There was a really interesting statistical paper publ 2012 linked in Mike Farb's most recent thread. I'm fascinated by the use of statistical applications to detect fraud.
You can step back and say, this pattern strongly suggests something's wrong, this race over here should be investigated.
I didn't to get fully into the statistics, but some of it - like the graph at fig 6 - is pretty easy to understand.
Statistical detection of systematic election irregularities
www.pnas.org/content/109/41/16469.full