Keeping liars and cheats out of a vote count isn't any harder than keeping them out of a jury. And in case any slip through, you make sure there are are representatives of the candidates keeping an eye on things, and on each other.

Clean elections take place all over the world, and I gather in most parts of the USA. If a state can't guarantee to find honest enough people to count the votes fairly, I'd question the wisdom of allowing it to decide who is going to be president.