This would be the minimum voter turnout for the cards cast computed as the sum of the maximum of the cards cast for each ballot possibly adjusted for cards shared between ballots.
There are several
ways to attack this problem, all of which have problems. "Possibly
adjusted for cards shared between ballots" is easier said than
done.
I think the most practical way to solve this is with a "precinct-wide" race. Pick a race that is voted on by everyone in the precinct (jurisdiction wide races are a good example), and use the times counted for that race as the turnout for that precinct. I am told that other systems do it like this.
This falls down when precinct splits have disjoint races, but I doubt that ever happens in reality.
Ken