You just need enough people to count the votes to return a result within a day or less.
I really don't think you're considering the logistics that would entail when you're dealing with over 150 entire planets
. It's nonsense to think you can meaningfully extrapolate from how it happens in a single country.
And again, what is your rush?
What is wrong
with the idea of taking the time to be sure the results are trustworthy? It's not like the winners have to take office by the end of election day or something. There's naturally going to be a period of transition between election and inauguration. So no damage is going to be done if it takes an extra day or three to collate and verify the results. And plenty of damage could be done if the process were rushed for no good reason.