One of the most bizarre and archaic aspects of the Australian electoral system is ballot paper ordering. From the AEC website:
The weaknesses of this system are obvious. In particular a small but significant proportion of the electorate chooses to vote 'down the line'. Known as a donkey vote, line voting can occur for the entire ballot or part of it when the voter is indifferent between the remaining candidates. For long ballots (such as those employed in the Senate) this is a genuine issue.
Fixed-order ballots introduce an additional issue: paradoxical "How To Vote Cards". As Antony Green notes in a review of the cards, candidates are highly vested in ensuring that their supporters produce valid votes. As all boxes need to be numbered in federal elections to be formally counted, parties may recommend a line vote (after voting for their candidate), in the process preferencing parties their supporters would traditionally consider odious.
Better than this is to randomise the order. This doesn't remove the issue of line voting, but it does remove its statistical effect on the outcome. To the best that I understand, the reason this hasn't been implemented is historical inertia rather than any currently relevant logic.*
As with many bizarre contemporary rituals the blindfolded double-draw selection process likely served a practical purpose in history: if randomisation on a ballot-by-ballot basis isn't possible, then the next best thing is to prevent any one individual from choosing the order.
Within Australia an alternate ordering system that partially addresses this is the Robson Rotation named after former Tasmanian Member of Parliament, Neil Robson. It was first implemented in Tasmania in 1980, followed by the ACT in 1995. In this the order is "rotated" between a limited number of permutations in the Hare-Clark system.
The rotation does not fully eliminate the issue of ordering as candidates are not completely randomised but merely rotated between permutations to enable each candidate to have an equal share of the first, last, and other key positions. As a result the issue of linear voting remains, reflected in the secondary preferences. Similar to the double-draw system this was due to a practical difficulty, in this case efficiently implementing a full set of permutations.**
In December 2021 a Bill to introduce Robson Rotation for Federal elections was introduced in the Senate. Due to the limited remaining sitting days it is unclear whether it will be able to be passed, receive assent, and commence by the coming election.***
While the Robson Rotation is feasible for a small to medium ballots, even it breaks down when the number of candidates grows too large. Indeed the proposed Bill reverts back to the status quo for candidates more than twelve - which brings us back to the blindfolds and balls malarkey that we have now.
With that in mind I introduce my no-nonsense, never-fail, can't-go-wrong method for randomising ballots when there's too many candidates for a Robson Rotation. And it's so simple it can be implemented in a single operation in Python:
That's it. Nothing fancy. Just randomise the damn thing.
Not that we should necessarily rely on a default random number generator for our ballots. But come on! We can and should do better than the fixed-order system that we have today.
* There is a slight efficiency gain for consistent ordering when dealing with a manual counting process. This is unlikely to be worth biasing the ballots through ordering.
** As noted by the Tasmanian Robson Rotation Discussion Paper, the number of permutations of N elements N!=N x (N-1) x ... x 1 grows rapidly (40,320 for 8 elements), so the limited sets used in practice (e.g. 420 for a seven candidate column in the ACT) are only designed to preserve uniformity down to the third level of preference.
*** The Bill additionally proposes to remove the requirement to number all candidates on the ballot paper. This is a little more contentious as it introduces new electoral strategies and can impact both positively and negatively on voting outcomes.