A "donkey vote" refers to a ballot completed by numbering candidates simply in the order in which they appear on the ballot form - rather than according to any genuine preference. The term originates from the idea that a donkey, lacking judgment, would just plod down the list in order.
Historically, a small proportion of voters do this out of indifference, laziness or as a matter of protest and politicians have always seen appearing first on the ballot as advantageous. This is why most Australian jurisdictions now use randomised ballot draws and why, in some elections where the "Robson Rotation" rules applies, candidate order is rotated across different printed ballots to spread the impact of donkey votes evenly rather than systematically favouring whoever happens to appear first on the ballot.