Optimizing a Redistricting Problem

Most mathematicians, when they start thinking about the redistricting problem, desperately want it to be an optimization problem. And that means you're trying to find something good or near optimal, not just something that's best. But there are a billion of fundamentally different ways to do it. It depends on all this rich combination of geometric and common sense. There is no reason to be confident that in the absence of partisan intent, 50 voting would lead to 50 50 representation.