Petrix Election Integrity Test

The Petrix Election Integrity Test

 * Take the vote tallies in each precinct for each candidate and arrange them separately in descending order.
 * Plot the relative performance of each candidate at each position.

The tallies should not be dependent on precinct size. All candidates should have large and small tallies with a similar distribution.

This test is better than Benford's law, as it is shows where and how the possible fraud happened. By arranging the vote tallies in descending order and comparing each position against each one removes the noise caused by the random distribution of voters.

Relation with Benford's law
Benford's law works if the data values are spread over several orders of magnitude. This is not usually the case in elections. For practical reasons election districts tend to be the same size. One polling place will typically serve 1 to 2 thousand voters. In rural areas the polling places may serve fewer people.

For the tallies to cluster around first digit value of other than 2 these two things are needed: If the precincts all have 1000 active voters and one candidate evenly gets about 50% of the vote, then the number 4 and 5 have highest scores in Benford's test.
 * Precincts are of similar size
 * The candidate gets a similar share of the votes in most precincts.

A non-1 cluster in Benford's test would show up as a nearly level portion in the Petrix graph. Similar levelness should be shown in the opponents plot and even more so in the size of the precincts. The candidate's tally cannot "out-level" the size of the precincts. If how ever an even number of votes, or any poorly randomized amount of extra votes is added to the tallies of one candidate, then it should show up as levelness.

Fraud needs to be properly randomized to not show up in Benford's test. It must have a similar distribution as the authentic data. Random number generators produce numbers that are evenly distributed over a linear range.

Test case: presidential elections in Finland in 2012
In the second round of the 2012 presidential elections in Finland Sauli Niinistö of the Conservative Party received 63% of the vote while Pekka Haavisto Green League got 37%

There is a slight change in the proportion of votes from large precincts to small precincts. This is easy to explain.


 * Small precincts are usually in the countryside.
 * Rural people are more likely to vote conservative.
 * Haavisto of the Green party represents Liberal values, his support is concentrated in big cities.

The spike for Niinistö on the extreme right comes from very small precincts.