We do know that beyond question literacy is correlated to the rise of democracy and constitutional republics in America-- Google answers:
"Education historian Lawrence A. Cremin, who has written several books
about American education, has concluded that literacy rates among
American whites were as high or higher than in provincial England, and
significantly above those in Ireland.
'At a time when estimates of adult male literacy in England ran
from 48 percent in the rural western midlands to 74 percent in the
towns . . . adult male literacy in the American colonies seems to have
run from 70 percent to virtually 100 percent . . . .'
(See Traditions of American Education, NY: Basic Books, 1977, and
American Education: The Colonial Experience, NY: Harper & Row, 1970.)"
That rate of about 20% illiteracy continued until the 1870s or so and began shrinking even further to 3% by 1940, according to History of Illiteracy in America.
So that appears to be the floor level of the education requirements. Is simple literacy the only requirement? It is well known that the Founding Fathers were not simply literate, but erudite intellectuals, and this was fairly common among the ruling class and those that were actually allowed to vote at the time.
I don't think the floor is higher than basic literacy however. I put literacy as the floor because of the pioneering work that James Surowiecki has conducted on the power of groups to make far superior decisions than experts, and gives additional reasons for some of the natural advantages of Democracy and some of their staying power comparitively.
If you put together a big enough and diverse group of people and ask them to make decisions affecting matters of general interest that group’s decisions will, over time, be intellectually superior to the isolated individual, no matter how smart or well-informed he is.
James Surowiecki, The Wisdom of Crowds
James March is Jack Steele Parker professor emeritus at Stanford University and the Stanford Graduate School of Education, best known for his research on organizations, behavioral theory and organizational decision making. Wiki Professor March found something very similar:
The development of knowledge may depend on maintaining an influx of the naïve and the ignorant and … competitive victory does not go reliably go to the properly educated.