Let us say the leftist economic system is put to a universal vote in Country X. Yet the vast majority of the voters including the working class reject it and will continue to do so for the foreseeable future. Would you try to democratically convince the people to change their minds or work for a revolution?
It depends on a number of things: Who organized the vote? Were the resourced used for propaganda by the two sides roughly equal? Do most people in Country X have personal experience of living under both of the systems they are being asked to choose between?
The last question really underlines the reason why such a vote can never be fair. When asked to choose between the status quo and radical change that they've never experienced before, most people will come down on the side of the status quo, nearly all the time and in any country - no matter what the status quo is or what kind of radical change is being proposed. It is extremely rare for a majority of people to prefer a system of which they have no personal experience in place of a system they already know. "Better the devil you know..."
Thus, I can guarantee that if your vote is held in a capitalist society, 99% of the time capitalism will win. And if your vote is held in a socialist society, 99% of the time socialism will win.
And a revolution can only happen that 1% of the time when the people have turned against the status quo in large numbers.
"When I give food to the poor, they call me a saint. When I ask why the poor have no food, they call me a communist."
- Dom Helder Camara, Brazilian archbishop
"Definition of a conservative: a person who believes that nothing should be done for the first time." - mikelepore