When we are talking about Votes (=a legal fiction, created by society through its laws), then yes I am a "social-constructivist", I suppose.
The Secretary of State has the final say so. It doesn't follow that she can't get it wrong.
As long as she does it legally, it does.
Now if she were to say "I decided a seven-day deadline was too long - get those vote tallies in within 37.37 hours", she would get it wrong. Or if she said, "Do not include the votes of any black people in your final tallies". Or if she said "Add the number 538 to your final tally for Mr. Gore." Or if she said "crack a raw egg onto each ballot and if the yoke slides to the left, count it for Mr. Gore; if the yoke slides to the right, count it for Mr. Bush."
So you see there are plenty of ways in which she could have "gotten it wrong". But as long as she follows the law as it was written before Election Day, there is no "getting it wrong". The term "wrong" doesn't even make sense; it does not apply to this situation.
Once again, we are talking about Votes here, which are legal fictions created by the actions of society through laws in the first place. The only question of importance is, Who got more Votes (not "ballots")? To discover the answer to this we have no choice but to appeal to the Laws which create those things known as Votes. Just looking at ballots isn't enough. One must look at those ballots in accordance with Election Laws. This was already done and cannot be repeated (you know, because of that little thing known as a "deadline").