Vanadium 50 said:
#2: The information comes from the losing candidate. Do you think that he is showing a random distribution of studies? Or do you think he is picking the one that makes his point best? If the latter, how many studies do you think he looked at before selecting the Mebane study? 2? 5? 10? 20? How significant is a 90% CL now?
#3: Mebane's study says "The value of j-hat for Rawl matches the value observed in Mebane (2010a; 2010b) for many losing legislative candidates in U.S. elections during the 1980s and 2000s, and so might not be considered all that unusual." That's not what the losing candidate's press release says Mebane's study is saying.
These are valid criticisms.
#4: Why would elections even follow Benford's Law at all? Benford's Law applies to systems with sizes that cover several orders of magnitude. Election precincts are set up to keep their sizes roughly the same.
A conference paper looking at the 2nd digit Benford's Law test is available
here. The paper does mention that its use as a method to detect election fraud is controversial, so this may be a valid criticism (I don't know enough about the test to say one way or the other).
#1: A 90% confidence level is very low indeed. At this threshold, in a world with perfect elections, we would declare about 47 Congressional elections fraudulent every cycle.
TheStatutoryApe said:
I'm no math wiz so I would not be capable of unraveling the numbers but from the quote in the article it seems they are saying there is a 90% confidence level of tampering, or that there is only a 10% chance that the voting patterns would have turned out this way.
Here's how you would interpret the result. According to Mebane, the 2nd digits from the vote counts should follow a certain distribution, derived from Benford's law. The results from the SC primary deviate significantly from the Benford's law distribution. Now, there are two possible explanations for this observed deviation:
1) The election results are valid and the deviation occurred by chance.
2) The election results are fraudulent.
(there may be other explanations, but for simplicity I'll just look at these two). Now, what is the probability that the SC results could occur by chance? If you assume that the 2nd digits of the vote counts are distributed according to Benford's law and generate millions of sets of vote counts from that theoretical distribution, only 10% of the results will show a deviation greater than the deviation shown by the 2010 primary results.
Now, to properly interpret these results, we should take a Bayesian approach. Let's say that one out of every thousand elections is fraudulent (this number is arbitrarily chosen for the purposes of this example, it is probably/hopefully an overestimation). This fraudulent election will fail the Benford's law test. However, of the other 999 elections, approximately 100 of them will also fail the Benford's Law. Therefore, of the 101 elections that fail the Benford law test, only 1 of them will have been fraudulent. Therefore, (given the assumed fraudulent election rate above) the likelihood that the election was fraudulent is still only about 1% (up from our prior probability of 0.1%). So, yes, given a rare event like a fraudulent election, even a test with a 90% confidence level does not give you much confidence that the election was fraudulent.
If the Benford's law test were the only piece of evidence we had, I would definitely agree with Vanadium. However, there are other pieces of evidence that point to possible fraud. One issue brought up by the fivethirtyeight post I mentioned previously, is that the voter turnout numbers for the Republican races look odd. There's also the
large discrepancies between absentee vs election day ballots (although discrepancies in this case are to be expected). Finally, there's the surprise of a candidate who did not campaign at all winning the election.
I do agree that these data certainly are not conclusive evidence of fraud/voting machine malfunction, and it would be very hard to prove so. However, I don't think the possibility can be fully dismissed. While I think human manipulation of the vote count is unlikely, I do wonder what the likelihood of voting machine malfunction is. The manufacturer of the South Carolina voting machines has had problems before (
http://techdirt.com/articles/20100609/1616099761.shtml). I guess a larger point that I'm trying to make here is that some of these issues could have been addressed if the voting machines included some sort of paper trail for auditing later on.