secret ballot

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A type of voting in which each person's vote is kept secret, but the amassed votes of various groups are revealed publicly.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun The voting system involving ballots available only at official polling places, prepared at public expense, containing the names of all candidates, and marked in secret at the polling places.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun a vote in which each person's choice is secret but the totaled votes are public