1540s, "small ball used in voting," also "secret vote taken by ballots," from Italian pallotte, diminutive of palla "ball," for small balls used as counters in secret voting, from a Germanic source, from PIE root *bhel- (2) "to blow, swell." Earliest references are to Venice. By 1776 extended to tickets or sheets of paper used in secret voting. Ballot box attested from 1670s; metonymically from 1834 as "system or practice of voting by ballot."
1540s, "to vote by secret method" (such as ballot balls), from ballot (n.). Related: Balloted; balloting.