Can Statistics Help Us Find Stolen Elections?

I grew up in Kansas and I still have relatives in the state who alerted me to this story. This post is about how statistics works including a chilling example that suggests (but is far from proving) election fraud in a large number of elections including the most recent Gubernatorial election in Kansas as reported in the Wichita Eagle. The elements of this story include the following.

  • Statistical analysis detected anomalous surges of votes in large precincts favoring main-stream Republicans over tea-party candidates and Republicans over Democrats.
  • These surges did not appear in elections with no Republicans in them.
  • Many electronic voting machines are made by a corporation that contributes more money to Republican candidates than Democratic ones.
  • Because they may need to service the machines very rapidly on election day, the machines have a back door for technicians.

The core tool of statistics is to create a model that fits a particular type of data. Once you have the model, then it is possible to look at a new collection of data and compute the chance that the new data fits the model. If that chance is very small then you can reject the hypothesis that nothing important changed. This probability – that the data fit the model- is called a p-value. It is customary to say that a result is statistically significant if the p-value is no more than 0.05. It is more accurate to report the p-value because then you have a better sense of how unlikely the event is. The value 0.05 is one-in-twenty. Sometimes, in my research, I’ve gotten numbers like 0.000000000000000000000000000723. Of course, with that sort of p-value the result is pretty obvious and you may be able to convince people you result is significant without using statistics.

The model I’m writing about today was developed by Francois Choquette and James Johnson and published to the web in 2012. I’ve linked their report here.

Statistician Beth Clarkson, of Wichita State University, wondered if the anomaly appeared in the 2014 mid-term elections. The model compares voting in precincts of different sizes in the same area. Because you’re averaging over smaller sets of voters you would expect the smaller precincts to be more variable, but to have roughly the same average as the larger precincts. The anomaly is that voter preferences shift to favor traditional Republicans in larger precincts. If you plot voter preferences you would expect a line that jitters more on the small end but one that is basically level.

What the statisticians found is that, in large precincts, there was a statistically significant deviation from the model in favor of non-tea party Republicans.

If the model that said that the plots of voter preference in small and large precincts should be mostly level was being defeated by an unknown demographic phenomenon, some sort of “who’s ahead” positive feedback loop, you wouldn’t expect it to favor one party. The statisticians also corrected for effects like an urban/rural split (many rural precincts are small, so you have to document the effect without them). The evidence is thus consistent with widespread, systematic voting fraud. Until guilty parties are actually located and documented, however, it is neither safe nor fair to shout “fraud”. The fact you cannot think of another explanation is not sufficient. In math we call this proof by lack of imagination and it is not a valid technique.

In the Kansas election the incumbent, Sam Brownback, was polling behind all the way through election day. The race was very close. An anomaly favoring Brownback occurred in Sedgwick county. The county keeps paper copies of the electronic ballots and Dr. Clarkson thought she could get a better sense of what was going on by examining these public records. As you might expect, she is now engaged in an open records lawsuit in Sedgwick County District Court to get access to the ballots. I will do no more than wonder why the county officials are acting in this fashion.

It is ironic that this sketchiness is happening in Kansas. The Kansas Secretary of State, Kris Kobach, has been making a great deal of noise about voter fraud in which non-citizens have voted. While I’m not sure, last time we checked he had less than ten examples which he was calling “wide spread voter fraud”. His solution was to force people to produce birth certificates in order to vote. Since a lot of people in Kansas were born at home, they don’t have birth certificates. The people without birth certificates, or without access to birth certificates, are more likely to vote Democratic. At this point you may wonder why I’m bringing this up.

Both Mr. Kobach’s attempt to put his party ahead by making it harder for his opponents to vote and the possible hacking-based election fraud only work if everyone is afraid of, or completely indifferent to, statistics. Choquette and Johnson documented a damning statistical anomaly three years ago and, mostly, no-one noticed. Dr. Clarkson independently verified their results and managed to generate some interest, but I heard about this from my mother-in-law (many thanks, Marjorie!) Kobach’s pretty much criminal attempt to disenfranchise his opponents relies on the inability of the public to check his claims against his evidence. Letting a couple of non-citizens vote is much better that preventing tens of thousands of citizens from voting – but if you don’t do the numbers, you don’t realize what’s going on. It’s a real Buffalo-Springfield moment.

I think it’s time we stop, children, what’s that sound? Everybody look what’s going down.

Mark Twain said that, “There are lies, damn lies, and statistics.”

It is common to cherry pick statistics to support a point that is actually not supported at all by the evidence and so I agree with Mr. Twain’s comment. Secretary of State Kobach screaming and yelling about a small number of instances of voter fraud to enable a huge act of governmental fraud is a perfect example of this. The problem is that statistics, used responsibly and professionally, really can be used to detect and document fraud, waste, injustice, and bad decisions. This is another place where the fear of math bites freedom and democracy in the anatomy.

Occupy Math would like to hear your examples of use and misuse of statistics. We would love to hear your comment or tweet.

I hope to see you here again,
Dan Ashlock
Department of Mathematics and Statistics
University of Guelph, Ontario, Canada


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