Macartan Humphreys sends along this article where he proves that the requirement of “compactness” in districting, if interpreted as requiring districts to be convex, does not by itself stop a majority party from gerrymandering:

Gerrymandering–the manipulation of electoral boundaries to maximize constituency wins|is often seen as a pathology of democratic systems. A commonly cited cure is to require that electoral constituencies have a `compact’ shape. But how much of a constraint does compactness in fact place on would-be gerrymanderers? By applying a theorem of Kaneko, Kano, and Suzuki (2004) to the two party situation we show that a gerrymanderer can always create equal sized convex constituencies that translate a margin of k voters into a margin of at least k constituency wins. Thus even with a small margin a majority party can win all constituencies. Moreover there always exists some population distribution such that all divisions into equal sized convex constituencies translate a margin of k voters into a margin of exactly k constituencies. Thus a convexity constraint can sometimes prevent a gerrymanderer from generating any wins for a minority party.