A form of secret ballot. Each voter has a black marble and a white marble. Once the issue on the floor has been discussed, each person puts one of their marbles into a bag. Once everyone has voted, the bag is tipped up, and the marbles counted.
In the Freemasons, I believe, when voting on whether someone should be admitted into the order, the presence of a single black marble is sufficient to deny their application. Hence the term blackballed.
(And they put the other marble in a second bag, so no one can tell how they voted by looking at the remaining marble.)
Is the secrecy compromised when a voter says, "Hey, I need my black/white marble back"?
Yes, but it would also be compromised by the person standing up and yelling "Hey! I voted against you, you turkey!" (One assumes that the voters want their votes to remain secret.)