In a working paper provided to GoodGawdAnotherBlog, Professor Walter Mebane concludes that his well-regarded election fraud diagnostics produce “scant evidence that any frauds occurred” in New York City during the April 19, 2016 primary between former Secretary of State Hillary Clinton and Senator Bernie Sanders. According to the “finite mixture” statistical model used, furthermore, there is “no evidence whatsoever that large or widespread frauds occurred.” The finite mixture model necessarily produces some ambiguity, however, and cannot catch all kinds of potential fraud, according to Professor Mebane.

As part of an ongoing effort to take allegations of election fraud seriously, without simply accepting or dismissing them up front, I approached two elections statistics professors previously consulted by FiveThirtyEight in their effort to suss out potential electronic hacking of a Democratic primary in South Carolina in 2010. Professor Mebane and Assistant Professor Michael G. Miller concluded in 2010 that the South Carolina results showed evidence of substantial fraud to a 90% degree of certainty.

While Professor Mebane plugged data into his finite mixture model, Miller applied the same Benford’s Law test used and reported on by FiveThirtyEight in 2010. My discussion with Miller, however, ended with a bizarre series of accusations leveled by Miller against me in email then on Twitter: “The author of this piece should not be a journalist,” Miller stated, and “there is no evidence of fraud in this election in the data I have analyzed…also Doug is B-squad.” For anyone interested in such mundanity, rather than going in tit for tat with Professor Miller’s tweets as mostly still present on his recent timeline, I have posted the full email exchange that led to him taking his ball of stats and leaving the playground.

At its heart, the finite mixture model uses sophisticated statistical formulations to measure voting outcomes versus an expected distribution based on detailed data of voter registrations and candidate results at the smallest level, in this case New York City’s 5,217 elections districts. Where results meet the model’s expectation of a fairly even and predictable distribution of votes across precincts or districts, they are termed “unimodal.” New York City’s results are, alternatively, “multi-modal.”

Multimodal results indicate that there is some unevenness to candidates’ expected vote distribution, but the model builds room for a level of ambiguity allowing for multi-modal results in situations where, for instance, strategic voting or concentrated get out the vote efforts may produce otherwise unexpected outcomes. “The few indications of ‘frauds’ that the model gives,” according to Mebane’s conclusion, “are readily interpreted as due to strategic behavior, most likely strategic behavior involving specially coordinated mobilizations to turnout and vote.” The key measurement is found in the far right hand column of the chart, from Mebane’s working paper, as reproduced here:

Rather than wading into all of the statistical details of the chart, the key columns for us are the far left column (by congressional district, or CD, as represented in New York City) and the far right hand column. Where figures in the right column reach .015 or greater, Mebane concludes that substantial fraud is highly likely to have occurred, but “[n]one of the pi + pe values in Table 2 are remotely as large as that.” (My publishing platform will not allow me to properly subscript the “i” and “e” in pi + pe.)

Notably, however, the largest value by far in the far right hand column is for Congressional District 9, which is wholly located in Brooklyn. Where most other results are orders of magnitude below .015 and only one (CD 8 in Queens) is even 20% of the way to a .015 result, CD 9 makes it over 60% of the way there.

I followed up with Professor Mebane to ask whether that result could be capturing the infamous purge of more than 100,000 Democratic voters in Brooklyn that has been the partial target of an Election Justice USA lawsuit and has seen two Brooklyn Board of Election’s officials relieved of duty without pay. “More facts can’t be bad,” Professor Mebane replied. “The finite mixture model is just a model. Another limitation of it that I’ve written about is that it’s insensitive to many patterns of voter suppression. If the voter purge did that, the effects might not show up in the model estimates.”

I am committed to completing investigations by two other avenues into potential fraud, like intentional voter suppression, that could avoid detection by the finite mixture model. I expect to publish a critical article relating to Democratic voter registration high jinks in the next week and a half. The topic under contention with Miller, however, will take a fair bit longer for me to publish on. I am awaiting key data requested under New York’s Freedom of Information Law.

Note: Professor Mebane intends to use the material in his working paper as a part of another academic piece he is preparing but has said he would host it on his personal website if there turns out to be sufficient interest. Statisticians interested in the data plugged into the finite mixture model and used for the aborted Benford’s Law Test results should email me at djjohnso@yahoo.com. Those wishing to reach me more securely could send me an encrypted message at an alternate address.