Simply taking turns is inefficient, since that may mean the wearier party being faced with the chore.

And by that what we mean is that they're absolutely identical, and it turns out that this here is not a double bond, it's not a single bond either, it's actually something in between.

The requirement that your turns sum to zero is necessary to keep you from getting caught in certain loops, such as one shaped like a capital G (try it out on paper to see what I mean).