Academic Paper for Exitpolologists: "Detecting Attempted Election Theft"

Detecting Attempted Election Theft: Vote Counts, Voting Machines and Benford's Law

Walter R. Mebane, Jr.
Professor, Department of Government, Cornell University, 217 White Hall, Ithaca, NY 14853

April 19, 2006

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This paper introduces statistical methods intended to help detect election fraud. Other methods, using regression-based techniques for outlier detection, have previously been proposed to help detect election anomalies (e.g. Wand, Shotts, Sekhon, Mebane, Herron, and Brady 2001; Mebane, Sekhon, and Wand 2001). The methods described here are distinctive in that they do not require that we have covariates to which we may reasonably assume the votes are related across political jurisdictions. For one set of methods I describe|methods based on tests of the distribution of the digits in reported vote counts|all that is needed are the vote counts themselves. I study the application of those methods to both precinct-level and voting machine-level vote tabulations. Part of the potential practical relevance of these methods is that situations in which little more than the vote counts are available may arise frequently in connection with actual election controversies.

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It's a pdf.
http://macht.arts.cornell.edu/wrm1/mw06.pdf

Walter R. Mebane, Jr.'s WebSite with more papers, including, "The Wrong Man is President! Overvotes in the 2000 Presidential Election in Florida"

http://macht.arts.cornell.edu/

I'm glad to see political scientists working on this issue, and not just statisticians, who sometimes tend to not understand the rhythms of American politics.

It seems to involve a natural distribution that that applies to voting data -- a non-random distribution of some kind. If the voting data IS random in certain ways it constitutes prima facie evidence of fraud.

That's from a cursory reading of the article. Mebane shoots right past it without explanation, probably because it's an academice paper. Sounds like an interesting concept, but there doesn't seem to be enough in the article to educate a layman.

But MathWorld can.:D

A phenomenological law also called the first digit law, first digit phenomenon, or leading digit phenomenon. Benford's law states that in listings, tables of statistics, etc., the digit 1 tends to occur with probability ∼30%, much greater than the expected 11.1% (i.e., one digit out of 9). Benford's law can be observed, for instance, by examining tables of logarithms and noting that the first pages are much more worn and smudged than later pages (Newcomb 1881). While Benford's law unquestionably applies to many situations in the real world, a satisfactory explanation has been given only recently through the work of Hill (1996).

http://mathworld.wolfram.com/BenfordsLaw.html

(Great album, ribofunk.)

I just didn't feel starting a search after two in the morning. :)

That is a fascinating paper. I had never heard of Benford's Law, namely that digits in large collections of numbers (like street addresses) are not random, but follow a special distribution in which earlier digits are overrepresented, with "1" occurring about 30% of the time.

Now precinct-level data contains nonrandom factors -- for example, all precincts may be designed so that they are about the same size. If all precincts contain a thousand voters and the parties are evenly split, 4s and 5s will be more common in the first digit of election results.

So Mebane proposes using the second digit, which should conform to Bemham's law more closely.

"The simula ions performed in Tables 10 and 11 suggest that an electorally intelligible and benign process can produce counts that often satisfy the second-digit Benham's Law. Suppose we take a process that we know produces such counts and perturb it in ways that mimic some ways vote fraud may occur. Does the Benford's Law test signal that there has been a distortion?"

Mebane tests several variations on two kinds of fraud -- including repeaters and multiplying totals by some factor, which includes discarding blocks of votes or switching them to another candidate.

Mebane finds that Benham's Law can catch repeaters only if they comprise at least 10% of the vote total. It's better at detecting fraud if a candidate receives more votes than expected, etc.

The result is that Mebane found that voting-machine-level results in Broward, Miami-Dade, and Pasco counties failed to match the Benham distribution. He mentions that there may be innocent reasons why this result might be caused by nonrandom allocation of voters (eg, audio-equipped machines).

I am thrilled to find out about this test. I want to see what he finds out about Ohio.

I'm not sure yet what I think the distribution of digits "ought" to be, but it merits further investigation. Neat paper. And Mebane presented it very effectively in Chicago.