The stinky thing about "blackball" is that some clubs have
a rule that a single blackball means exclusion of an applicant.

The ball was originally a pebble (calculus).

From Ovid's Metamorphoses

Mos erat antiquus niveis atrisque lapillis,
his damnare reos, illis absolvere culpa;
tunc quoque sic lata est sententia tristis, et omnis
calculus inmitem demittitur ater in urnam.
Quae simul effudit numerandos versa lapillos,
omnibus e nigro color est mutatus in album,
candidaque Herculeo sententia numine facta
solvit Alemoniden.

It was an ancient custom of that land
to vote with chosen pebbles, white and black.
The white absolved, the black condemned the man.
And so that day the fateful votes were given--:
all cast into the cruel urn were black!
Soon as that urn inverted poured forth all
the pebbles to be counted, every one
was changed completely from its black to white,
and so the vote adjudged him innocent.
By that most fortunate aid of Hercules
he was exempted from the country's law.
[transl. by Brookes More]