See this Cleveland Plain Dealer story, which describes how Republican Party campaign officials and party officers worked with state election officials to engineer a method to keep the Libertarian gubernatorial ticket off this year’s ballot. The trial is still proceeding on September 30. Thanks to Kevin Knedler for the link.
UPDATE: also see this story.
You may be confusing causality and correlation.
Women didn’t vote in the 18th and 19th Century and the country thrived.
Women did vote in the 19th century in some states and territories.
The first three were 1890, 1893, and 1894. When was the Australian ballot introduced?