Approval with Optional Conditional-votes
AOC conditionality can be described in terms of what it does for the voter.
A conditional approval isn't counted unless it is reciprocated.
It can be said in more detail, but a little more wordily:
Call a ballot's unconditionally-approved candidates its "favorites".
A ballot on which C is favorite is called a C-favorite ballot.
For each pair of candidates, C and D, the number of ballots on which D, but not C is favorite, and which conditionally approve C must at least equal the number on which C, but not D is favorite, and which conditionally approve D. Otherwise enough C-but-not-D-favorite ballots' conditional approvals of D are ignored to achieve the above-described parity condition.
But people will understand that, in examples like the one below, it's good if the voter can make an approval conditional upon reciprocity:
(If you haven't been on the list lately, you might not have seen this "Approval bad-example":
27: A>B 24: B>A 49: C
The A voters should approve B, and the B voters should approve A. But what if the A voters approve B, and the B voters don't approve A? Then B will win, and the B voters will have successfully taken advantage of the A voters' co-operativeness and sincerity.
That's the co-operation/defection problem, or the chicken dilemma.
If you're an A voter, you'd be glad to hear that you can give a conditional approval to B, an approval that is conditional upon reciprocity.