Rumor, Reality, and Math Errors in Elections

Overview

This group of web pages explains a math anomaly in the New Mexico 2022 election audit and explains how the reader can decide for themselves whether the anomaly is a math error and whether to believe the audit report's conclusions. These pages also offer recommendations for improvement and are backed by a report and a spreadsheet.

The New Mexico election website contains election audit reports to reassure the public that nefarious actors have not tampered with voting machines and created inaccurate election results. However, a math anomaly in the 2022 election audit caused about 40% of New Mexico's largest county not to be audited -- a large enough range to affect outcomes. There is no way to know if the math anomaly was inadvertent or the result of a nefarious actor, but the audit report cannot logically offer reassurance in either case.

The audit report has been online since the fall of 2023 without acknowledgement of the anomaly, potentially creating unjustified reassurance. The next web page The Math Error in One Minute shows the reader how to verify that the anomalous report is still online. Another web page Rumor vs. Reality vs. Math Errors discusses the implications of acknowledging the error. The last web page is a Summary of Recommendations.

Background on Random Election Audits

New Mexico voters fill out paper ballots, which computers count by the morning after the election. Yet, before any candidate takes office, a Risk-Limiting Audit (RLA) recounts paper ballots by hand in precincts randomly selected by dice roll. The audit effectively checks the accuracy of the voting machines and computers.

To illustrate, the table below shows the names of the first 100 Bernalillo County precincts. In 2022, random dice rolls selected the 24 precincts shown in red. To change the outcome of a race, a nefarious actor would have to compromise multiple precincts -- let us say 12 of the 100 precincts. In advance of the election, the nefarious actor would have to choose 12 precincts and then compromise them without knowing which ones the dice would later select for audit. The likelihood of a nefarious actor getting away undetected is a math problem in probability similar to computing the odds in roulette.

An Exercise for the Reader

To understand random audits, put yourself in the mind of a nefarious actor. Assume the table above is a map of a hypothetical county with rectangular precincts. Since local races apply to physically compact regions, assume you will need to tamper with an array of precincts 4 tall and 3 wide. For example, PCTs (precincts) 6-9, 26-29, and 46-49 form a 4x3 array with all black text indicating the dice did not select any of them. If you move your eye around the table, can you find the placements of all unaudited 4x3 arrays? Hint: There are three such placements in total.

Now for the hard part. The dice are not rolled until after the election, so can you pick an unaudited 4x3 array without considering the color of the text? There are 68 placements of 4x3 arrays. If you do not know which precincts will be audited, all 68 placements will be equally good, so the best you can do is pick a placement at random. For the 2022 dice roll, 3 of the 68 placements evaded selection by the dice. So, a random pick would have a 65/68 = 95.6% chance of being audited and of you getting caught.

To do better, you would need information about the pattern of audits before the dice roll. For example, gamblers can use "loaded dice" to cheat this way.

Next Step

The process is theoretically sound, but 2022 election audit applied a "software fixup" to the dice values that did not function correctly. A lay person can see this on the page The Math Error in One Minute.