Examining suspected voter fraud in Chicago

I read an interesting article today suggesting that there could have been some fraud in the Presidential election taking place in Chicago and Philadelphia.  Each of these cities reported double-digit precincts where Romney received zero votes.  This seems rather odd, and it has incited some people to decry voter fraud in these precincts.  Some have responded by saying that there are probably plenty of precincts where Romney received all of the vote.  I decided to see if I could find any information about precincts where Obama received zero votes.

I did find some.  This article reports there were a few precincts in Utah where Obama receive zero votes.  The article gives us some good information about a few of the precincts where Romney won by a score of 14-0, 17-0, and 14-0.  The article also mentions that in some counties Romney received more than 84% of the vote.

Since this has happened to both candidates, it must be a statistical anomaly; one of those strange things that looks weird at first, but makes perfect sense.  Clearly there is no voter fraud in Chicago, or Philadelphia, or Cleveland.  Or is it?

The difference between the Utah precincts and the Chicago precincts is the number of people voting.  What is the probability that Obama would receive zero votes in a precinct of 14 voters if he has a 16% chance of getting a vote in that county?  I asked R.  dbinom(0,14,.16) = .087.  An 8% chance is hardly a freak coincidence.  Overall, Obama took 27.8% of the vote in Utah, so the probability of him getting 0 votes in a precinct of 14 voters is almost right on 1%.  And according to the Utah election results, there are 2332 precincts in Utah.  I don't know how many of them have 14 voters, but considering that most of the state is rural it doesn't seem outlandish to think that there are a lot.  And if there are at least 300 such precincts then it would be downright expected for us to find 3 precincts where Romney collected 100% of the vote.

Now let's look at the 15th precinct in Chicago's 7th Ward where Obama won by a score of 526-0.  It is reported in the article that Obama received 98.6% of the vote in that Ward.  What is the probability of getting all 526 votes in a precinct if that is the case?  dbinom(0,526,.014) = 0.00060153 or about 6 one-hundredths of a percent.

The 17th Ward in Chicago went 98.3% to Obama.  What is the probability that the 38th precinct would go 576-0?  5.138381e-05, about 5 one-thousandths of a percent.

How about that 3rd precinct in the 27th Ward?  That ward went 89.3% to Obama and the precinct went 381-0 in favor of Obama.  What is the probability of that?  1.881074e-19

So I don't think that the fact that Romney won 100% of the vote in any of those Precincts in Utah is nearly as extraordinary as what Obama managed to pull of in Chicago.  It's interesting to see how the number of voters can make such a big difference in the likelihood of each of these events happening.  When you've only got 14 voters, pulling of a shutout isn't all that spectacular.