How big were the biggest elections during the ancient era?
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Presumably this would be ancient Rome during the early Empire. The best numbers available come, I think, from Augustus' official autobiography. The English text can be found here. In paragraph 8 he says that in the Empire-wide census of 14CE "were counted 4,937,000 of the heads of Roman citizens". Now, it seems to be a vexing questions for historians what this number actually means - some think it includes women and children, who could not vote. Also, a great number of the citizens didn't live in Rome so could not vote.
How many voting citizens resided in Rome then? Well, in paragraph 15 Augustus goes on to say: "I gave to 320,000 plebs of the city HS 240 per man". So, I'd say 320,000 is your brutto number. How many of those actually bothered to show up for the elections? I don't know; to judge by modern participation ratios, it could be as few as 20%, i.e. 64,000.
Of course, it is rather ironic that absolutely nothing hinged on the result of the elections at that time.
EDIT: Playing it safely, we can go for Athens at its height. There are various estimates of how many citizens there were, but 50,000 is very near the top of the high end. There we can presume a very high participation ratio (Athens, the birthplace of direct democracy and all that). So I'd shoot at about 40,000. Maybe Republican Rome had more but not by an order of a magnitude. Perhaps experts on Roman assemblies could weigh in here.
EDIT2: The modern high end estimate for Athenian citizen population is the work of Mogens Herman Hansen who developed what he calls "the shotgun method". A brief summary of the figures I was relying on can be found here.
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