Compensate for Fallibility

I think that wide use of voting can compensate for fallibility. How? Here's a thought experiment.
No one is perfect. Just imagine the best leaders you can, they still make mistakes. Perhaps less than the average person, but probably 5% of the time. So, if they are in a position to make the decisions, 5% of them are wrong.
Now, imagine instead putting the decision to a vote. If, on average all the voters are right only 60% of the time (greater than 50% will do), then the majority carries the day and, in theory, every decision is right!
OK, maybe this sounds too good to be true, but this analysis suggests that direct democracy will lead to more good choices than experts/leaders make on their own. It is likely to be more right than a vote in parliament, partly because it uses a bigger population but mostly because the electorate are more independent, not pressured by party whips or lobbyists.