Here's a compactness measure I haven't seen proposed before: Compose a district boundary out of line segments. The "thickness" of a line segment is the closest distance of any voter to any point on that line segment. Minimize the total of the length of segments divided by their thickness.
It is, of course, not an easy measure to maximize. In particular, small perturbations of boundaries could give big changes, and the measure would go infinite if any boundary crossed over a voter. However, I suspect that "simulated annealing" would do a decent job. But it is easier than travel time to calculate, and more sensitive to population distribution than splitline or purely perimeter-based districting. At any rate, you'd probably have to do it with a contest to find the best answer. JQ
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