New Zealand was the first country to allow women to vote (in 1893), while the United Arab Emirates is the most recent addition to this list, adding women's suffrage in 2006.The United States finally began allowing women to vote in 1920, after the ratification of the 19th Amendment to the Constitution.Saudi Arabia is the only country that still does not allow its women to vote.he United States finally began allowing women to vote in 1920, after the ratification of the 19th Amendment to the Constitution. Saudi Arabia is the only country that still does not allow its women to vote.