Synonyms for Vote (same or very similar meaning)
WordNet sense 1 (the total number of votes cast):
voter turnout
WordNet sense 2 (a legal right guaranteed by the 15th amendment to the US constitution; guaranteed to women by the 19th amendment):
suffrage, right to vote
WordNet sense 3 (a choice that is made by counting the number of people in favor of each alternative):
ballot, balloting, voting
From the ODE community, based on WordNet
add/edit