The story
From donkey (“fool”) + vote, from donkeys often being depicted as clumsy and lacking intelligence (see ass). First attested in 1962.
Etymology from Wiktionary, CC BY-SA 4.0.
donkey vote
Today it means: The act of casting a vote in an election using a preferential voting system, by specifying the candidates in the order in which they are listed on the ballot paper (i.e., by numbering the choices sequentially from top to bottom, ignoring what they represent). Full definition →