Certain countries which refer to themselves as democratic actually aren't. While the citizens may nominally have the right to vote, in reality, government cronies are busy stuffing ballot boxes. But, how does one determine the difference between a popular, yet legitimately elected, government and one that cheated in order to win? Researchers from Austria demonstrate that statistics can answer this question.

For instance, in Spain's 2008 parliamentary election, the voter turnout was nearly 74% and the winning party won almost 44% of the vote. (Remember that European countries are multi-party systems.) The researchers examined Spain's electoral units (what we refer to as "precincts") and mapped them on a 2D histogram according to both percentage voter turnout and percentage for winning party. The precincts throughout the country clustered around those values (forming what is known as a 2D Gaussian distribution). Though there are exceptions (e.g., Canada), fair elections tend to produce this similar "fingerprint." (See figure.)

Now, take a look at Russia's 2012 presidential election. Notice a cluster of precincts in the upper-right corner. These precincts had nearly 100% voter turnout, and nearly 100% of the votes were cast for Vladimir Putin. This would be described, charitably, as an irregularity. The same pattern was seen in Russia's 2011 parliamentary election, as well as in Uganda's 2011 presidential election. Also, notice that particularly in the Russian elections, there is a "smear" toward the upper-right corner of the graph. This indicates what the authors refer to as "incremental" fraud.

Ironically, given that most of the precincts gave Putin around 60% of the vote in 2012, most likely, he didn't need to stuff ballot boxes in order to win. (But, it never hurts to be safe, just in case.)

It is often said, "Statistics don't lie, but liars use statistics." Perhaps it is time to modify that adage to, "Statistics don't lie, but liars stuff ballot boxes."

Source: Peter Klimek, Yuri Yegorov, Rudolf Hanel, and Stefan Thurner. "Statistical detection of systematic election irregularities." PNAS September 24, 2012. (Published online before print September 24, 2012, doi: 10.1073/pnas.1210722109)