Gerrymandering: Good or Bad?

Before I forget the idea (which may have already been done), here's a possible way to model the effects of gerrymandering of congressional districts.

Imagine there is an area (state) which needs to be divided into N districts. Voters belong to one of two groups (R and D). Each sub area has a normally distributed percentage d of type D voters (and 1-d of R voters). If districts are assigned randomly, then the expected percentage of D voters in each district is simply d. However, if gerrymandering is allowed, then districts can be created with clear majorities of D and R voters. Will this be good or bad for voters? One way to measure welfare would be to measure the probability that a voter's representative would be in the same group. The higher the probability, the better off are the voters.

One other consideration, of course, is competition. The conventional wisdom is that voters are better off if seats are competitive because representatives will be more responsive to voter desires. However, even if a D or R always wins a particular district, there's no reason why (in this model) it has to be the same D or R. Competition at the primary level is still competition.