Gerrymandering/Optimization of electoral districts for one particular party

You might look at Hodge, Marshall and Patterson, "Gerrymandering and Convexity", The College Mathematics Journal, Vol. 41, No. 4 (September 2010), pp. 312-324 http://www.jstor.org/stable/pdfplus/10.4169/collmathj.41.4.0312.pdf

If $P$ and $A$ are the perimeter and area, then it's $P^2/A$ that you would want to limit. But it's not really workable. Firstly, there's the obvious problem of coastal constituencies, where the perimeter is not well-defined. Secondly, you could still get around the rule by making the boundary as nearly circular as possible, with a few fingers extending into (or out of) the territory of your supporters (or opponents) -- in a big city, these fingers would not have to be very long to make a difference in voter preference.

Take a look at the paper: http://weblaw.haifa.ac.il/he/Events/eveFile/bizarreness090909.pdf and the many references there.