The only sum being preserved in your example is the total. And I'm not referring to only a repeat of the simple addition.
County A reports 50 votes for Candidate X, and 53 for candidate Y.
State uses 53 votes for candidate X, and 50 for candidate Y. Nothing subtle about that. Candidate X is focused on HIS vote count, and County A ought to detect this transposition (I know it need not appear as transposition error) without any help.
I have seen the voting machine trick, where the starting count of 0 is obtained by preloading +100 to the destined winner, and -100 to the destined loser, but that bias is hidden from view. Vote subtotals though, starting at the precinct level, are visible.
> “Vote subtotals though, starting at the precinct level, are visible.”
At the precinct level, all is good. What you see at precinct may not be the same as what I see for your precinct at county or state computers but on the other hand, I may see what you see but we both do not see what is happening at other precincts or counties. We need a team or software coordinating the aggregation process.
There have been many, many election challenges where ‘irregularities’ are noted. When covering millions of votes, or tens of millions of votes, the verification process becomes intractable or uneconomical unless better systems are put in place.
I have to leave now. In the meantime, reread and study the examples upstream.