As we do it in Spain and i think in most western countries, there is more than one person counting the votes and each one controls the others and verifying that is correct.Even there are people from different parties surveying the count.
And the non-party people are chosen at random from inhabitants of the area, they pay you a misery and most of them don't want to be there, they just want to finish and if no one says nothing and everything is correct they go home if not maybe they have to begin again to count so they are motivated to do it right.
