It's funny how things happen sometimes. After the New Hampshire primary last Tuesday there were some suggestions that the Democratic primary might have been tampered with. I have taken part in some discussions of this on and off the blog, and my basic take was that

Given the impossibility of getting my hands on disaggregated exit poll data and the observation that the exit polls matched the election results (but see below), I decided not to give the issue any more thought. That is, I ceased to take it seriously. Update [2008-1-14 14:21:2 by Migeru]: It appears that Zogby has released some of his pre-election poll raw data allowing aggregation on the basis of whether the voter would have their vote counted by hand or machine. However, the same hasn't been done for the exit poll data, that I am aware. Edison or whomever should do as Zogby has done to allow a precint-by-precinct comparison of exit polls (not pre-election polls) and vote counts.

However, supporters of both Ron Paul and Dennis Kucinich among other people didn't lay this to rest and started posting fragmentary statistical analyses of actual voting data. These got more and more elaborate until, earlier today, Drew, who had nagging suspicions and so had been tracking what the blogosphere was saying about this issue, pointed me to a couple of websites that changed my mind, because they contain serious statistical analysis of the kind I suggest in 3) above, albeit performed only on the election data, not on exit polls. But that is actually probably better as I'll also discuss below it appears exit polls are normalised to match the actual results because their purpose is not to predict results, but to try to show how various socioeconomic variables correlate with vote patterns .

Now I think there is a high likelihood that the vote counts for Obama and Clinton were exchanged by Diebold voting machines. Update [2008-1-14 14:21:2 by Migeru]: However, I have tried to replicate the statistical results detailed below and I have not been able to (see the comments for details), which casts some doubt on the "smoking guns" for fraud. The correlation between Clinton/Obama vote swing and vote counting method is robust, but referring back to the intro, in point 3) I stressed the need for socioeconomic correlations to be studied and this hasn't happened yet - the same point was made by Continuation in the blog post I linked to below. Point 2) seems to be well established, but with the "smoking gun" gone, the likelihood of fraud goes down a notch.

The first indication that something might be amiss came in this comment by ThatBritGuy:

From a comment by "soros" at the big orange monster:



Thursday 1/10: Bruce O'Dell writes: Theron Horton and I have confirmed that based on the official results on the New Hampshire Secretary of State web site, there is a remarkable relationship between Obama and Clinton votes, when you look at votes tabulated by op-scan versus votes tabulated by hand: Clinton Optical scan 91,717 52.95%

Obama Optical scan 81,495 47.05% Clinton Hand-counted 20,889 47.05%

Obama Hand-counted 23,509 52.95% The percentages appear to be swapped. This seems highly unusual.

COMMENT #57 [Permalink]

... TruthIsAll



Brad, the coincidence is even greater than that. The numbers match to within .0001% ! Optical Scan

Clinton 91,717 52.9507%

Obama 81,495 47.0493%

Total 173,212 Hand Counted

Clinton 20,889 47.0494%

Obama 23,509 52.9506%

Total 44,398

Then there is this other indication from the Election Defense Alliance The coincidence is even more suspicious than it appears as the percentages match to 5 decimal places, as was discovered by a commenter on Brad Blog Let's do a back of the envelope calculation... Let's take the percentages "measured" from the optical scan ballots. Suppose you have a biased coin with a head on each side, Clinton or Obama, and with a 52.9507% probability of coming up Clinton and a 47.0493% probability of coming up Obama. Now take the total number of hand-counted votes. Toss that coin 44,398 times. What do you expect? Well, the expected number of Clintons is 44,398 * 0.529507 = 23509.1 which is exactly as observed for Obama, and the expected number of Obamas is 20888.9 which is also exactly as observed for Clinton. Now, the expected variance of a coin toss will be 0.529507 * 0.470493 = 0.249129, so the expected variance of 44,398 coin tosses is 11060.8 and the standard deviation is the square root of that, or 105.2 so you would expect the observed vote counts to deviate from the expected ones by about 100 votes in either direction. The fact that they match to within 1 vote means that the match is too good to be true. We're talking as unlikely as a 3-sigma deviation. If you're a teaching assistant and a student turns in a lab report with data of this quality you suspect them of doctoring their data to match the textbook answer and call them to your office for cross-examination.

So, these data contain not one but two red flags. The first is that the vote percentages are exchanged, and the second, more subtle red flag, is that the vote counts are too god to be true.

Update [2008-1-15 13:23:36 by Migeru]: This is all well and good, but Drew and I downloaded the official (but provisional) vote counts and the list of precincts using optical-scan machines from the New Hampshire Secretary of State website and were not able to duplicate this uncanny coincidence. Kudos to the stormy present who, in the comments, noted a 3-4 vote discrepancy in the vote totals between the Secretary of State's county summaries and the EDA numbers quoted above. The Election Defense Alliance has subsequently issued a correction:

EDA has subsequently learned that the list of hand-count voting districts in New Hampshire that it used in its initial analysis on January 10, 2008 was outdated; shortly after that list was downloaded a revised list was published by the New Hampshire Secretary of State with fourteen hand-count precincts converted to Diebold optical scan.

Now for the couple of links that I got from Drew that convinced me that something really is amiss by addressing my suggested tests in point 3) above the fold.

The first one is from "Brian" at Black Box Voting:

I wanted to do a quick statistical analysis of the results. This is far from complete, but the results thus far do not contradict our initial suspicions.



First a very basic statistics primer. We assume that our samples are subject to "noise" (random variation). Obviously the percent vote counts are not going to be the same in every precinct, so when we see what we think is a trend (like Obama doing better in hand-counted precincts) we ask, "what is the probability (p) of this apparent trend arising by chance?" If the probability is less than 5% (p < 0.05) we say that the result is "statistically significant."



Ok, now the results.



First I ran a chi-squared contingency table tests with Yates correction. for both the democrat and republican results. ... Thus we can say with a high degree of certainty that there is a relationship between the counting method and the election results. The probability of the aforementioned discrepancies occurring by chance is less than 1 in 100 billion.



This does not mean however that counting method causes different voting percentages, just that they are correlated. It could be that something else (e.g., size of town) causes both. As a quick control I did the same chi-squared analysis, but looking at just whether people voted democrat or republican. Below, the columns are machine counted, hand counted and the rows are republican, democrat. ... That is, while the machine counted precincts tended to vote slightly more republican (54.9% vs. 54.6%) this result was not significant (p > 0.05).



If one was cheating by vote substitution one would not want to change republican ballots to democratic or vice versa for obvious reasons. It is interesting that the machine/hand counted precincts have such different results within each election, but are almost identical between the two elections.



The next question is whether other factors can explain the discrepancy. This is very much a work in progress. Preliminary results indicate that neither Obama's nor Clinton's percentages have a significant correlation with precinct size. They both fit a line with slope zero. This would suggest (very preliminary) that the trend of smaller precincts tending to use hand counts cannot explain the discrepancy.

Some people offered the explanation that smaller precincts tend not to use Diebold machines and also tend to favor Obama, for whatever sociological reasons. As someone put the election data in computer-readable format on the web, and as I am slightly versed in statistical analysis using the R package, I decided to run some tests. ... In hand-counted precincts, which make up 20.2% of the votes, Obama gets 38.6% and Clinton gets 34.9%. In Diebold-counted ones, Clinton makes 39.6% and Obama gets 36.3%. This is the basis for the initial claims of vote rigging.



Claims which are countered by the observation that precincts where the votes are hand-counted are small, non-urban precincts. Urbanity is, of course, a well-known factor affecting political choices. ... Actually there is a very significant correlation at p < 0.002 between Clinton's score and the precinct size, and an even better correlation between Clinton's score and voting method, and yet a better correlation between precinct size and voting method.



We cannot say much more without going to multivariate statistics. Fortunately, thanks to GNU R, mere mortals can benefit from multi-variate statistical modeling. ... These cryptic lines mean that Hillary's score can be computed by 38.59% plus the Democratic size divided by 384911.5 (which is 1/2.598e-6) minus 4.64 percentage points whenever the voting method is by hand.



So it is estimated that voting method accounts for 4.64 percentage points of Hillary's score.



How much variability does this linear formula remove from the data? The standard deviation (on a precinct by precinct basis) of Hillary's score is about 7.8 percentage points. ... Look at the t value! As you can see, voting method explains a lot better than precinct size. ... Now let's think a little bit. There could very well be a politically meaningful parameter correlated with voting method besides precinct size. As Diebold has connections with Republicans, it could be that Republicans favor Diebold. Could it be that the Republican to Democrat size ratio explains the voting method?



I'll spare you the R screen dump: the p-value of the correlation coefficient being 0.69, the R to D size ratio doesn't seem to explain anything.

PRESIDENTIAL PRIMARY - JANUARY 8, 2008

Results of the Presidential Primary will be posted at the above link after tabulation is complete (Wednesday, January 9, 2008)

Press Release Regarding Republican and Democratic Recounts

But the one that really blew my socks off was this other one from the blog Continuation So, after I told Drew that this Continuation guy had hit jackpot, he decided to forward a bunch of these links to the Kucinich campaign to help them with the recount effort. Apparently Drew ended up on the phone with Kucinich, who would really appreciate having a detailed report of the statistical evidence before Monday (US time). And why, oh, why would Kucinich need as watertight as possible a report on so short a notice? Because, as you can see from the PDF press release linked to herethe New Hampshire Secretary of State is required to estimate the cost of a full recount, which would have to be paid by Kucinich (at least for the Democratic recount). Kucinich is not exactly swimming in cash, and also he's sticking his neck out on this (he effectively called a full recount on a limb) and has some of his own credibility at stake if the recount ends up confirming the original result.

Here are a bunch of links to other blog posts, media sources and data sources that you are welcome to look at if you are so inclined. I am personally going to go to sleep now and tomorrow I'll run my own set of regressions to try to independently validate the evidence presented here. So, if you have any suggestions on how best to do that, please put them in the comments. And please poke as many holes into this as you can.

reddit [precinct-level data used by Continuation]

BlackBoxVoting Forums 1

BlackBoxVoting Forums 2

CheckTheVotes.com

The Boston Globe [results by town]

BlackBoxVoting Forums 3

New Hampshire Primary: postmortem [hand-counted vs. machine-counted as function of precint size calculator]

list of Accuvote-using NH precints

What the exit polls tell us [Booman Tribune diary by dataguy]

ET comment by Drew J Jones

MSNBC

Bradblog

BlackBoxVoting NH voting tables demographic data by town [excel]