That simply does not work. The "slices" are done so that each slice have roughly the same amount of people. So if one party has sliced things so that all the

That simply does not work. The "slices" are done so that each slice have roughly the same amount of people. So if one party has sliced things so that all the slices are nicely cracked and packed, the "picking" just doesn't matter. The slicing is the picking. However, a variation of your idea is to have each party take turns drawing districts. But that doesn't really work, because you'd quickly learn that the winning strategy is to draw districts to maximize the other party's voters. Because you want to force the other party to draw districts favorable to you.