It's a false legend promoted by today's democratic governments.
In fact democracy in Ancient Greece wasn't how we know it today:
-It was only limited at the city of Athen
-Only adult rich men born in Athen with both the parents citizens of Athen could vote, in fact that was a minority
Most important
-People absolutely didn't like democracy, not who couldn't vote, they didn't care, but philosophers like Plato.
If you want I'll link sources in the comments, now I'm not at home.
I would say that the probable order of the cartographic events would be 1) a first attempt at a world map in the 5th and 6th centuries 2) the travels of Marco Polo 3) the Mercator projection in the mid 1500's and finally the 4) Robinson projection in 1963.
The answer is the third one