the issue. You will not be able to detect (or at least confirm) meaningful differences between DIebold-counted and hand-counted towns without statistics.

    In the words of Jon stewart, you are “hurrr-rrr-rrting america” by not discussing the real debate, which is a statistically significant and extremely unlikely deviation from chance fluctuations in Hillary’s votes due to vote method, AFTER CONTROLLING FOR DEMOGRAPHICS.

    You have detracted from the real issue here and have taken the debate back a step in what appears to be willfuly (but I assume is not) ignorant skepticism.

  25. #25 Mark C. Chu-Carroll
    January 17, 2008

    CHCH:

    I posted this before I saw your post. But even so, I remain *very* skeptical of any supposed cheating.

    As Mike pointed out in his analysis, there are quite a number of confounding factors that make it very difficult to do a correct statistical analysis. What your analysis suggests is that there is *some* causative factor. But to identify that causative factor, you need to be certain that you’ve eliminated any other correlative factors.

    Mike’s look at the data showed that when you control for precinct size, most of the supposed “Diebold effect” disappears. The effect completely disappears in both large and small precincts – it only remains in the medium sized precincts.

    So most of the so-called diebold effect correlates strongly with something other than voting-machine cheating – something which is much more reasonably explained by campaign strategy focusing on population centers.

    To make the voting machine cheating scenario work, you’ve got to suppose that the cheating only occurred in a specific subset of districts – the medium-sized precincts.

    That doesn’t make sense. It just doesn’t seem to fit. It really looks like there’s some other factor that correlates with voting machines, which you aren’t controlling for in your analysis. That’s not a particularly surprising conclusion, since there are so many factors which can affect an election which are not included in the available information.

    In any case – I want to see a manual recount of the voter-verified paper ballots, which would detect any cheating.

  26. #26 CHCH
    January 17, 2008

    Mark, Mike’s look at the data can hardly be consisdered “controlling for precinct size,” which I have done for all 200+ precincts STATISTICALLY, i.e., the way these things actually should be done.

    I have also controlled for a Clinton campaigning presence.

    If you think a manual recount will solve this, it is even MORE clear that you didn’t do much reading before opining here. Look at the chain of custody issues in NH, for example.

  27. #27 CHCH
    January 17, 2008

    To clarify, I am not advocating that there was election fraud. I am saying there is a statistically significant effect that needs to be explained, and I had (naively?) hoped for an intelligent, reasoned, and informed opinion on what that might be. Everything you bring up I have already considered AND controlled-for.

  28. #28 CHCH
    January 17, 2008

    An apology is in order – you wrote this post prior to my post, and although you might be faulted for not looking at the BBV forum threads or various other evidence that had accumulated by that time, the oversight is not as egregious as I thought.

    Sorry for the harsh words.

  29. #29 vanderleun
    January 17, 2008

    “Never forget the recount riots in Florida” I’m sorry but I seem to have forgotten “riots.” Were there any? There was a lot of argument and acrimony as I recall, but I don’t recall any rioting.

  30. #30 Andrew Briscoe
    January 19, 2008

    Coin:
    That was a specific precinct, not the whole state. Also non-anonymous voting does not mean that the information has to be public, it could be tightly regulated and examined only by qualified independent agencies. Also the user could have a key to check and make sure their vote was counted.

    Mark:
    I agree a recount could help, but don’t you think its a bit of a stretch to say that cheating paper ballots is impossible? Not that this is proof or anything but http://www.bbvforums.org/forums/messages/1954/71404.html?1200663040.

  31. #31 Bob O'H
    January 21, 2008

    I know it’s a bit late to be seen here, but Andrew Gelman has a post up about an analysis of the data. I like his rather snarky “Now it’s time to hear from the experts”.

    Bob

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