# 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.

Like Benford's law this test will also show clustering in numerical values, but highlight it in a real-life context. 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.

### 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.

### Relation with Benford's law

Benford's law looks for clustering in numbers as a sign of manipaulation or possible fraud. It 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:

- Precincts are of similar size
- The candidate gets a similar share of the votes in most precincts.

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.

A non-1 cluster in Benford's test would show up as a nearly level portion in the Petrix graph. Similar levelness or clustering should be shown in the size of the precincts. The candidate's tally should not "out-level" the size of the precincts.

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. If a poorly randomized amount of extra votes is added to the tallies of one candidate, then it should show up as clustering.