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.