[supreme_loquat]

> You could have each precinct count the first round

This is just centralized tallying with extra steps. You can't finish the first round without results from every precinct, that's the point. To finish the first round, you need to know who has the fewest first choice votes across the entire population, so each precinct would have to give the entire first choice votes distribution to the centralized location. But once a precinct knows the first choice distribution, by definition that means all the ballots have been cast and you also have all the second choice and lower ballot data as well, and eventually all the data will have to make its way to the centralized location so you may as well just give all the ballot data to the central location at one time (well, technically not all the ballot data is used because irv/ranked choice actually doesn't use all of it, but that's another discussion).