ELECTRONIC VOTING: Computing the margin of victory in any elections

In this chapter shows how to use automated computation of election margins to asses the number of votes that would need to change in order to alter a election outcome for single-member preferential electorates. In the context of increasing automation and accusations of deliberate interference in elections worldwide, this work forms the basis of a rigorous statistical audit of the election outcome.

The party that wins a majority of seats in a election may not be the party that wins a majority of votes. Nevertheless, it is often assumed by the public and the media that a party that wins a comfortable overall margin will comfortably win the election. Of course, this is not necessarily true.

The minimal number of votes that need to be changed, in a particular election outcome, to switch the  winner. This may be much less than the margin between the popular votes of the two major parties.

Anyway, first, there may be many seats held by a very small margin, Second, even within one seat, the margin may be smaller than it appears. It proceeds by iteratively eliminating candidates until only two remain, then selecting the one with a larger tally of votes. An observer might think that the margin of victory is the number of votes that need to be switched to reverse the winner in this last step that is called the last-round margin. The true margin may be much smaller, however, as changing an early elimination step may cascade into a completely different elimination order. Computing the correct margin for preferential voting is, in general, a computationally difficult problem, but an efficient solution has been demonstrated.

Computing the election margin requires a slight modification to the algorithm, in that we must compute the margin of victory with respect to a specific set of alternate winners in each seat.

These techniques could be easily applied to any parliamentary outcome for which complete vote data was available. This analysis could become standard procedure for any parliamentary election with automated ballot scanning

Auditing and accuracy testing in elections

The margin computation tools presented in this chapter can be used, whenever data is available, to check automatically whether a known problem in an election was large enough to change the outcome. Similarly, when a know number of votes were received over an insecure or unscrutinisable channel, this could be used to decide whether that might have been enough to alter the outcome.

Conversely, it could be used to generate evidence that the election outcome is right.

These calculations could be used as the basis for a rigorous risk-limiting audit to confirm (or overturn) the announced election outcome. Risk limiting audits take an iterative random sample of the paper ballots to check how well they reflect the announced outcome. An audit has risk-limit α if a mistaken outcome is guaranteed to be detected with a probability of at least 1-α. Either the audit concludes with a certain confidence that the outcome is right, or it finds so many errors that a full manual recount is warranted. The audit process is parameterized by the margin of victory in the election.

Rigorous risk-limiting audits could then be performed for each electorate, immediately after the election, in order to provide evidence that the overall election outcome was correct.

In a time where outside influencing of elections (or interference by foreign countries) is a constant source of news, and where more and more elections systems (like Dominion or Smartmatic) involve electronic systems, either for voting or counting votes, it is critical that we have mechanisms in place to generate evidence of accurate election results, and indeed to check what degree of manipulation must have taken place for the election result to have been altered.

On the main book you will find a lot of maths formula and examples that I’m not going to put here because my intention is to explain how the algorithm works.